The upper limit of *γ*1 is *γ*1 ≤ 0 under Assumption 2\* with *m* = 1 or *γ*1 ≤ E[*Y* | *A* = 1, *M* = 1] – E[*Y* | *A* = 0, *M* = 1] under Assumption 3\* with *a* = 0 and *m* = 1. These upper limits are equal to those of α = E[*Y*(1) | *A* = 1, *M* = 1] – E[*Y*(1) | *A* = 0, *M* = 1] for the sensitivity analysis of the PSE in Section 3.2. Unfortunately, the lower limit of *γ*1 cannot be derived under these assumptions, even when Assumption 1 is added, because we are considering interventions on not only exposure *A* but also intermediate *M* (see Appendix 2). Furthermore, it is somewhat difficult to interpret these assumptions because of intervention on the intermediate *M*. The upper limit

= å = = - = = = = -G (4)

^), where *s* and *t* are replaced by the estimates *s*

mothers, *i.e.*, Pr(*M* = 1 | *A* = 0) and Pr(*M* = 0 | *A* = 0):

1

*m*

var(*s*

^)var(*t* ^ ) + *s*2 var(*t* ^ ) + *t* 2 var(*s*

0

to Assumptions 2 and 3 for the PSE:

=

1

*m* g

the weighted means of the two crude risk differences and Γ, *i.e.*,

0

=

both limits of the confidence interval for the first term in equation (4).

*Assumption* 2 \*. E *Y* (1, *m*) | *A*= 1, *M* =*m* ≤ E *Y* (1, *m*) | *A*= 0, *M* =*m* for all *m*.

*Assumption* 3 \*. E *Y* (0, *m*) | *A*=*a*, *M* =*m* ≤ E *Y* (1, *m*) | *A*=*a*, *M* =*m* for all *a* and *m*.

If there is no interaction between the effects of exposure *A* and intermediate *M* on outcome *Y* in the sense that E[*Y*(1,*m*)] – E[*Y*(0,*m*)] does not vary with *m*, the CDE and NDE coincide. The difference between a total effect and a CDE cannot generally be interpreted as an indirect effect and thus cannot be used to assess mediation. This is because when there is an interaction between the effects of exposure *A* and intermediate *M* on outcome *Y*, the CDEs may differ from the total effect even when *A* is not a cause of *M*. When there is an interaction between *A* and *M*, the CDEs will differ with different values of *m*, and thus one of the CDEs will differ from a total effect. Therefore, in general, CDEs cannot be used for decomposition of a total effect into direct and indirect effects. We note that the CDE will often be of greater interest in policy [39], and the NDE will often be of greater interest in the evaluation of etiology [39-41].

Similar to the CDE, the NDE is also a causal effect concerning the whole population, and it can be estimated from the data under certain assumptions [42,43]. However, neither the CDE nor the NDE can be identified when an unmeasured confounder exists between the intermediate and the outcome, as in Figure 1. Therefore, sensitivity analysis techniques have been discussed to assess their magnitudes [4,44-48]. In the next subsection, a simple sensitivity analysis method for the NDE is presented. Methods for the CDE are found elsewhere [4,44,47].

#### **4.2. Sensitivity analysis method for the natural direct effect**

Although the monotonicity assumption (Assumption 1) was necessary to derive a simple sensitivity analysis formula for the PSE, this assumption is not required to derive one for the NDE.

For each possible value of intermediate *M* (= 0, 1), we consider the following sensitivity parameter:

$$\gamma\_m = \mathbb{E}\mathbb{E}\left[Y\begin{pmatrix} 1 & m \end{pmatrix} \mid A = 1, \ M = m\right] - \mathbb{E}\mathbb{E}\left[Y\begin{pmatrix} 1 & m \end{pmatrix} \mid A = 0, \ M = m\right].$$

The sensitivity parameter *γ*1 = E[*Y*(1,1) | *A* = 1, *M* = 1] – E[*Y*(1,1) | *A* = 0, *M* = 1] is a contrast of infant mortality risks for two subpopulations. In a manner similar to the sensitivity parameter *α* for the PSE, the first subpopulation with (*A*, *M*) = (1, 1) consists of smoking mothers whose infants had a low birth weight, and the second subpopulation with (*A*, *M*) = (0, 1) comprises non-smoking mothers whose infants had a low birth weight. We then consider whether the infants in these two subpopulations would have lived or died if we had intervened to fix mothers to be smokers and infants to have a low birth weight; *i.e.*, we consider *Y*(1,1). The contrast between the infant mortality risks in these two subpopulations under this particular intervention is our sensitivity parameter, *γ*1. This parameter differs from *α* for the PSE in that it considers two interventions, which fix *A* to 1 and *M* to 1, whereas *α* considers one interven‐ tion, which fixes *A* to 1. As described above, it is not realistic to consider an intervention to fix the birth weight of an infant. This is a disadvantage of using the sensitivity parameter *γ*1 in the smoking-birth weight context. Analogously, the other sensitivity parameter, *γ*0 = E[*Y*(1,0) | *A* = 1, *M* = 0] – E[*Y*(1,0) | *A* = 0, *M* = 0], can be interpreted. The parameters are not identified from the observed data.

We now consider a weighted mean of the sensitivity parameters *γ*1 and *γ*0, where the respective weights are the probabilities of infants with low birth weights and not from non-smoking mothers, *i.e.*, Pr(*M* = 1 | *A* = 0) and Pr(*M* = 0 | *A* = 0):

This decomposition may help in understanding the meaning of the NDE, *i.e.*, the NDE is a

If there is no interaction between the effects of exposure *A* and intermediate *M* on outcome *Y* in the sense that E[*Y*(1,*m*)] – E[*Y*(0,*m*)] does not vary with *m*, the CDE and NDE coincide. The difference between a total effect and a CDE cannot generally be interpreted as an indirect effect and thus cannot be used to assess mediation. This is because when there is an interaction between the effects of exposure *A* and intermediate *M* on outcome *Y*, the CDEs may differ from the total effect even when *A* is not a cause of *M*. When there is an interaction between *A* and *M*, the CDEs will differ with different values of *m*, and thus one of the CDEs will differ from a total effect. Therefore, in general, CDEs cannot be used for decomposition of a total effect into direct and indirect effects. We note that the CDE will often be of greater interest in policy [39], and the NDE will often be of greater interest in the evaluation of etiology [39-41]. Similar to the CDE, the NDE is also a causal effect concerning the whole population, and it can be estimated from the data under certain assumptions [42,43]. However, neither the CDE nor the NDE can be identified when an unmeasured confounder exists between the intermediate and the outcome, as in Figure 1. Therefore, sensitivity analysis techniques have been discussed to assess their magnitudes [4,44-48]. In the next subsection, a simple sensitivity analysis method for the NDE is presented. Methods for the CDE are found elsewhere [4,44,47].

Although the monotonicity assumption (Assumption 1) was necessary to derive a simple sensitivity analysis formula for the PSE, this assumption is not required to derive one for the

For each possible value of intermediate *M* (= 0, 1), we consider the following sensitivity

The sensitivity parameter *γ*1 = E[*Y*(1,1) | *A* = 1, *M* = 1] – E[*Y*(1,1) | *A* = 0, *M* = 1] is a contrast of infant mortality risks for two subpopulations. In a manner similar to the sensitivity parameter *α* for the PSE, the first subpopulation with (*A*, *M*) = (1, 1) consists of smoking mothers whose infants had a low birth weight, and the second subpopulation with (*A*, *M*) = (0, 1) comprises non-smoking mothers whose infants had a low birth weight. We then consider whether the infants in these two subpopulations would have lived or died if we had intervened to fix mothers to be smokers and infants to have a low birth weight; *i.e.*, we consider *Y*(1,1). The contrast between the infant mortality risks in these two subpopulations under this particular intervention is our sensitivity parameter, *γ*1. This parameter differs from *α* for the PSE in that it considers two interventions, which fix *A* to 1 and *M* to 1, whereas *α* considers one interven‐ tion, which fixes *A* to 1. As described above, it is not realistic to consider an intervention to fix the birth weight of an infant. This is a disadvantage of using the sensitivity parameter *γ*1 in the smoking-birth weight context. Analogously, the other sensitivity parameter, *γ*0 = E[*Y*(1,0) | *A* = 1, *M* = 0] – E[*Y*(1,0) | *A* = 0, *M* = 0], can be interpreted. The parameters are not identified from

direct component of the total effect and does not act through the intermediate.

**4.2. Sensitivity analysis method for the natural direct effect**

*γm* =E *Y* (1, *m*)| *A*=1, *M* =*m* −E *Y* (1, *m*)| *A*=0, *M* =*m* .

NDE.

parameter:

48 Current Topics in Public Health

the observed data.

$$\Gamma = \sum\_{m=0}^{1} \gamma\_m \Pr(M = m \mid A = 0). \tag{3}$$

After calculating the crude risk differences E[*Y* | *A* = 1, *M* = *m*] – E[*Y* | *A* = 0, *M* = *m*] and probabilities Pr(*M* = *m* | *A* = 0) for *m* = 0, 1, the NDE can be expressed as the difference between the weighted means of the two crude risk differences and Γ, *i.e.*,

$$\text{NDE} = \sum\_{m=0}^{1} \{ \mathbb{E}[Y \mid A=1, M=m] - \mathbb{E}[Y \mid A=0, M=m] \} \Pr(M=m \mid A=0) - \Gamma. \tag{4}$$

The variance of the first term in equation (4) is calculated by the delta method, var(*s* ^*t* ^ ) = var(*s* ^)var(*t* ^ ) + *s*2 var(*t* ^ ) + *t* 2 var(*s* ^), where *s* and *t* are replaced by the estimates *s* ^ and *t* ^ . In a manner similar to the sensitivity analysis for the PSE, the sensitivity analysis for the NDE can be conducted easily. The sensitivity parameters *γ*0 and *γ*1 are set by the investigator according to what is considered plausible. The parameters can be varied over a range of plausible values to examine how the conclusions change according to the different parameter values. However, to obtain the confidence interval of the true NDE for the fixed values of *γm*, we must calculate not only the variance of the first term in equation (4) but also the variance of Γ, because Γ depends on the probabilities Pr(*M* = *m* | *A* = 0), which must be estimated from the observed data. However, if *γm* were constant across the strata of *m*, Γ would no longer depend on Pr(*M* = *m* | *A* = 0), and thus we could simply subtract Γ from both limits of the confidence interval for the first term in equation (4) to obtain the confidence interval for the true NDE. Similarly, for a data set large enough that the estimates of Pr(*M* = *m* | *A* = 0) were very precise, the approximate confidence interval for the true NDE could be obtained by subtracting Γ from both limits of the confidence interval for the first term in equation (4).

We can determine the upper limits of *γm* by using the following assumptions, which are similar to Assumptions 2 and 3 for the PSE:

*Assumption* 2 \*. E *Y* (1, *m*) | *A*= 1, *M* =*m* ≤ E *Y* (1, *m*) | *A*= 0, *M* =*m* for all *m*.

*Assumption* 3 \*. E *Y* (0, *m*) | *A*=*a*, *M* =*m* ≤ E *Y* (1, *m*) | *A*=*a*, *M* =*m* for all *a* and *m*.

The upper limit of *γ*1 is *γ*1 ≤ 0 under Assumption 2\* with *m* = 1 or *γ*1 ≤ E[*Y* | *A* = 1, *M* = 1] – E[*Y* | *A* = 0, *M* = 1] under Assumption 3\* with *a* = 0 and *m* = 1. These upper limits are equal to those of α = E[*Y*(1) | *A* = 1, *M* = 1] – E[*Y*(1) | *A* = 0, *M* = 1] for the sensitivity analysis of the PSE in Section 3.2. Unfortunately, the lower limit of *γ*1 cannot be derived under these assumptions, even when Assumption 1 is added, because we are considering interventions on not only exposure *A* but also intermediate *M* (see Appendix 2). Furthermore, it is somewhat difficult to interpret these assumptions because of intervention on the intermediate *M*. The upper limit of *γ*0 is *γ*0 ≤ 0 under Assumption 2\* with *m* = 0 or *γ*0 ≤ E[*Y* | *A* = 1, *M* = 0] – E[*Y* | *A* = 0, *M* = 0] under Assumption 3\* with *a* = 0 and *m* = 0. From these upper limits of *γm*, the upper limit of Γ is calculated using equation (3).

Assumptions 2\* and 3\* (2 and 3) relate to monotone treatment selection and monotone treatment response regarding the exposure, respectively. We can also make these types of assumptions about the intermediate [49]:

*Assumption* 4. E *Y* (*a*, *m*) | *A*=*a*, *M* = 0 ≤ E *Y* (*a*, *m*) | *A*=*a*, *M* = 1 for all *a* and *m*.

*Assumption* 5. E *Y* (*a*, 0) | *A*=*a* \*, *M* =*m* ≤ E *Y* (*a*, 1) | *A*=*a* \*, *M* =*m* for all *a*, *a* \*, and *m*.

In the context of the smoking-birth weight example, Assumption 4 implies that infants with a low birth weight, representing the subpopulation with (*A*, *M*) = (*a*, 1), would be a less healthy than infants who did not have a low birth weight, representing the subpopulation with (*A*, *M*) = (*a*, 0), where maternal smoking status is common among these two subpopulations. Assumption 5 implies that in the subpopulation with (*A*, *M*) = (*a\**, *m*), the infant mortality risk would be higher if infants had a low birth weight than if infants did not have a low birth weight. As this would indeed be the case, Assumptions 4 and 5 seem arguably reasonable. Under these assumptions, although ranges of *γm* cannot be derived, the range of Γ can be derived as follows:

**Figure 3.** Sensitivity analysis of the natural direct effect (per 1,000 live births); the solid line indicates the natural direct

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51

The result of this sensitivity analysis for the NDE suggests that maternal smoking has a directly harmful effect on infant mortality. Thus, the birth-weight paradox is also resolved in terms of

**5. Relationship between the principal strata effect and the natural direct**

We briefly discuss the relationship between the PSE and NDE. Again, we note that the individual NDE is defined as NDE(*ω*) ≡ *Y*(1,*M*(0)) – *Y*(0,*M*(0)). It can then be shown that, when there is no natural direct effect for any individual, there is no principal strata effect [50], *i.e.*,

To prove this theorem, we consider a probability of *Y*(1) – *Y*(0) = 0 conditional on {*M*(0) = 1, *M*(1) = 1}, *i.e.*, Pr(*Y*(1) – *Y*(0) = 0 | *M*(0) = 1, *M*(1) = 1). This indicates a probability that the PSE is equal to 0. We prove Theorem 1 by showing that this probability is equal to 1 under the

where the first equation is from the decomposition of the total effect to the NDE and NIE, the second is by NDE(*ω*) = 0, and the third is because *Y*(1,*M*(*a*)) is equal to *Y*(1,1) conditional on

effect and broken lines indicate 95% confidence intervals

*Theorem* 1. If NDE(*ω*) = 0 for all *ω*, then PSE = 0.

Pr(*Y* (1)−*Y* (0)=0|*M* (0)=1, *M* (1)=1)

=Pr(0=0|*M* (0)=1, *M* (1)=1)

*M*(*a*) = 1. This completes the proof.

assumption that NDE(*ω*) = 0 for all *ω*. The proof is as follows:

=Pr(*Y* (1, *M* (1))−*Y* (1, *M* (0)) + NDE(*ω*)=0|*M* (0)=1, *M* (1)=1)

=Pr(*Y* (1, *M* (1))−*Y* (1, *M* (0))=0|*M* (0)=1, *M* (1)=1)

=Pr(*Y* (1, 1)−*Y* (1, 1)=0|*M* (0)=1, *M* (1)=1)

the NDE.

**effect**

=1,

−(1− *p*0){E *Y* | *A*=1, *M* =1 −E *Y* | *A*=1, *M* =0 } ≤*Γ* ≤ *p*0{E *Y* | *A*=1, *M* =1 −E *Y* | *A*=1, *M* =0 }.

While Assumptions 2\* and 3\* can lead to only the upper limit, Assumptions 4 and 5 can lead to both limits. Furthermore, when Assumption 1 is added, under Assumptions 1 and 5, the lower limit of Γ is improved to:

$$I \succeq -(p\_1 - p\_0) \{ \mathbf{E} \sqcap Y \mid A = 1, \ M = 1 \} - \mathbf{E} \sqcap Y \mid A = 1, \ M = 0 \} \bot$$

However, neither the lower nor the upper limit can be derived under only one of the Assump‐ tions 4 and 5.

#### **4.3. Illustration**

We now apply this intervention-based approach to the NCHS data shown in Table 1. To calculate the NDE defined by equation (4), we determine a range of values for Γ. Under Assumptions 2\* and 3\*, the respective upper limits of *γ*0 and *γ*1 per 1,000 live births were calculated as *γ*0 ≤ 0 and *γ*1 ≤ –12.6. By substituting these upper limits into equation (3), we obtained Γ ≤ –0.7 per 1,000 live births. Under Assumptions 4 and 5, the range of Γ per 1,000 live births was calculated as –44.0 ≤ Γ ≤ 2.6. Under Assumptions 1 and 5, the lower limit was improved to Γ ≥ –2.4 per 1,000 live births. Therefore, we set the range of Γ per 1,000 live births as –2.4 ≤ Γ ≤ –0.7. Because the sample size was large, we obtain the approximate confidence interval for the true NDE by subtracting Γ from both limits of the confidence interval for the first term in equation (4). The result of the sensitivity analysis over this range of Γ is shown in Figure 3. With this range of Γ, the lower and upper limits of the NDE per 1,000 live births were 2.4 (95% CI: 2.0, 2.7) and 4.0 (95% CI: 3.7, 4.4), respectively.

Causal Inference with Intermediates: Simple Methods for Principal Strata Effects and Natural Direct Effects http://dx.doi.org/10.5772/53193 51

**Figure 3.** Sensitivity analysis of the natural direct effect (per 1,000 live births); the solid line indicates the natural direct effect and broken lines indicate 95% confidence intervals

The result of this sensitivity analysis for the NDE suggests that maternal smoking has a directly harmful effect on infant mortality. Thus, the birth-weight paradox is also resolved in terms of the NDE.

### **5. Relationship between the principal strata effect and the natural direct effect**

We briefly discuss the relationship between the PSE and NDE. Again, we note that the individual NDE is defined as NDE(*ω*) ≡ *Y*(1,*M*(0)) – *Y*(0,*M*(0)). It can then be shown that, when there is no natural direct effect for any individual, there is no principal strata effect [50], *i.e.*,

*Theorem* 1. If NDE(*ω*) = 0 for all *ω*, then PSE = 0.

of *γ*0 is *γ*0 ≤ 0 under Assumption 2\* with *m* = 0 or *γ*0 ≤ E[*Y* | *A* = 1, *M* = 0] – E[*Y* | *A* = 0, *M* = 0] under Assumption 3\* with *a* = 0 and *m* = 0. From these upper limits of *γm*, the upper limit of

Assumptions 2\* and 3\* (2 and 3) relate to monotone treatment selection and monotone treatment response regarding the exposure, respectively. We can also make these types of

*Assumption* 4. E *Y* (*a*, *m*) | *A*=*a*, *M* = 0 ≤ E *Y* (*a*, *m*) | *A*=*a*, *M* = 1 for all *a* and *m*.

*Assumption* 5. E *Y* (*a*, 0) | *A*=*a* \*, *M* =*m* ≤ E *Y* (*a*, 1) | *A*=*a* \*, *M* =*m* for all *a*, *a* \*, and *m*.

In the context of the smoking-birth weight example, Assumption 4 implies that infants with a low birth weight, representing the subpopulation with (*A*, *M*) = (*a*, 1), would be a less healthy than infants who did not have a low birth weight, representing the subpopulation with (*A*, *M*) = (*a*, 0), where maternal smoking status is common among these two subpopulations. Assumption 5 implies that in the subpopulation with (*A*, *M*) = (*a\**, *m*), the infant mortality risk would be higher if infants had a low birth weight than if infants did not have a low birth weight. As this would indeed be the case, Assumptions 4 and 5 seem arguably reasonable. Under these assumptions, although ranges of *γm* cannot be derived, the range of Γ can be derived as follows:

−(1− *p*0){E *Y* | *A*=1, *M* =1 −E *Y* | *A*=1, *M* =0 } ≤*Γ* ≤ *p*0{E *Y* | *A*=1, *M* =1 −E *Y* | *A*=1, *M* =0 }.

While Assumptions 2\* and 3\* can lead to only the upper limit, Assumptions 4 and 5 can lead to both limits. Furthermore, when Assumption 1 is added, under Assumptions 1 and 5, the

However, neither the lower nor the upper limit can be derived under only one of the Assump‐

We now apply this intervention-based approach to the NCHS data shown in Table 1. To calculate the NDE defined by equation (4), we determine a range of values for Γ. Under Assumptions 2\* and 3\*, the respective upper limits of *γ*0 and *γ*1 per 1,000 live births were calculated as *γ*0 ≤ 0 and *γ*1 ≤ –12.6. By substituting these upper limits into equation (3), we obtained Γ ≤ –0.7 per 1,000 live births. Under Assumptions 4 and 5, the range of Γ per 1,000 live births was calculated as –44.0 ≤ Γ ≤ 2.6. Under Assumptions 1 and 5, the lower limit was improved to Γ ≥ –2.4 per 1,000 live births. Therefore, we set the range of Γ per 1,000 live births as –2.4 ≤ Γ ≤ –0.7. Because the sample size was large, we obtain the approximate confidence interval for the true NDE by subtracting Γ from both limits of the confidence interval for the first term in equation (4). The result of the sensitivity analysis over this range of Γ is shown in Figure 3. With this range of Γ, the lower and upper limits of the NDE per 1,000 live births were

Γ is calculated using equation (3).

50 Current Topics in Public Health

lower limit of Γ is improved to:

tions 4 and 5.

**4.3. Illustration**

*Γ* ≥ −(*p*1 − *p*0){E *Y* | *A*=1, *M* =1 −E *Y* | *A*=1, *M* =0 }.

2.4 (95% CI: 2.0, 2.7) and 4.0 (95% CI: 3.7, 4.4), respectively.

assumptions about the intermediate [49]:

To prove this theorem, we consider a probability of *Y*(1) – *Y*(0) = 0 conditional on {*M*(0) = 1, *M*(1) = 1}, *i.e.*, Pr(*Y*(1) – *Y*(0) = 0 | *M*(0) = 1, *M*(1) = 1). This indicates a probability that the PSE is equal to 0. We prove Theorem 1 by showing that this probability is equal to 1 under the assumption that NDE(*ω*) = 0 for all *ω*. The proof is as follows:

Pr(*Y* (1)−*Y* (0)=0|*M* (0)=1, *M* (1)=1) =Pr(*Y* (1, *M* (1))−*Y* (1, *M* (0)) + NDE(*ω*)=0|*M* (0)=1, *M* (1)=1) =Pr(*Y* (1, *M* (1))−*Y* (1, *M* (0))=0|*M* (0)=1, *M* (1)=1) =Pr(*Y* (1, 1)−*Y* (1, 1)=0|*M* (0)=1, *M* (1)=1) =Pr(0=0|*M* (0)=1, *M* (1)=1) =1,

where the first equation is from the decomposition of the total effect to the NDE and NIE, the second is by NDE(*ω*) = 0, and the third is because *Y*(1,*M*(*a*)) is equal to *Y*(1,1) conditional on *M*(*a*) = 1. This completes the proof.

The converse of this theorem does not hold: the absence of a PSE does not imply the absence of a NDE. Nevertheless, from the contraposition of this theorem, when there is a PSE, there must be some individuals for whom there is a NDE. The results of the sensitivity analyses in Sections 3.3 and 4.3 showed that the true PSE was not smaller than 0 and that the true NDE was larger than 2.3. The results do not contradict the contraposition of Theorem 1.

proaches estimate two different effects (effects for two different populations), and these may in fact be in different directions. Before these approaches are applied, it is important to be clear

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The approaches described in this chapter are applicable to a number of similar settings in all areas of epidemiological research. As the existing literature has made clear, conditioning on an intermediate can be problematic and can give rise to severe biases. In many contexts, conditioning on an intermediate is not necessary and is best avoided. Nevertheless, there are cases in which conditioning on an intermediate is of scientific or policy interest. We have shown that alternative approaches can be used to draw inferences in such settings. Although these methodological tools are imperfect and need to be interpreted carefully, they can be useful in

Appendices 1 and 2 outline the derivations of the equations and inequalities presented in Sections 3 and 4, respectively. As noted in Section 2, we assume that no confounder exists between *A* and *M* or between *A* and *Y*. This assumption leads to the independency assumption that *M*(*a*), *Y*(*a*), and *Y*(*a*,*m*) are independent of *A*. In addition, we require two assumptions. The first is the no-interference assumption that one individual's outcome does not depend on the exposure status of other individuals. The second is the consistency assumption that when *A = a*, the potential outcomes *Y(a)* and *M(a)* are equal to the observed outcomes *Y* and *M*, respec‐ tively. Likewise, we assume that when *A = a* and *M = m*, the potential outcome *Y(a,m)* is equal to *Y*. For simplicity, we use the notations *Eij(a)* = E[*Y(a)* | *M*(0) = *i*, *M*(1) = *j*] and *πij* ≡ Pr(*M*(0) =

**Appendix 1: Derivations of equations and inequalities in Section 3**

PSE≡*E*11(1)− *E*11(0)

**Proof that Assumption 2 is equivalent to assuming that** *E***01(1) ≤** *E***11(1) and** *E***00(1) ≤** *E***01(1)**

= 1 – *p*1, π11 + π10

= *p*0, *and*π01 + π00 = 1 – *p*0 (A1)

=E *Y* (1)|*M* (0)=1 −E *Y* (0)|*M* (0)=1 =E *Y* (1)| *A*=0, *M* =1 −E *Y* (0)| *A*=0, *M* =1 ={E *Y* (1)| *A*=1, *M* =1 −α}−E *Y* (0)| *A*=0, *M* =1 =E *Y* | *A*=1, *M* =1 −E *Y* | *A*=0, *M* =1 −α, where the second equation is by Assumption 1, the third is by the independency and consistency assumptions, the fourth is by using α = E[*Y*(1) | *A* = 1, *M* = 1] – E[*Y*(1) | *A* = 0, *M* = 1], and the last is again by the consistency assumption.

about the scientific or policy question.

examining conditional and direct effects.

**Appendix**

*i*, *M*(1) = *j*).

**Derivation of equation (1)**

Using α, PSE can be expressed as follows:

The relationship between π*ij* and *pa* = Pr(*M* = 1 | *A* = *a*) is

π11 + π01 = *p*1, π10 + π00

### **6. Conclusion**

In this chapter, we described two approaches related to calculating the effect of an exposure on an outcome that is conditional on potential intermediates or one that does not act through the intermediate. Here, we made an impractical assumption in the observational studies that no confounder exists between the exposure and the outcome or between the exposure and the intermediate. Nevertheless, the methodologies described here also hold conditional on confounders if no unmeasured confounder exists between these variables. We considered a risk difference as the effect measure, but the methodologies can be extended to other effect measures.

Each approach has a unique interpretation and its own strengths and weaknesses. In the principal stratification approach, one conditions on the subpopulation for which the inter‐ mediate would occur irrespective of exposure. An advantage of this approach is that the subpopulation is a particularly high-risk group in which the intermediate will necessarily occur. A disadvantage is that we do not know who is in the subpopulation such that the intermediate will occur irrespective of the exposure. In the intervention-based approach, the NDE appears to capture the effect of an exposure on the outcome if the intermediate was set to what it would be when the exposure is set to 0. An advantage of this approach is that it can be used to decompose the total effect into direct and indirect components. A disadvantage is that it is difficult to understand the meaning of the NDE from the form. In addition, it is difficult to interpret the sensitivity parameter for the sensitivity analysis, although this may be avoided by applying a parametric model [46].

In many studies, the total effect of the exposure on the outcome in the whole population may be of central interest, and then none of the approaches described here are required. The approaches described here are of relevance only when the investigators are interested in the direct effect of the exposure not acting through the intermediate or the effect of the exposure on the outcome for certain groups at high risk for the intermediate. In some birth weight settings, the exposure or intervention under study may occur after birth in some cases [6]. In these cases, birth weight becomes a pre-exposure baseline variable, and the approaches described here are not needed. These settings should be distinguished from those similar to the birth-weight paradox. When the approaches described here are of relevance, both the PSE and NDE may be in a consistent direction in some situations, as seen in Sections 3.3 and 4.3. However, it is important to note that the two approaches need not give effect estimates in the same direction. Having effect estimates in different directions with the two approaches is not necessarily an indication that one of the estimates is in the wrong direction. The two ap‐ proaches estimate two different effects (effects for two different populations), and these may in fact be in different directions. Before these approaches are applied, it is important to be clear about the scientific or policy question.

The approaches described in this chapter are applicable to a number of similar settings in all areas of epidemiological research. As the existing literature has made clear, conditioning on an intermediate can be problematic and can give rise to severe biases. In many contexts, conditioning on an intermediate is not necessary and is best avoided. Nevertheless, there are cases in which conditioning on an intermediate is of scientific or policy interest. We have shown that alternative approaches can be used to draw inferences in such settings. Although these methodological tools are imperfect and need to be interpreted carefully, they can be useful in examining conditional and direct effects.

### **Appendix**

The converse of this theorem does not hold: the absence of a PSE does not imply the absence of a NDE. Nevertheless, from the contraposition of this theorem, when there is a PSE, there must be some individuals for whom there is a NDE. The results of the sensitivity analyses in Sections 3.3 and 4.3 showed that the true PSE was not smaller than 0 and that the true NDE

In this chapter, we described two approaches related to calculating the effect of an exposure on an outcome that is conditional on potential intermediates or one that does not act through the intermediate. Here, we made an impractical assumption in the observational studies that no confounder exists between the exposure and the outcome or between the exposure and the intermediate. Nevertheless, the methodologies described here also hold conditional on confounders if no unmeasured confounder exists between these variables. We considered a risk difference as the effect measure, but the methodologies can be extended to other effect

Each approach has a unique interpretation and its own strengths and weaknesses. In the principal stratification approach, one conditions on the subpopulation for which the inter‐ mediate would occur irrespective of exposure. An advantage of this approach is that the subpopulation is a particularly high-risk group in which the intermediate will necessarily occur. A disadvantage is that we do not know who is in the subpopulation such that the intermediate will occur irrespective of the exposure. In the intervention-based approach, the NDE appears to capture the effect of an exposure on the outcome if the intermediate was set to what it would be when the exposure is set to 0. An advantage of this approach is that it can be used to decompose the total effect into direct and indirect components. A disadvantage is that it is difficult to understand the meaning of the NDE from the form. In addition, it is difficult to interpret the sensitivity parameter for the sensitivity analysis, although this may be avoided

In many studies, the total effect of the exposure on the outcome in the whole population may be of central interest, and then none of the approaches described here are required. The approaches described here are of relevance only when the investigators are interested in the direct effect of the exposure not acting through the intermediate or the effect of the exposure on the outcome for certain groups at high risk for the intermediate. In some birth weight settings, the exposure or intervention under study may occur after birth in some cases [6]. In these cases, birth weight becomes a pre-exposure baseline variable, and the approaches described here are not needed. These settings should be distinguished from those similar to the birth-weight paradox. When the approaches described here are of relevance, both the PSE and NDE may be in a consistent direction in some situations, as seen in Sections 3.3 and 4.3. However, it is important to note that the two approaches need not give effect estimates in the same direction. Having effect estimates in different directions with the two approaches is not necessarily an indication that one of the estimates is in the wrong direction. The two ap‐

was larger than 2.3. The results do not contradict the contraposition of Theorem 1.

**6. Conclusion**

52 Current Topics in Public Health

measures.

by applying a parametric model [46].

Appendices 1 and 2 outline the derivations of the equations and inequalities presented in Sections 3 and 4, respectively. As noted in Section 2, we assume that no confounder exists between *A* and *M* or between *A* and *Y*. This assumption leads to the independency assumption that *M*(*a*), *Y*(*a*), and *Y*(*a*,*m*) are independent of *A*. In addition, we require two assumptions. The first is the no-interference assumption that one individual's outcome does not depend on the exposure status of other individuals. The second is the consistency assumption that when *A = a*, the potential outcomes *Y(a)* and *M(a)* are equal to the observed outcomes *Y* and *M*, respec‐ tively. Likewise, we assume that when *A = a* and *M = m*, the potential outcome *Y(a,m)* is equal to *Y*. For simplicity, we use the notations *Eij(a)* = E[*Y(a)* | *M*(0) = *i*, *M*(1) = *j*] and *πij* ≡ Pr(*M*(0) = *i*, *M*(1) = *j*).

#### **Appendix 1: Derivations of equations and inequalities in Section 3**

#### **Derivation of equation (1)**

Using α, PSE can be expressed as follows:

PSE≡*E*11(1)− *E*11(0) =E *Y* (1)|*M* (0)=1 −E *Y* (0)|*M* (0)=1 =E *Y* (1)| *A*=0, *M* =1 −E *Y* (0)| *A*=0, *M* =1 ={E *Y* (1)| *A*=1, *M* =1 −α}−E *Y* (0)| *A*=0, *M* =1 =E *Y* | *A*=1, *M* =1 −E *Y* | *A*=0, *M* =1 −α,

where the second equation is by Assumption 1, the third is by the independency and consistency assumptions, the fourth is by using α = E[*Y*(1) | *A* = 1, *M* = 1] – E[*Y*(1) | *A* = 0, *M* = 1], and the last is again by the consistency assumption.

#### **Proof that Assumption 2 is equivalent to assuming that** *E***01(1) ≤** *E***11(1) and** *E***00(1) ≤** *E***01(1)**

The relationship between π*ij* and *pa* = Pr(*M* = 1 | *A* = *a*) is

$$
\pi\_{11} + \pi\_{01} = \mathfrak{p}\_1,\\
\pi\_{10} + \pi\_{0\_{0}} = \mathfrak{l} - \mathfrak{p}\_1,\\
\pi\_{11} + \pi\_{1\_{0}} = \mathfrak{p}\_0,\\
\text{and}\\
\pi\_{0\_{1}} + \pi\_{00} = \mathfrak{l} - \mathfrak{p}\_0 \tag{\mathcal{A}\ \mathbb{I}}.\tag{\mathcal{A}\ \mathbb{I}}
$$

because Pr(*M*(*a*) = *m*) = Pr(*M*(*a*) = *m* | *A* = *a*) = Pr(*M* = *m* | *A* = *a*) by the independency and consistency assumptions. Furthermore, because E[*Y*(*a*) | *A* = 1, *M* = 1] = E[*Y*(*a*) | *M*(1) = 1] by the independency assumption, this conditional expectation can be expressed as

$$\mathsf{H}\mathsf{T}\mathsf{Y}\left(\mathsf{a}\right)\left|\mathcal{A}=\mathsf{I},\,\mathcal{M}=\mathsf{I}\right.\left.\begin{array}{c}\pi\_{11}\mathsf{E}\_{11}\left(\mathsf{a}\right)+\pi\_{01}\mathsf{E}\_{01}\left(\mathsf{a}\right)\\\pi\_{11}+\pi\_{01}\end{array}\right.\tag{4.2}$$

*p*0α + (1− *p*0)α '= −(*p*1 − *p*0){E *Y* | *A*=1, *M* =1 −E *Y* | *A*=1, *M* =0 }. (A12)

http://dx.doi.org/10.5772/53193

55

Causal Inference with Intermediates: Simple Methods for Principal Strata Effects and Natural Direct Effects

Then, a range of α under Assumption 2 is derived by α ≤ 0 and by substituting α' ≤ 0 into (A12).

= 1, *M* = 1] – E[*Y* | *A* = 0, *M* = 1] and by substituting α' ≤ E[*Y* | *A* = 1, *M* = 0] – E[*Y* | *A* = 0, *M* = 0] into (A12).

Using β 1 = *E* 11(1) – *E* 01(1), β 2 = *E* 11(0) – *E* 10(0) and β 3 = π 10, (A2) with *a* = 1 can be expressed as

α =E *Y* (1)| *A*=1, *M* =1 −E *Y* (1)| *A*=0, *M* =1 ≤E *Y* (1)| *A*=1, *M* =1 −E *Y* (0)| *A*=0, *M* =1 =E *Y* | *A*=1, *M* =1 −E *Y* | *A*=0, *M* =1 , and similarly α' ≤ E[*Y* | *A* = 1, *M* = 0] – E[*Y* | *A* = 0, *M* = 0]. Thus, a range of α under Assumption 3 is derived by α ≤ E[*Y* | *A*

E *Y* | *A*=1, *M* =1 = (π11 + π01)*E*11(1)−π01{*E*11(1)− *E*01(1)}

= *E*11(1)− *p*1 −(*p*0 −π10) *p*1

= *E*11(1)− *p*1 − *p*0 + β3 *p*1

E *Y* | *A*=0, *M* =1 = (π11 + π10)*E*11(0)−π10{*E*11(0)− *E*10(0)}

= *E*11(0)− π10 *p*0

= *E*11(0)− β3 *p*0 β2.

π11 + π01

β1,

π11 + π01

E *Y* (1, *M* (0))| *A*=0, *M* (0)=*m* Pr(*M* (0)=*m*| *A*=0)

{E *Y* (1, *m*)| *A*=1, *M* =*m* −γ*m*}Pr(*M* =*m*| *A*=0)

E *Y* (1, *m*)| *A*=0, *M* =*m* Pr(*M* =*m*| *A*=0)

E *Y* | *A*=1, *M* =*m* Pr(*M* =*m*| *A*=0)−Γ,

where the first equation is by the independency assumption, the third is by the consistency assumption, and the fourth is by γ*m* = E[*Y*(1,*m*) | *A* = 1, *M* = *m*] – E[*Y*(1,*m*) | *A* = 0, *M* = *m*]. The simpler calculation expresses E[*Y*(0,*M*(0))] as

{*E*11(0)− *E*10(0)}

{*E*11(1)− *E*01(1)}

Under Assumption 3,

**Derivation of equation (2)**

**Derivation of equation (4)**

and (A3) with *a* = 0 can be expressed similarly as

The difference between these two equations leads to equation (2).

Using γ*m* and Γ, E[*Y*(1,*M*(0))] can be expressed as follows:

**Appendix 2: Derivations of equations and inequalities in Section 4**

E *Y* (1, *M* (0)) =E *Y* (1, *M* (0))| *A*=0 =∑ *m*

> =∑ *m*

> =∑ *m*

> =∑ *m*

Similarly,

$$\mathsf{E}\mathsf{Y}\mathsf{Y}\left(\mathsf{a}\right)\left|\mathsf{A}=\mathsf{0},\,\mathsf{M}=\mathsf{I}\right.\left.\mathsf{I}\right]=\frac{\mathsf{\pi}\_{11}\mathsf{E}\_{11}\left(\mathsf{a}\right)+\mathsf{\pi}\_{10}\mathsf{E}\_{10}\left(\mathsf{a}\right)}{\mathsf{\pi}\_{11}+\mathsf{\pi}\_{10}},\tag{\mathsf{A}}\tag{\mathsf{A}}\mathsf{3}$$

$$\mathsf{E}\mathsf{T}^{\mathsf{Y}}(\mathsf{a})\left|\mathcal{A}=\mathsf{I},\,\mathcal{M}=\mathsf{O}\right.\tag{7.4} \\ \mathcal{A}=\mathsf{O}\frac{\mathsf{r}\_{10}\mathsf{E}\_{10}(\mathsf{a})+\mathsf{r}\_{00}\mathsf{E}\_{00}(\mathsf{a})}{\mathsf{r}\_{10}+\mathsf{r}\_{00}},\tag{7.5}$$

$$\mathsf{H}\mathsf{T}\mathsf{Y}\left(\mathsf{a}\right)\left|\mathcal{A}=\mathsf{0},\,\mathcal{M}=\mathsf{O}\right.\tag{7.45}\\\begin{aligned}\mathsf{T}\_{\mathsf{O}\_{1}}\mathsf{E}\_{\mathsf{O}\_{1}}(\mathsf{a})+\mathsf{T}\_{\mathsf{O}\mathsf{O}}\mathsf{E}\_{\mathsf{O}\mathsf{O}}(\mathsf{a})\\\end{aligned}\right.\tag{7.46}$$

As π 10 = 0 (no defier exists) under Assumption 1, (A1) reduces to

π11 = *p*0, π00 = 1 – *p*1, and π01 = *p*1 – *p*0,

where it is assumed that π 01 > 0 (*i.e.*, *p* 1 > *p* 0). Using α = E[*Y*(1) | *A* = 1, *M* = 1] – E[*Y*(1) | *A* = 0, *M* = 1] and α' = E[*Y*(1) | *A* = 1, *M* = 0] – E[*Y*(1) | *A* = 0, *M* = 0], (A2)–(A5) with *a* = 1 can be expressed respectively as

$$\mathsf{E}\mathsf{Y}\left\{\mathsf{A}=\mathsf{I},\,\mathsf{M}=\mathsf{I}\right\}=\frac{\mathsf{\mathcal{D}\_{\mathsf{O}}\mathsf{E}\_{11}(\mathsf{I})+(\mathsf{\mathcal{D}}\_{1}-\mathsf{\mathcal{D}}\_{0})\mathsf{E}\_{01}(\mathsf{I})}{\mathsf{\mathcal{D}}\_{1}},\tag{\mathsf{A}6}$$

$$\mathsf{T}\mathsf{T}\mathsf{Y}\begin{Bmatrix}\mathsf{A}=\mathsf{I},\,\mathsf{M}=\mathsf{I}\end{Bmatrix} = \mathsf{T}\mathsf{J} - \mathsf{a} = \mathsf{E}\_{11}(\mathsf{I}),\tag{\mathsf{A}\mathsf{T}}$$

$$\mathsf{E}\mathsf{I}\mathsf{I}\mathsf{Y}\ \left\{ \mathsf{A}=\mathsf{I},\,\,\mathsf{M}=\mathsf{O}\right\} = \mathsf{E}\_{\mathsf{O}\mathsf{O}}(\mathsf{I}),\tag{\mathsf{A}\mathsf{B}}$$

$$\mathbf{E}\mathbf{f}\mathbf{Y}\begin{vmatrix}\mathbf{A}=\mathbf{I},\;\mathcal{M}=\mathbf{0}\end{vmatrix} - \mathbf{a}^\* = \frac{(\boldsymbol{\mu}\_1-\boldsymbol{\mu}\_0)\boldsymbol{\mathsf{E}}\_{\mathrm{O}1}(1) + (1-\boldsymbol{\mu}\_1)\boldsymbol{\mathsf{E}}\_{\mathrm{O}0}(1)}{1-\boldsymbol{\mu}\_0}.\tag{8.9}$$

The differences between (A6) and (A7) and between (A8) and (A9) lead to, respectively

$$\boldsymbol{\sigma} = \frac{\boldsymbol{\rho}\_{1} - \boldsymbol{\rho}\_{0}}{\boldsymbol{\rho}\_{1}} \Big[ \boldsymbol{\varepsilon}\_{\odot 1}(\boldsymbol{\Upsilon}) - \boldsymbol{\varepsilon}\_{1 \cdot 1}(\boldsymbol{\Upsilon}) \Big],$$

$$\boldsymbol{\sigma} \,\,\, = \frac{\boldsymbol{\rho}\_{1} - \boldsymbol{\rho}\_{0}}{\boldsymbol{\Upsilon} - \boldsymbol{\rho}\_{0}} \Big[ \boldsymbol{\varepsilon}\_{\odot 0}(\boldsymbol{\Upsilon}) - \boldsymbol{\varepsilon}\_{\odot 1}(\boldsymbol{\Upsilon}) \Big].$$

Assumption 2 with *m* = 1 is equivalent to α ≤ 0, and that with *m* = 0 is equivalent to α' ≤ 0. Thus, Assumption 2 is equal to assuming that *E* 01(1) ≤ *E* 11(1) with *m* = 1 and *E* 00(1) ≤ *E* 01(1) with *m* = 0, because *p* 1 > *p* 0 by assumption.

#### **Derivations of ranges of α under Assumptions 2 and 3**

Substituting (A7) into (A6) gives

$$\mathsf{E}\_{\mathsf{D}1}(\mathsf{1}) = \mathsf{E} \mathsf{I} \\ \mathsf{Y} \left| \mathsf{A} = \mathsf{I}, \ \mathsf{M} = \mathsf{I} \right. \mathsf{I} + \frac{\mathsf{p\_{\mathsf{D}}}}{\mathsf{p\_{\mathsf{I}}} - \mathsf{p\_{\mathsf{D}}}} \mathsf{a}, \tag{\mathsf{A} \,\mathsf{10}}$$

and substituting (A8) into (A9) leads to

$$\mathsf{f}\_{\mathsf{D}1}(\mathsf{1}) = \mathsf{f} \mathsf{f} \\ \mathsf{Y} \left| \mathsf{A} = \mathsf{I}, \,\,\mathsf{M} = \mathsf{O} \right. \left. \frac{1 - \mathsf{p}\_{\mathsf{D}}}{\mathsf{p}\_{1} - \mathsf{p}\_{\mathsf{D}}} \mathsf{a} \,\, \mathsf{I} \right. \tag{A11}$$

Given that these two equations are equal, some algebra yields

Causal Inference with Intermediates: Simple Methods for Principal Strata Effects and Natural Direct Effects http://dx.doi.org/10.5772/53193 55

$$
\Delta \sigma\_0 \mathbf{a} + (\mathbb{1} - \mu\_0) \mathbf{a}^\circ = - (\mathbb{1}\_1 - \mu\_0) \mathbf{\{\{\mathbf{E}\}^\circ\} \,\, \mathbb{A} = \mathbb{1}, \, \mathbb{M} = \mathbb{1}, \, \mathbb{M} = \mathbb{1}, \, \mathbb{M} = \mathbb{1}, \, \mathbb{M} = \mathbb{O}\}.\tag{8.12}
$$

Then, a range of α under Assumption 2 is derived by α ≤ 0 and by substituting α' ≤ 0 into (A12).

Under Assumption 3,

because Pr(*M*(*a*) = *m*) = Pr(*M*(*a*) = *m* | *A* = *a*) = Pr(*M* = *m* | *A* = *a*) by the independency and consistency assumptions. Furthermore, because E[*Y*(*a*) | *A* = 1, *M* = 1] = E[*Y*(*a*) | *M*(1) = 1] by the independency assumption, this conditional

π11 + π01

π11 + π10

π10 + π00

π01 + π00

*p*1

1− *p*0

{*E*01(1)− *E*11(1)},

{*E*00(1)− *E*01(1)}.

*p*1 − *p*0

*p*1 − *p*0

Assumption 2 with *m* = 1 is equivalent to α ≤ 0, and that with *m* = 0 is equivalent to α' ≤ 0. Thus, Assumption 2 is equal

E *Y* | *A*=1, *M* =1 −α = *E*11(1), (A7) E *Y* | *A*=1, *M* =0 = *E*00(1), (A8)

π11 = *p*0, π00 = 1 – *p*1, and π01 = *p*1 – *p*0, where it is assumed that π 01 > 0 (*i.e.*, *p* 1 > *p* 0). Using α = E[*Y*(1) | *A* = 1, *M* = 1] – E[*Y*(1) | *A* = 0, *M* = 1] and α' = E[*Y*(1) | *A*

. (A2)

, (A3)

, (A4)

. (A5)

, (A6)

. (A9)

α, (A10)

α '. (A11)

E *Y* (*a*)| *A*=1, *M* =1 = π11*E*11(*a*) + π01*E*01(*a*)

E *Y* (*a*)| *A*=0, *M* =1 = π11*E*11(*a*) + π10*E*10(*a*)

E *Y* (*a*)| *A*=1, *M* =0 = π10*E*10(*a*) + π00*E*00(*a*)

E *Y* (*a*)| *A*=0, *M* =0 = π01*E*01(*a*) + π00*E*00(*a*)

E *Y* | *A*=1, *M* =1 = *p*0*E*11(1) + (*p*1 − *p*0)*E*01(1)

E *Y* | *A*=1, *M* =0 −α '= (*p*1 − *p*0)*E*01(1) + (1− *p*1)*E*00(1)

α = *p*1 − *p*0 *p*1

α '= *p*1 − *p*0 1− *p*0

to assuming that *E* 01(1) ≤ *E* 11(1) with *m* = 1 and *E* 00(1) ≤ *E* 01(1) with *m* = 0, because *p* 1 > *p* 0 by assumption.

*E*01(1)=E *Y* | *A*=1, *M* =1 + *p*0

*E*01(1)=E *Y* | *A*=1, *M* =0 − 1− *p*0

As π 10 = 0 (no defier exists) under Assumption 1, (A1) reduces to

**Derivations of ranges of α under Assumptions 2 and 3**

Given that these two equations are equal, some algebra yields

Substituting (A7) into (A6) gives

and substituting (A8) into (A9) leads to

= 1, *M* = 0] – E[*Y*(1) | *A* = 0, *M* = 0], (A2)–(A5) with *a* = 1 can be expressed respectively as

The differences between (A6) and (A7) and between (A8) and (A9) lead to, respectively

expectation can be expressed as

54 Current Topics in Public Health

Similarly,

$$\begin{split} \alpha &= \mathsf{E} \mathsf{I} \mathsf{V} \left( \mathsf{1} \right) \mid \mathcal{A} = \mathsf{1}, \,\,\mathsf{M} = \mathsf{1} \mathsf{J} - \mathsf{E} \mathsf{I} \mathsf{V} \left( \mathsf{1} \right) \mid \mathcal{A} = \mathsf{0}, \,\,\mathsf{M} = \mathsf{1} \mathsf{J} \\ &\simeq \mathsf{E} \mathsf{V} \left( \mathsf{1} \right) \mid \mathcal{A} = \mathsf{1}, \,\,\mathsf{M} = \mathsf{1} \mathsf{J} - \mathsf{E} \mathsf{I} \mathsf{V} \left( \mathsf{O} \right) \mid \mathcal{A} = \mathsf{0}, \,\,\mathsf{M} = \mathsf{1} \mathsf{J} \\ &= \mathsf{E} \mathsf{V} \mathsf{V} \left( \mathsf{A} = \mathsf{1}, \,\,\mathsf{M} = \mathsf{1} \mathsf{J} - \mathsf{E} \mathsf{I} \mathsf{V} \mid \mathcal{A} = \mathsf{0}, \,\,\mathsf{M} = \mathsf{1} \mathsf{J} \right). \end{split}$$

and similarly α' ≤ E[*Y* | *A* = 1, *M* = 0] – E[*Y* | *A* = 0, *M* = 0]. Thus, a range of α under Assumption 3 is derived by α ≤ E[*Y* | *A* = 1, *M* = 1] – E[*Y* | *A* = 0, *M* = 1] and by substituting α' ≤ E[*Y* | *A* = 1, *M* = 0] – E[*Y* | *A* = 0, *M* = 0] into (A12).

#### **Derivation of equation (2)**

Using β 1 = *E* 11(1) – *E* 01(1), β 2 = *E* 11(0) – *E* 10(0) and β 3 = π 10, (A2) with *a* = 1 can be expressed as

$$\begin{split} \mathbb{E}\|\mathcal{T}\mid\mathcal{A}=\mathbb{1},\ \mathcal{M}=\mathbb{1} \Big\| &= \frac{(\pi\_{11}+\pi\_{\mathcal{O}1})\mathbb{E}\_{11}(\mathbb{1}) - \pi\_{\mathcal{O}1}\{\mathcal{E}\_{11}(\mathbb{1}) - \mathcal{E}\_{\mathcal{O}1}(\mathbb{1})\}}{\pi\_{11}+\pi\_{\mathcal{O}1}} \\ &= \mathbb{E}\_{11}(\mathbb{1}) - \frac{\mathcal{D}\_{1} - (\mathcal{D}\_{0} - \pi\_{10})}{\mathcal{D}\_{1}} \Big\{\mathcal{E}\_{11}(\mathbb{1}) - \mathcal{E}\_{\mathcal{O}1}(\mathbb{1})\Big\} \\ &= \mathbb{E}\_{11}(\mathbb{1}) - \frac{\mathcal{D}\_{1} - \mathcal{D}\_{0} + \mathcal{B}\_{3}}{\mathcal{D}\_{1}} \beta\_{1}, \end{split}$$

and (A3) with *a* = 0 can be expressed similarly as

$$\begin{split} \mathbb{E}\|\mathcal{Y}\mid\mathcal{A}=\mathcal{O},\ \mathcal{M}=\mathsf{I}\mathbf{J} &= \mathsf{I}\mathbf{J} = \frac{\langle \boldsymbol{\pi}\_{11} + \boldsymbol{\pi}\_{1\bullet} \rangle \mathcal{E}\_{1\prime 1} \langle \mathbf{O} \rangle - \boldsymbol{\pi}\_{1\bullet} \langle \boldsymbol{\mathcal{E}}\_{1\prime 1} \langle \mathbf{O} \rangle - \boldsymbol{\mathcal{E}}\_{1\bullet} \langle \mathbf{O} \rangle}{\boldsymbol{\pi}\_{1\prime 1} + \boldsymbol{\pi}\_{\bullet 1}} \\ &= \mathsf{E}\_{1\prime 1}(\mathbf{O}) - \frac{\mathsf{T}\_{1\bullet}}{\mathsf{P}\_{\bullet}} \Big\{ \mathsf{E}\_{1\prime 1}(\mathbf{O}) - \mathsf{E}\_{1\bullet}(\mathbf{O}) \Big\} \\ &= \mathsf{E}\_{1\prime 1}(\mathbf{O}) - \frac{\mathsf{B}\_{3}}{\mathsf{P}\_{\bullet}} \mathsf{B}\_{2} . \end{split}$$

The difference between these two equations leads to equation (2).

#### **Appendix 2: Derivations of equations and inequalities in Section 4**

#### **Derivation of equation (4)**

Using γ*m* and Γ, E[*Y*(1,*M*(0))] can be expressed as follows:

$$\begin{split} \mathsf{E}\{\mathsf{Y}(\mathsf{1},\mathsf{M}\langle\mathsf{O}\rangle)\} &= \mathsf{E}\{\mathsf{Y}(\mathsf{1},\mathsf{M}\langle\mathsf{O}\rangle)\,\|\,\mathsf{A}=\mathsf{O}\} \\ &= \sum\_{m} \mathsf{E}\{\mathsf{Y}(\mathsf{1},\mathsf{M}\langle\mathsf{O}\rangle)\,\|\,\mathsf{A}=\mathsf{O},\ \mathsf{M}\langle\mathsf{O}\rangle=m\} \mathsf{P}r(\mathsf{M}\,\langle\mathsf{O}\rangle=m\,\|\,\mathsf{A}=\mathsf{O}) \\ &= \sum\_{m} \mathsf{E}\{\mathsf{Y}(\mathsf{1},\mathsf{m})\,\|\,\mathsf{A}=\mathsf{O},\ \mathsf{M}=m\} \mathsf{P}r(\mathsf{M}=m\,\|\,\mathsf{A}=\mathsf{O}) \\ &= \sum\_{m} \{\mathsf{E}\{\mathsf{Y}(\mathsf{1},\mathsf{m})\,\|\,\mathsf{A}=\mathsf{I},\ \mathsf{M}=m\}-\mathsf{Y}\_{m}\} \mathsf{P}r(\mathsf{M}=m\,\|\,\mathsf{A}=\mathsf{O}) \\ &= \sum\_{m} \mathsf{E}\{\mathsf{Y}\,\|\,\mathsf{A}=\mathsf{I},\ \mathsf{M}=m\}\mathsf{P}r(\mathsf{M}=m\,\|\,\mathsf{A}=\mathsf{O})-\mathsf{I}, \end{split}$$

where the first equation is by the independency assumption, the third is by the consistency assumption, and the fourth is by γ*m* = E[*Y*(1,*m*) | *A* = 1, *M* = *m*] – E[*Y*(1,*m*) | *A* = 0, *M* = *m*]. The simpler calculation expresses E[*Y*(0,*M*(0))] as

$$\begin{aligned} \mathsf{E}\mathsf{E}\mathsf{Y}\left(\mathsf{O},\ \mathsf{M}\left(\mathsf{O}\right)\right) &= \mathsf{E}\mathsf{E}\mathsf{Y}\left(\mathsf{O}\right) \\ &= \mathsf{E}\mathsf{E}\mathsf{Y}\left(\mathsf{A}=\mathsf{O}\right) \\ &= \sum\_{m} \mathsf{E}\mathsf{L}\mathsf{Y}\left(\mathsf{A}=\mathsf{O},\ \mathsf{M}=m\right)\mathsf{P}\mathsf{r}\left(\mathsf{M}=m\mid\mathsf{A}=\mathsf{O}\right) .\end{aligned}$$

The difference between these two equations leads to equation (4).

#### **The reason that the lower limit of γm cannot be derived under Assumptions 2\* and 3\***

A range of α can be derived because (A10) and (A11) are equal. In the setting in which γ*m* is used instead of α and α', under Assumption 1, the following equations are derived, instead of (A10) and (A11):

$$\mathsf{E}\_{\mathsf{O}1}(\mathsf{I},\ \mathsf{I}) = \mathsf{E}\mathsf{I}\mathsf{Y}\begin{vmatrix}\mathsf{A}=\mathsf{I},\ \mathsf{M}=\mathsf{I}\end{vmatrix} + \frac{\mathsf{p}\_{\mathsf{O}}}{\mathsf{p}\_{1}-\mathsf{p}\_{\mathsf{O}}}\mathsf{p}\_{1},\tag{\mathsf{A}\ \mathsf{I}\mathsf{B}}\mathsf{Y}.\tag{\mathsf{A}\ \mathsf{T}\mathsf{S}}$$

**Author details**

Japan

**References**

377-392.

2009; 23(5) 394-402.

Yasutaka Chiba1\* and Etsuji Suzuki2

Sciences, Okayama University, Japan

*lic Health* 2001; 22(1) 189-212.

*idemiology* 2002; 31(1) 163-165.

*Epidemiology* 2010; 21(4) 540-551.

*Paediatric and Perinatal Epidemiology* 1991; 5(4) 243-257

fects. *Epidemiology* 1992; 3(2) 143-155.

1 Division of Biostatistics, Clinical Research Center, Kinki University School of Medicine,

Causal Inference with Intermediates: Simple Methods for Principal Strata Effects and Natural Direct Effects

http://dx.doi.org/10.5772/53193

57

2 Department of Epidemiology, Graduate School of Medicine, Dentistry and Pharmaceutical

[1] Greenland S, Morgenstern H. Confounding in health research. *Annual Review of Pub‐*

[2] Robins JM, Greenland S. Identifiability and exchangeability for direct and indirect ef‐

[3] Cole SR, Hernán MA. Fallibility in estimating direct effects. *International Journal of Ep‐*

[4] VanderWeele T.J. Bias formulas for sensitivity analysis for direct and indirect effects.

[5] Kiely JL. Some conceptual problems in multivariable analyses of perinatal mortality.

[6] Kiely JL, Kleinman JC. Birth-weight-adjusted infant mortality in evaluations of peri‐ natal care: towards a useful summary measure. *Statistics in Medicine* 1993; 12(3-4)

[7] Kramer MS. Biology vs. methodology in investigating causal pathways for infant

[8] Hernández-Díaz S, Schisterman EF, Hernán MA. The birth-weight "paradox" uncov‐

[9] Schisterman EF, Whitcomb BW, Mumford SL, Platt RW. Z-scores and the birth‐

[10] Whitcomb BW, Schisterman EF, Perkins NJ, Platt RW. Quantification of colliderstratification bias and the birthweight paradox. *Paediatric and Perinatal Epidemiology*

[11] Wilcox AJ, Weinberg CR, Basso O. On the pitfalls of adjusting for gestational age at

weight paradox. *Paediatric and Perinatal Epidemiology* 2009; 23(5) 403-413.

mortality. *Paediatric and Perinatal Epidemiology* 2009; 23(5) 414-416.

ered? *American Journal of Epidemiology* 2006; 164(11) 1115-1120.

birth. *American Journal of Epidemiology* 2011; 174(9) 1062-1068.

$$\mathbb{E}\_{\mathbb{O}1}(\mathbb{1},\mathbb{O}) = \mathbb{E}\mathbb{Y}^{\mathbb{Y}} \left| \mathcal{A} = \mathbb{1}, \,\mathcal{M} = \mathbb{O} \right| - \frac{\mathbb{1} - \mu\_{\mathbb{O}}}{\mu\_{1} - \mu\_{\mathbb{O}}} \nu\_{\mathbb{O}}.\tag{A14}$$

where *Eij*(*a*,*m*) = E[*Y*(*a*,*m*) | *M*(0) = *i*, *M*(1) = *j*]. Because these two equations are not equal, the lower limit of γ 0 (γ 1) cannot be derived using the upper limit of γ 1 (γ 0) under Assumptions 2\* and 3\*, even under Assumption 1.

#### **Derivations of ranges of Γ under Assumptions 4 and 5 and Assumptions 1 and 5**

By the consistency assumption, E[*Y*(1,*m*) | *A* = 1, *M* = *m*] = E[*Y* | *A* = 1, *M* = *m*]. Using Assumptions 4 and 5, the following inequality can be derived:

$$\begin{split} \mathop{\mathsf{E}}\_{m} \mathsf{E} \mathsf{E} \mathsf{Y} (\mathsf{1}, \mathsf{m}) \| \mathsf{ } \mathsf{A} = \mathsf{0}, \ \mathsf{M} = m \mathsf{I} \| \mathsf{Pr}(\mathsf{M} = m \mid \mathsf{A} = \mathsf{0}) \simeq \mathop{\mathsf{E}}\_{m} \mathsf{E} \mathsf{Y} (\mathsf{1}, \mathsf{1}) \| \mathsf{ } \mathsf{A} = \mathsf{0}, \ \mathsf{M} = m \mathsf{I} \| \mathsf{Pr}(\mathsf{M} = m \mid \mathsf{A} = \mathsf{0}) \\ &= \mathsf{E} \mathsf{Y} \mathsf{Y} (\mathsf{1}, \mathsf{1}) \| \mathsf{A} = \mathsf{0} \| \\ &= \mathsf{E} \mathsf{Y} \mathsf{Y} (\mathsf{1}, \mathsf{1}) \| \mathsf{A} = \mathsf{1} \| \\ &= \sum\_{m} \mathsf{E} \mathsf{Y} \mathsf{Y} (\mathsf{1}, \mathsf{1}) \| \mathsf{A} = \mathsf{1}, \ \mathsf{M} = m \mathsf{J} \mathsf{P} \mathsf{r} (\mathsf{M} = m \mid \mathsf{A} = \mathsf{1}) \\ &\approx \sum\_{m} \mathsf{E} \mathsf{Y} (\mathsf{1}, \mathsf{1}) \| \mathsf{A} = \mathsf{1}, \ \mathsf{M} = \mathsf{1} \mathsf{P} \mathsf{r} (\mathsf{M} = m \mid \mathsf{A} = \mathsf{1}) \\ &= \mathsf{E} \mathsf{Y} \mathsf{Y} \, \| \mathsf{A} = \mathsf{1}, \ \mathsf{M} = \mathsf{1} \mathsf{Z} \mathsf{N} \end{split}$$

where the first inequality is by Assumption 5 with *a* = 1 and *a\** = 0, the third equation is by the independency assumption, and the fifth inequality is by Assumption 4 with *a* = 1 and *m* = 1. Substituting the above equation and inequality into equation (3) leads to

$$\begin{split} \mathsf{T} &\simeq \sum\_{\mathsf{m}} \mathsf{E} \mathsf{T} \mathsf{Y} \mid \mathsf{A} = \mathsf{1}, \ \mathsf{M} = \mathsf{m} \mathsf{J} \mathsf{Pr}(\mathsf{M} = \mathsf{m} \mid \mathsf{A} = \mathsf{O}) - \mathsf{E} \mathsf{I} \mathsf{Y} \mid \mathsf{A} = \mathsf{1}, \ \mathsf{M} = \mathsf{1} \\ &= -\{\mathsf{E} \mathsf{f} \mathsf{Y} \mid \mathsf{A} = \mathsf{1}, \ \mathsf{M} = \mathsf{1}\} - \mathsf{E} \mathsf{I} \mathsf{Y} \mid \mathsf{A} = \mathsf{1}, \ \mathsf{M} = \mathsf{O} \mathsf{J} \mathsf{P} \mathsf{r}(\mathsf{M} = \mathsf{O} \mid \mathsf{A} = \mathsf{O}). \end{split}$$

A similar calculation gives the upper limit.

Equations (A13) and (A14) hold under Assumption 1 and *E* 01(1,0) ≤ *E* 01(1,1) holds under Assumption 5 with *a* = 1, *a\** = 0 and *m* = 1. Substituting (A13) and (A14) into this inequality leads to

$$\mathbb{P}\_{\bullet} - (\boldsymbol{\rho}\_{1} - \boldsymbol{\rho}\_{\bullet}) \{ \mathsf{E} \mathsf{T} \boldsymbol{\lambda}^{\prime} \mid \mathsf{A} = \mathsf{I}, \ \mathsf{M} = \mathsf{I} \} - \mathsf{E} \mathsf{T} \boldsymbol{\lambda}^{\prime} \mid \mathsf{A} = \mathsf{I}, \ \mathsf{M} = \mathsf{O} \} \simeq \boldsymbol{\rho}\_{\mathcal{O}} \boldsymbol{\nu}\_{1} + (1 - \boldsymbol{\rho}\_{\mathcal{O}}) \boldsymbol{\nu}\_{\mathcal{O}} = \mathsf{I} \ \mathsf{I}$$

#### **Acknowledgements**

This work was supported partially by Grant-in-Aid for Scientific Research (No. 23700344) from the Ministry of Education, Culture, Sports, Science, and Technology of Japan.

### **Author details**

E *Y* (0, *M* (0)) =E *Y* (0)

**The reason that the lower limit of γm cannot be derived under Assumptions 2\* and 3\***

under Assumption 1, the following equations are derived, instead of (A10) and (A11):

**Derivations of ranges of Γ under Assumptions 4 and 5 and Assumptions 1 and 5**

E *Y* (1, *m*)| *A*=0, *M* =*m* Pr(*M* =*m*| *A*=0)≤∑

The difference between these two equations leads to equation (4).

inequality can be derived:

56 Current Topics in Public Health

∑ *m*

inequality into equation (3) leads to

A similar calculation gives the upper limit.

**Acknowledgements**

Γ ≥∑ *m*

0 and *m* = 1. Substituting (A13) and (A14) into this inequality leads to

=E *Y* | *A*=0 =∑ *m*

*E*01(1, 1)=E *Y* | *A*=1, *M* =1 + *p*0

*E*01(1, 0)=E *Y* | *A*=1, *M* =0 − 1− *p*0

where *Eij*(*a*,*m*) = E[*Y*(*a*,*m*) | *M*(0) = *i*, *M*(1) = *j*]. Because these two equations are not equal, the lower limit of γ 0 (γ 1) cannot be derived using the upper limit of γ 1 (γ 0) under Assumptions 2\* and 3\*, even under Assumption 1.

By the consistency assumption, E[*Y*(1,*m*) | *A* = 1, *M* = *m*] = E[*Y* | *A* = 1, *M* = *m*]. Using Assumptions 4 and 5, the following

*m*

=∑ *m*

≤∑ *m*

E *Y* | *A*=1, *M* =*m* Pr(*M* =*m*| *A*=0)−E *Y* | *A*=1, *M* =1 = −{E *Y* | *A*=1, *M* =1 −E *Y* | *A*=1, *M* =0 }Pr(*M* =0| *A*=0).

Equations (A13) and (A14) hold under Assumption 1 and *E* 01(1,0) ≤ *E* 01(1,1) holds under Assumption 5 with *a* = 1, *a\** =

−(*p*1 − *p*0){E *Y* | *A*=1, *M* =1 −E *Y* | *A*=1, *M* =0 }≤ *p*0γ1 + (1− *p*0)γ0 =Γ.

This work was supported partially by Grant-in-Aid for Scientific Research (No. 23700344) from

the Ministry of Education, Culture, Sports, Science, and Technology of Japan.

where the first inequality is by Assumption 5 with *a* = 1 and *a\** = 0, the third equation is by the independency assumption, and the fifth inequality is by Assumption 4 with *a* = 1 and *m* = 1. Substituting the above equation and

=E *Y* (1, 1)| *A*=0 =E *Y* (1, 1)| *A*=1

=E *Y* | *A*=1, *M* =1 ,

A range of α can be derived because (A10) and (A11) are equal. In the setting in which γ*m* is used instead of α and α',

E *Y* | *A*=0, *M* =*m* Pr(*M* =*m*| *A*=0).

*p*1 − *p*0

*p*1 − *p*0

γ1, (A13)

γ0, (A14)

E *Y* (1, 1)| *A*=0, *M* =*m* Pr(*M* =*m*| *A*=0)

E *Y* (1, 1)| *A*=1, *M* =*m* Pr(*M* =*m*| *A*=1)

E *Y* (1, 1)| *A*=1, *M* =1 Pr(*M* =*m*| *A*=1)

Yasutaka Chiba1\* and Etsuji Suzuki2

1 Division of Biostatistics, Clinical Research Center, Kinki University School of Medicine, Japan

2 Department of Epidemiology, Graduate School of Medicine, Dentistry and Pharmaceutical Sciences, Okayama University, Japan

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**Chapter 4**

**Use of Analytical Methods and**

Peter Papoh Ndibewu and Prince Ngobeni

Additional information is available at the end of the chapter

ical methodologies for public health researchers or practitioners.

http://dx.doi.org/10.5772/54006

**1. Introduction**

*In-silico* **Techniques in Public Health Research**

In this chapter, we briefly summarize the concept of analytical methodologies used for de‐ tecting, measuring, and/or monitoring in public health research. Additionally, this chapter describes *in silico* ADME, ADMET and ADME/Tox approaches or models relevant to analyt‐

Recently, adopted technologies to cope with this type of scientific demand in terms of drug development and testing are the applications of *in silico* techniques used in pharmaceutical companies in the process of drug discovery (Ndibewu et al., 2012; Vallero, 2012; Lipinski et al., 1997; Leeson & Springthorpe, 2007). Two fast growing examples involve the use of cheminformatics (also known as chemoinformtaics) and chemical informatics which is the use of computer and informational techniques, applied to a range of problems in the field of chemistry (Langdon et al., 2011; Brown, 2011). These *in silico* techniques are employed in pharmaceutical companies in the process of drug discovery (Lipinski, 2004). These methods can also be used in chemical and allied industries in various other forms (Pradeep, 2009). Combined with the accuracy of data obtained with validated analytical methods, this en‐ compasses the mixing of those information resources necessary to transform data into infor‐ mation and information into knowledge for the intended purpose of making better decisions faster in the area of drug lead identification and optimization. The outcome is clearly the ef‐ ficiency in public health research and the beneficiary is mankind. In the section that follows, we briefly summarize *in silico* pharmacokinetics, widely designated as ADME approaches or models relevant to analytical methodologies for public health researchers or practitioners (Yamashita & Hashida, 2004). Pharmacokinetics is the study of the time course of a drug within the body and incorporates the processes of absorption, distribution, metabolism and

> © 2013 Ndibewu and Ngobeni; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

> © 2013 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

and reproduction in any medium, provided the original work is properly cited.

## **Use of Analytical Methods and** *In-silico* **Techniques in Public Health Research**

Peter Papoh Ndibewu and Prince Ngobeni

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/54006

### **1. Introduction**

[41] Hafeman DM, Schwartz S. Opening the black box: a motivation for the assessment of

[42] Petersen ML, Sinisi SE, van der Laan MJ. Estimation of direct causal effects. *Epidemi‐*

[43] VanderWeele TJ. Marginal structural models for the estimation of direct and indirect

[44] Kaufman S, Kaufman JS, MacLehose RF, Greenland S, Poole C. Improved estimation of controlled direct effects in the presence of unmeasured confounding of intermedi‐

[45] Imai K, Keele L, Yamamoto T. Identification, inference and sensitivity analysis for

[46] VanderWeele TJ, Vansteelandt S. Odds ratios for mediation analysis with a dichoto‐

[47] Chiba Y. Monte-Carlo sensitivity analysis for controlled direct effects using marginal structural models in the presence of confounded mediators. *Communications in Statis‐*

[48] Tchetgen Tchetgen EJ, Shpitser I. Semiparametric theory for causal mediation analy‐ sis: efficiency bounds, multiple robustness, and sensitivity analysis. *Annals of Statis‐*

[49] Chiba Y. Bounds on controlled direct effects under monotonic assumptions about

[50] VanderWeele TJ. Simple relations between principal stratification and direct and in‐

mediators and confounders. *Biometrical Journal* 2010; 52(5) 628-637.

direct effects. *Statistics and Probability Letters* 2008; 78(17) 2957-2962.

mous outcome. *American Journal of Epidemiology* 2010; 172(12) 1339-1348.

mediation. *International Journal of Epidemiology* 2009; 38(4) 838-845.

ate variables. *Statistics in Medicine* 2005; 24(11) 1683-1702.

causal mediation effects. *Statistical Science* 2010; 25(1) 51-71.

*tics – Theory and Methods* 2012; 41(10) 1739-1749.

*ology* 2006; 17(3) 276-284.

60 Current Topics in Public Health

*tics* (in press).

effects. *Epidemiology* 2009; 20(1) 18-26.

In this chapter, we briefly summarize the concept of analytical methodologies used for de‐ tecting, measuring, and/or monitoring in public health research. Additionally, this chapter describes *in silico* ADME, ADMET and ADME/Tox approaches or models relevant to analyt‐ ical methodologies for public health researchers or practitioners.

Recently, adopted technologies to cope with this type of scientific demand in terms of drug development and testing are the applications of *in silico* techniques used in pharmaceutical companies in the process of drug discovery (Ndibewu et al., 2012; Vallero, 2012; Lipinski et al., 1997; Leeson & Springthorpe, 2007). Two fast growing examples involve the use of cheminformatics (also known as chemoinformtaics) and chemical informatics which is the use of computer and informational techniques, applied to a range of problems in the field of chemistry (Langdon et al., 2011; Brown, 2011). These *in silico* techniques are employed in pharmaceutical companies in the process of drug discovery (Lipinski, 2004). These methods can also be used in chemical and allied industries in various other forms (Pradeep, 2009). Combined with the accuracy of data obtained with validated analytical methods, this en‐ compasses the mixing of those information resources necessary to transform data into infor‐ mation and information into knowledge for the intended purpose of making better decisions faster in the area of drug lead identification and optimization. The outcome is clearly the ef‐ ficiency in public health research and the beneficiary is mankind. In the section that follows, we briefly summarize *in silico* pharmacokinetics, widely designated as ADME approaches or models relevant to analytical methodologies for public health researchers or practitioners (Yamashita & Hashida, 2004). Pharmacokinetics is the study of the time course of a drug within the body and incorporates the processes of absorption, distribution, metabolism and

© 2013 Ndibewu and Ngobeni; licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2013 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

excretion (ADME) (Van de Waterbeemd & Gifford, 2003). The extent of distribution will de‐ pend on the structural and physicochemical properties of the compound (Fig. 1).

**Figure 1.** ADME flow chart showing volume of distribution (Vd): is a theoretical concept connecting administered dose with actual initial concentration (Co) present in circulation, Vd = Dose/Co; Unbound volume, Vdu = Vd/fu, where fu is the fraction of unbound; Clearance (Cl) of the drug from the body mainly takes place via the liver and the kidney; Bioavail‐ ability is given by area under the curve (AUC) = F x Dose/Cl; Half-life (t1/2) is the time taken for a drug concentration in plasma to reduce by 50% (is function of the clearance and volume of distribution, and determines how often a drug needs to be administered (t1/2 = 0.693Vd/Cl) (Van de Waterbeemd & Gifford, 2003).

(a)

Use of Analytical Methods and *In-silico* Techniques in Public Health Research

http://dx.doi.org/10.5772/54006

63

(b)

(c)

**Figure 2.** a. An analysis of the crucial ADME processes for which predictive models are available or are being devel‐ oped (Carlson & Segall, 2002). b. Prediction paradigm ranging from models for simple physicochemical properties (Hbonding capacity, Molecular mass, Solubility and lipophilicity (log*D*)) to models for ADME properties (% drug absorbed & bioavailability, clearance, volume of distribution and half-life (t1/2)) to complex endpoints (binding (IC50), to molecular target of new drug and its required dose and toxicity potential (Waterbeemd & Gifford, 2003). c. The evolu‐

tion of drug discovery and the changing role of ADME studies I (Waterbeemd & Gifford, 2003)

Figure 2 shows a simple ADME decision-making flow sheet which will incorporate predic‐ tors for volume of distribution, oral bioavailability, half-life (t1/2), distribution\protein bind‐ ing module including percentage plasma protein binding values (*%PPB*) and drug affinity constant to human serum albumin represented by log *Ka HSA* constants. The adaptability of this simple form has continuously refine existing models by building on larger and higherquality data sets crucial to the success of the *in silico* approaches as grouped by Van de Wa‐ terbeem and Gifford (2003) in the form of problem areas for which predictive models could be helpful (Fig. 2). And during these past few years, the range of models have further ex‐ panded to include, for example, models for various transporters, metabolism by non-P450 enzymes, plasma protein binding, and so (Lu et al., 2003; Ekins et al., 2001).

Figures 2a and 2b outline the parameters in the prediction of a safe drug given in acceptable dose, which it is ultimately hoped will be reliably obtainable from molecular structure and appropriate descriptors using a suite of predictive models. This expression had earlier been made clear by Japertas and coworkers (2011).

Use of Analytical Methods and *In-silico* Techniques in Public Health Research http://dx.doi.org/10.5772/54006 63

excretion (ADME) (Van de Waterbeemd & Gifford, 2003). The extent of distribution will de‐

**Volume of distribution** quote from the document or the summary of an interesting point. You can position

pend on the structural and physicochemical properties of the compound (Fig. 1).

**Volume of distribution** quote from the document or the summary of an interesting point. You can position

**Half-life Oral**

**Figure 1.** ADME flow chart showing volume of distribution (Vd): is a theoretical concept connecting administered dose with actual initial concentration (Co) present in circulation, Vd = Dose/Co; Unbound volume, Vdu = Vd/fu, where fu is the fraction of unbound; Clearance (Cl) of the drug from the body mainly takes place via the liver and the kidney; Bioavail‐ ability is given by area under the curve (AUC) = F x Dose/Cl; Half-life (t1/2) is the time taken for a drug concentration in plasma to reduce by 50% (is function of the clearance and volume of distribution, and determines how often a drug

Figure 2 shows a simple ADME decision-making flow sheet which will incorporate predic‐ tors for volume of distribution, oral bioavailability, half-life (t1/2), distribution\protein bind‐ ing module including percentage plasma protein binding values (*%PPB*) and drug affinity

this simple form has continuously refine existing models by building on larger and higherquality data sets crucial to the success of the *in silico* approaches as grouped by Van de Wa‐ terbeem and Gifford (2003) in the form of problem areas for which predictive models could be helpful (Fig. 2). And during these past few years, the range of models have further ex‐ panded to include, for example, models for various transporters, metabolism by non-P450

Figures 2a and 2b outline the parameters in the prediction of a safe drug given in acceptable dose, which it is ultimately hoped will be reliably obtainable from molecular structure and appropriate descriptors using a suite of predictive models. This expression had earlier been

**Dosing regim: How often?**

needs to be administered (t1/2 = 0.693Vd/Cl) (Van de Waterbeemd & Gifford, 2003).

enzymes, plasma protein binding, and so (Lu et al., 2003; Ekins et al., 2001).

constant to human serum albumin represented by log *Ka*

made clear by Japertas and coworkers (2011).

**bioavailability**

**Clearance Absorption**

**Dosing regim: How much?**

*HSA* constants. The adaptability of

**Volume of distribution** quote from the document or the summary of an interesting point. You can position

62 Current Topics in Public Health

**Figure 2.** a. An analysis of the crucial ADME processes for which predictive models are available or are being devel‐ oped (Carlson & Segall, 2002). b. Prediction paradigm ranging from models for simple physicochemical properties (Hbonding capacity, Molecular mass, Solubility and lipophilicity (log*D*)) to models for ADME properties (% drug absorbed & bioavailability, clearance, volume of distribution and half-life (t1/2)) to complex endpoints (binding (IC50), to molecular target of new drug and its required dose and toxicity potential (Waterbeemd & Gifford, 2003). c. The evolu‐ tion of drug discovery and the changing role of ADME studies I (Waterbeemd & Gifford, 2003)

In figure 2c (Waterbeemd & Gifford, 2003), the form *a* depicting the classical project-collabo‐ ration approach between chemistry, biology and drug metabolism (ADMES) groups in the 1990s is shown to *b* which is a much more automated world at the start of this millennium in which combinatorial chemistry (*CombiChem*), high throughput screening and ADME studies are linked together in a streamlined fashion.

mans are needed to determine background levels in the population and levels at which bi‐ ological effects occur. For example, Abdel-Rahman et al. (1980a & 1980b) developed a method to quantitatively and qualitatively measure the metabolites of chlorine dioxide

In the absence of sensitive and reliable methods for determining diseases vector-borne me‐ tabolites and biomarkers of exposure, mechanistic models of tissue distribution of drug compounds have been used (Rowley et al., 1997) to assess levels at which biological effects occur in the population and mitigate disease occurrence. Poulin et al. (Poulin & Theil, 2002; Poulin & Krishna, 1995) developed tissue composition-based equations for calculating tis‐

The following expressions are used (equations 1 and 2) (Yamashita & Hashida, 2004):

*PV V V V f P x*

*DV V V V f P x DV V V V* + ++ = + ++

Po:w is the n-octanol:buffer partition coefficient of non-ionized species at pH 7.4.

and water (*w*), t is the tissue, p is the plasma and *fu* is the unbound fraction.

( 0.3 ) ( 0.7 ) ( 0.3 ) ( 0.7 ) *o w nlp php wt pht Up*

*PV V V V f*

( 0.3 ) ( 0.7 ) ( 0.3 ) ( 0.7 ) 1 *vo w nlt pht wt pht Up*

*vo w nlp php wp php*

D\*vo:w is the olive oil:buffer partition coefficient of both the nonionized and ionized species at pH 7.4, V is the fractional tissue volume content of neutral lipids (*nl*), phospholipids (*ph*),

These equations are based on the assumption that each tissue and plasma is a mixture of lip‐

The first term of these equations is based on the drug Lipophilicity-hydrophilicity balance of tissues and plasma due to their lipid and water contents, while the second term of the equation considers the binding to common proteins present in plasma and plasma intersti‐

**3. Use of** *In-silico* **techniques and chemical informatics in health research**

Even though disease mapping has been done for over a hundred years, historically, the focus in health research has been on person and conventional medicinal chemistry targeting specif‐ ic disease treatment with little regard for the implications of *de novo* molecular design costs. Also, the need for high throughput screening in drug discovery research for public health in‐ terest has surfaced as a top priority in the last decade (Norris et al., 2000; Green et al, 1974).

ids, water and plasma proteins in which the drug can be homogeneously distributed.

*o w nlp php wp php Ut*

:

:

\* :

:

) in biological fluids. These biomarkers may be used to indirectly

Use of Analytical Methods and *In-silico* Techniques in Public Health Research

http://dx.doi.org/10.5772/54006

65

+ ++ = + ++ (1)

(2)

(e.g., ClO2

tial space.

, and ClO-

measure chlorine dioxide exposure.

sue-plasma partition coefficients (Pt:p).

:

*t pnonadipose*

: \*

*t p adipose*

It should be noted that all three activities shown in figure 3 can even be carried out by sepa‐ rate companies of research units or even researchers in health departments or for health in‐ terest. A good example is the Medical Research Council (MRC) of South Africa which supports unit health research projects towards a nationally planned and prioritized health sectors. Furthermore, the wide introduction of *in silico* and high-speed in vivo methods could redefine the traditional meaning of ADME to Automated Decision-Making Engine. To reflect, one sees that considerable effort has equally been devoted into the development of *in silico* models for the prediction of oral absorption (Veber et al., 2002; Agoram et al., 2001; Parrott & Lavé, 2002; Yu et al., 2000). This range from the simplest models based on a single descriptor, such as log P or log *D*, or polar surface area, which is a descriptor of hydrogenbonding potential to combo or meta- or QSAR models.

### **2. Analytical methods in health research**

As analytical methods become increasingly sophisticated and capable for the detection of each component in a sample (Barnes & Dourson, 1988), including biological systems (Kote-Jarai et al. 2011), it is critical to separate and quantify them. Methods such as mass spectrom‐ etry (MS) and high performance chromatography (HPLC) routinely ensure these in many laboratories around the world (Thorp et al., 2011). HPLC instrumentations provide crucial analytical data (Beitler, 1995) used to calculate or predict drug's affinity constants (*log Ka HSA*) (Packard et al., 1996; Endo et al., 1982). For nearly half a century, analytical and testing methods as opposed to empirical approaches have played a key role in the identification of key diseases causative toxins (Barnes & Dourson, 1988; Bathija, 2003) and drug-like com‐ pounds to cure them (Kote-Jarai et al., 2011; Moore & Carpenter, 1999).

In this process, as tons of data are being produced with the analytical chemists struggling to make sense out of the bunch, the health researcher and health practitioners are faced with a constant task to make better and faster decisions in the area of disease treatment and pre‐ vention based on laboratory results. In the midst of all this, there is the requirement not only to produce efficient drugs, in enough quantities, to cure diseases but their development at the pace at which pandemics are spreading around the globe is also required, for example, cancer and HIV & AIDS.

As far as the identification of data needs is crucial in clinical laboratories, the quest for methods to determine biomarkers of exposure and effect of diseases in the public health is also growing fast. Hence, analysis of metabolites of drugs in humans or animals can pro‐ vide a biomarker of exposure that is sensitive to low levels of exposure and correlates well with exposure concentrations. Methods for determining biomarkers of exposure in hu‐ mans are needed to determine background levels in the population and levels at which bi‐ ological effects occur. For example, Abdel-Rahman et al. (1980a & 1980b) developed a method to quantitatively and qualitatively measure the metabolites of chlorine dioxide (e.g., ClO2 - , and ClO- ) in biological fluids. These biomarkers may be used to indirectly measure chlorine dioxide exposure.

In figure 2c (Waterbeemd & Gifford, 2003), the form *a* depicting the classical project-collabo‐ ration approach between chemistry, biology and drug metabolism (ADMES) groups in the 1990s is shown to *b* which is a much more automated world at the start of this millennium in which combinatorial chemistry (*CombiChem*), high throughput screening and ADME studies

It should be noted that all three activities shown in figure 3 can even be carried out by sepa‐ rate companies of research units or even researchers in health departments or for health in‐ terest. A good example is the Medical Research Council (MRC) of South Africa which supports unit health research projects towards a nationally planned and prioritized health sectors. Furthermore, the wide introduction of *in silico* and high-speed in vivo methods could redefine the traditional meaning of ADME to Automated Decision-Making Engine. To reflect, one sees that considerable effort has equally been devoted into the development of *in silico* models for the prediction of oral absorption (Veber et al., 2002; Agoram et al., 2001; Parrott & Lavé, 2002; Yu et al., 2000). This range from the simplest models based on a single descriptor, such as log P or log *D*, or polar surface area, which is a descriptor of hydrogen-

As analytical methods become increasingly sophisticated and capable for the detection of each component in a sample (Barnes & Dourson, 1988), including biological systems (Kote-Jarai et al. 2011), it is critical to separate and quantify them. Methods such as mass spectrom‐ etry (MS) and high performance chromatography (HPLC) routinely ensure these in many laboratories around the world (Thorp et al., 2011). HPLC instrumentations provide crucial analytical data (Beitler, 1995) used to calculate or predict drug's affinity constants (*log Ka*

(Packard et al., 1996; Endo et al., 1982). For nearly half a century, analytical and testing methods as opposed to empirical approaches have played a key role in the identification of key diseases causative toxins (Barnes & Dourson, 1988; Bathija, 2003) and drug-like com‐

In this process, as tons of data are being produced with the analytical chemists struggling to make sense out of the bunch, the health researcher and health practitioners are faced with a constant task to make better and faster decisions in the area of disease treatment and pre‐ vention based on laboratory results. In the midst of all this, there is the requirement not only to produce efficient drugs, in enough quantities, to cure diseases but their development at the pace at which pandemics are spreading around the globe is also required, for example,

As far as the identification of data needs is crucial in clinical laboratories, the quest for methods to determine biomarkers of exposure and effect of diseases in the public health is also growing fast. Hence, analysis of metabolites of drugs in humans or animals can pro‐ vide a biomarker of exposure that is sensitive to low levels of exposure and correlates well with exposure concentrations. Methods for determining biomarkers of exposure in hu‐

pounds to cure them (Kote-Jarai et al., 2011; Moore & Carpenter, 1999).

*HSA*)

are linked together in a streamlined fashion.

64 Current Topics in Public Health

bonding potential to combo or meta- or QSAR models.

**2. Analytical methods in health research**

cancer and HIV & AIDS.

In the absence of sensitive and reliable methods for determining diseases vector-borne me‐ tabolites and biomarkers of exposure, mechanistic models of tissue distribution of drug compounds have been used (Rowley et al., 1997) to assess levels at which biological effects occur in the population and mitigate disease occurrence. Poulin et al. (Poulin & Theil, 2002; Poulin & Krishna, 1995) developed tissue composition-based equations for calculating tis‐ sue-plasma partition coefficients (Pt:p).

The following expressions are used (equations 1 and 2) (Yamashita & Hashida, 2004):

$$P\_{t:p\,nomdiyse} = \frac{P\_{o:w}(V\_{nlp} + 0.3V\_{php}) + (V\_{wt} + 0.7V\_{pht})}{P\_{o:w}(V\_{nlp} + 0.3V\_{php}) + (V\_{wp} + 0.7V\_{php})} \ge \frac{f\_{l1p}}{f\_{l1t}}\tag{1}$$

$$P\_{t:p\,adjust} = \frac{D\_{vc:w}^{\ast}(V\_{nlt} + 0.3V\_{plt}) + (V\_{wt} + 0.7V\_{plt})}{D\_{vc:w}^{\ast}(V\_{nlp} + 0.3V\_{plp}) + (V\_{wp} + 0.7V\_{plp})} \ge \frac{f\_{l1p}}{1} \tag{2}$$

Po:w is the n-octanol:buffer partition coefficient of non-ionized species at pH 7.4.

D\*vo:w is the olive oil:buffer partition coefficient of both the nonionized and ionized species at pH 7.4, V is the fractional tissue volume content of neutral lipids (*nl*), phospholipids (*ph*), and water (*w*), t is the tissue, p is the plasma and *fu* is the unbound fraction.

These equations are based on the assumption that each tissue and plasma is a mixture of lip‐ ids, water and plasma proteins in which the drug can be homogeneously distributed.

The first term of these equations is based on the drug Lipophilicity-hydrophilicity balance of tissues and plasma due to their lipid and water contents, while the second term of the equation considers the binding to common proteins present in plasma and plasma intersti‐ tial space.

#### **3. Use of** *In-silico* **techniques and chemical informatics in health research**

Even though disease mapping has been done for over a hundred years, historically, the focus in health research has been on person and conventional medicinal chemistry targeting specif‐ ic disease treatment with little regard for the implications of *de novo* molecular design costs. Also, the need for high throughput screening in drug discovery research for public health in‐ terest has surfaced as a top priority in the last decade (Norris et al., 2000; Green et al, 1974). However, the testing of much lead drug-like candidates often fails because of unsatisfactory ADME properties (Zmuidinavicius et al., 2003). In handling this challenge, ADME studies employing *in silico* techniques to improve the rate of success in the more costly downstream stages of drug development before clinical trials has gain tremendous interest in public health research methodologies. In this light, *in silico* ADME studies use various models developed for predicting ADME properties of compounds from their chemical structures and integrat‐ ing them to simulate the kinetics at the organ or body levels Carlson & Segall, 2002; Podlogar et al., 2001; Ekins et al., 2001). Data-based approaches such as quantitative structure-activity relationship (QSAR) (Zhaou et al., 2001, Yoshida & Topliss, 2000), similarity searches, 3D-QSAR (Jones et al., 1996) and structure-based methods such as ligand-protein docking and pharmacophore modeling are amongst approaches currently used. In addition, several meth‐ ods of integrating ADME properties to predict pharmacokinetics at the organ or body level have been studied (Agatonovic-Kustrin, 2001; Van de Waterbeemd, 2001; Ho et al., 2000; Jaco‐ by et al., 2009; Lave et al., 1999). All these effort is to reduce the risk of late-stage attrition of drug development and to optimize screening and testing by looking at only the promising compounds. Recently, researchers have equally develop keen interest in *de novo* molecular de‐ sign (Good et al., 1995; Clark et al., 1995), predictive modeling, graph theory, molecular simi‐ larity and diversity, virtual ligand docking, scaffold hopping (Langdon et al., 2010), multiobjective optimization Nicolaou et al., 2007), molecular descriptors, bioisosteric replacement, machine learning and evolutionary algorithms (Gillet, 2008).

sets. For examples, multiple linear regressions (MLR) and partial least square (PLS) (Norind‐

Use of Analytical Methods and *In-silico* Techniques in Public Health Research

**References Descriptors** *N R2* **RMSE** Levin19 Log(P.MW-1/2) 22 0.83 - Abraham and coworkers10,24 Solvation parameters (A, B, E, S, Vx) 18 0.95 0.48

Bodor and Buchwald11 Log*P*(log*D*) 58 0.90 0.62 Liu et al.5 Log*D*, PSA, vsa base 23 0.74 0.50

These illustrations show how *in silico* chemistry or cheminformatics and high-throughput screening have increased the possibility of finding new lead compounds at much shorter time periods than conventional medicinal chemistry. With judicious selection of lead com‐ pounds and constant monitoring of physical properties (especially Lipophilicity (equation 1) or other major physchem parameter) during optimization, medicinal chemists have an op‐ portunity to help alleviate the appalling attrition rates, estimated at 93–96% (Norris et al., 2000) in clinical drug development (Bhal et al.,. This means that physicochemical properties in small-molecule drug discovery are completely under the control of medicinal chemists and can easily be calculated before chemical synthesis. It is, however, important to empha‐ size here that when interpreting results from prediction models, that the predictions are on‐ ly as good as the dataset used to create the model. So when we calculate a prediction, if the training set does not contain chemical structures that are similar to the particular compound in question, the predicted result may not be reliable, regardless of the actual result of the

From various literature sources (Bhal, 2007; Sazonovas et al., 2010), it is reported that ADME and toxicity prediction models can be a valuable part of many different research workflows, including virtual screening, metabolite identification, impurity analysis and chemical safety, reliability index (*RI*) value (0 – 1) in addition to the predicted probability result (Japertas et al., 2010) which is an indicator of how well spatial chemical space around a particular com‐

Log*P*, different *MW* functions

This literature Log*P*, HD, HA, Vx, ion fractions (p*Ka* function)

**Table 1.** Summary of QSAR Models for Predicting LogPS (Lanevskij et al., 2008)

pound is represented within the training set of the model (Fig. 3)

30 0.87 0.52

http://dx.doi.org/10.5772/54006

67

7-37 0.80-0.96 -

125a 0.84 0.48

53b 0.82 0.49

er & Österberg, 2001).

Luco and Marchevsky25 (review of earlier studies)

Training set; bValidation set.

a

prediction.

In the last decade, a wide variety of descriptors used in QSAR studies have been developed (Khan et al., 2009; Miners et al., 2006). A subset of these descriptors is potentially useful for predicting ADME properties. Many QSAR studies on BBB permeation of drugs have been published recently. In the big junk of these works (Wichmann et al., 2007; Zhao et al., 2007; Cuadrado et al., 2007; Katritzky et al., 2006; Garg & Verma, 2006; Hemmateenejad et al., 2006; Narayanan & Gunturi, 2005) experimental data are represented as log*BB* constants or as qualitative (binary) index subdividing all compounds into 'CNS positive' and "CNS neg‐ ative" classes according to presence or lack of central nervous system (CNS) activity. Table 1 summarizes the most notable QSAR models (log*PS*) representing blood/brain partitioning coefficients at equilibrium conditions (log*BB*)( Goodwin & Clark, 2005; Abbott, 2004) show‐ ing that typical data sets involved only 20-30 compounds.

Log*PS* is based on *in vivo* kinetic permeability measurements using intravenous administra‐ tion (Oldendorf, 1971), brain uptake index (Bickel, 2005; Oldendorf, 1971) and *in situ* perfu‐ sion in rat or mouse (Bickel, 2005; Dagenais et al., 2000; Takasato et al., 1984;). Where, *P* (cm s-1) is observed permeability across BBB, whereas *S* (cm2 /g) is surface area of brain capillary endothelium which equals to ~ 100 – 130 cm2 in rats (Abraham, 2004; Bodor & Buchwald, 1999). PS product can be calculated from Kety-Renkin-Crone equation of capillary transport (*Kin* = F. (1- e*-PS/F*)), and by its physical meaning, *PS* is equal to the unidirectional influx rate constant (Kin) corrected for cerebral blood flow (*F*). Earlier attempts of log*PS* prediction were largely restricted by the lack of high quality data. A subset of statistical techniques can deal with larger sets of molecular descriptors aimed at finding relationships or patterns in data

sets. For examples, multiple linear regressions (MLR) and partial least square (PLS) (Norind‐ er & Österberg, 2001).

**Table 1.** Summary of QSAR Models for Predicting LogPS (Lanevskij et al., 2008)

However, the testing of much lead drug-like candidates often fails because of unsatisfactory ADME properties (Zmuidinavicius et al., 2003). In handling this challenge, ADME studies employing *in silico* techniques to improve the rate of success in the more costly downstream stages of drug development before clinical trials has gain tremendous interest in public health research methodologies. In this light, *in silico* ADME studies use various models developed for predicting ADME properties of compounds from their chemical structures and integrat‐ ing them to simulate the kinetics at the organ or body levels Carlson & Segall, 2002; Podlogar et al., 2001; Ekins et al., 2001). Data-based approaches such as quantitative structure-activity relationship (QSAR) (Zhaou et al., 2001, Yoshida & Topliss, 2000), similarity searches, 3D-QSAR (Jones et al., 1996) and structure-based methods such as ligand-protein docking and pharmacophore modeling are amongst approaches currently used. In addition, several meth‐ ods of integrating ADME properties to predict pharmacokinetics at the organ or body level have been studied (Agatonovic-Kustrin, 2001; Van de Waterbeemd, 2001; Ho et al., 2000; Jaco‐ by et al., 2009; Lave et al., 1999). All these effort is to reduce the risk of late-stage attrition of drug development and to optimize screening and testing by looking at only the promising compounds. Recently, researchers have equally develop keen interest in *de novo* molecular de‐ sign (Good et al., 1995; Clark et al., 1995), predictive modeling, graph theory, molecular simi‐ larity and diversity, virtual ligand docking, scaffold hopping (Langdon et al., 2010), multiobjective optimization Nicolaou et al., 2007), molecular descriptors, bioisosteric replacement,

In the last decade, a wide variety of descriptors used in QSAR studies have been developed (Khan et al., 2009; Miners et al., 2006). A subset of these descriptors is potentially useful for predicting ADME properties. Many QSAR studies on BBB permeation of drugs have been published recently. In the big junk of these works (Wichmann et al., 2007; Zhao et al., 2007; Cuadrado et al., 2007; Katritzky et al., 2006; Garg & Verma, 2006; Hemmateenejad et al., 2006; Narayanan & Gunturi, 2005) experimental data are represented as log*BB* constants or as qualitative (binary) index subdividing all compounds into 'CNS positive' and "CNS neg‐ ative" classes according to presence or lack of central nervous system (CNS) activity. Table 1 summarizes the most notable QSAR models (log*PS*) representing blood/brain partitioning coefficients at equilibrium conditions (log*BB*)( Goodwin & Clark, 2005; Abbott, 2004) show‐

Log*PS* is based on *in vivo* kinetic permeability measurements using intravenous administra‐ tion (Oldendorf, 1971), brain uptake index (Bickel, 2005; Oldendorf, 1971) and *in situ* perfu‐ sion in rat or mouse (Bickel, 2005; Dagenais et al., 2000; Takasato et al., 1984;). Where, *P* (cm

1999). PS product can be calculated from Kety-Renkin-Crone equation of capillary transport (*Kin* = F. (1- e*-PS/F*)), and by its physical meaning, *PS* is equal to the unidirectional influx rate constant (Kin) corrected for cerebral blood flow (*F*). Earlier attempts of log*PS* prediction were largely restricted by the lack of high quality data. A subset of statistical techniques can deal with larger sets of molecular descriptors aimed at finding relationships or patterns in data

/g) is surface area of brain capillary

in rats (Abraham, 2004; Bodor & Buchwald,

machine learning and evolutionary algorithms (Gillet, 2008).

66 Current Topics in Public Health

ing that typical data sets involved only 20-30 compounds.

s-1) is observed permeability across BBB, whereas *S* (cm2

endothelium which equals to ~ 100 – 130 cm2

These illustrations show how *in silico* chemistry or cheminformatics and high-throughput screening have increased the possibility of finding new lead compounds at much shorter time periods than conventional medicinal chemistry. With judicious selection of lead com‐ pounds and constant monitoring of physical properties (especially Lipophilicity (equation 1) or other major physchem parameter) during optimization, medicinal chemists have an op‐ portunity to help alleviate the appalling attrition rates, estimated at 93–96% (Norris et al., 2000) in clinical drug development (Bhal et al.,. This means that physicochemical properties in small-molecule drug discovery are completely under the control of medicinal chemists and can easily be calculated before chemical synthesis. It is, however, important to empha‐ size here that when interpreting results from prediction models, that the predictions are on‐ ly as good as the dataset used to create the model. So when we calculate a prediction, if the training set does not contain chemical structures that are similar to the particular compound in question, the predicted result may not be reliable, regardless of the actual result of the prediction.

From various literature sources (Bhal, 2007; Sazonovas et al., 2010), it is reported that ADME and toxicity prediction models can be a valuable part of many different research workflows, including virtual screening, metabolite identification, impurity analysis and chemical safety, reliability index (*RI*) value (0 – 1) in addition to the predicted probability result (Japertas et al., 2010) which is an indicator of how well spatial chemical space around a particular com‐ pound is represented within the training set of the model (Fig. 3)

*%PPB* values represent the overall fraction of drug bound in human plasma, i.e. accounts for interactions with different proteins: albumin, α-1-acid glycoprotein, liproteins, SHBG, trans‐ ortion, etc. In vitro measurements of the extent of plasma protein binding usually involve equilibrium dialysis, ultrafiltration or ultracentrifugation methods. The supplementary dis‐ tribution/Vd module calculates apparent volume of distribution of drugs in human body ex‐ pressed in litres per *Kg* body weight (*L/Kg*). This expression is given as: *%PPB* = (1-*fu) x 100%,* Where *fu* is a fraction of free (unbound) drug in plasma (0 -1). Note that predictive

ing to Similarity) modeling methodology consisting of global (baseline) statistical model (based on *PLS* with multiple bootstrapping, using a predefined set of fragmental descrip‐ tors), and local correction to baseline prediction (based on the analysis of model perform‐ ance for similar compounds from the training set = self-training library). Because of the percentage (*%PPB*) scale platform of the overall protein binding in plasma, values are linear‐ ized prior to modeling and converted to apparent serum affinity constants, *log Kapp,* the main parameter used in modeling. With this, final prediction can be converted back to *%PPB* us‐

> log % 100% 1 log

*K PPB x*

*app app*

Model Applicability Domain (MAD) (*RI ≥ 0.3*) is taken from Bhal et al. (2012) and shown in figures 4. In equation (y), the local part of the model provides the basis for estimating relia‐ bility of prediction by means of calculated Reliability Index (*RI*) values that range from 0 – 1. 0 means unreliable prediction and 1 fully reliable or ideal prediction. The *RI* values can also be used for interpreting prediction results, for example in setting the cut-off point (*RI = 0.3*), meaning that if compound falls outside of the MAD, the respective prediction should be to‐

HSA are derived using GALAS (Global, Adjusted Locally Accord‐

Use of Analytical Methods and *In-silico* Techniques in Public Health Research

http://dx.doi.org/10.5772/54006

69

*K* = + (4)

HSA models, validation set compounds within

*HSA*.

HSA values for validation set compounds (ACD/Log*D* Suite).

models for %PPB and loga

ing the following expression (Bhal et al., 2007):

To illustrate the performance of *%PPB* and loga

**Figure 4.** Predicted *versus* observed *%PPB* and loga

tally discarded from further analysis irrespective of *%PPB* and *loga*

**Figure 3.** Model applicability domain versus proprietary chemical space, predicted using ACD/Log*D* Suite (Bhal & Coworkers, 2007)

The development of *in silico* technologies or chemical informatics over the last 20 years has, thus, provided a more powerful and rapid ability to examine clinical decision-making and answers to critical public research health issues based on scientifically validated models from an un biased an empirical question based on a minimally biased appraisal of all the relevant empirical studies. This, in turn, has fostered the discussion of policy of drug discov‐ ery relevant to health issues as well as health services and planning, in conjunction with the use of clinical investigations and disease surveillance. Such reviews aim to improve ethically relevant decisions in public healthcare research or policy. With this in mind, identification of a lead compound or biochemical starting point for a drug discovery program has been high‐ lighted recently as a critically important activity, reflected by lead generation strategies be‐ ing widely implemented in the pharmaceutical industry (Jupertas, 2007).

For a more robust process, calculated quantitative parameters will provide further informa‐ tion though slightly different from the core predictive pharmacokinetic data. These parame‐ ters show great inter relation. Such parameters include the drug's affinity constants (*log Ka HSA*) to human serum albumin (the major carrier protein in plasma). Experimental data come from direct chromatographic determination of binding strength to that particular pro‐ tein. These parameters are usually calculated as follows (Bhal et al. 2007):

$$\log K\_a^{HSA} = \log \left( \frac{[LA]}{[L[A]]} \right). \tag{3}$$

Where [LA] is the concentration of ligand bound to albumin, [L] is that of free ligand, and [A] is the concentration of free albumin which, estimated at ~ 0.6 *mM* in human plasma.

*%PPB* values represent the overall fraction of drug bound in human plasma, i.e. accounts for interactions with different proteins: albumin, α-1-acid glycoprotein, liproteins, SHBG, trans‐ ortion, etc. In vitro measurements of the extent of plasma protein binding usually involve equilibrium dialysis, ultrafiltration or ultracentrifugation methods. The supplementary dis‐ tribution/Vd module calculates apparent volume of distribution of drugs in human body ex‐ pressed in litres per *Kg* body weight (*L/Kg*). This expression is given as: *%PPB* = (1-*fu) x 100%,* Where *fu* is a fraction of free (unbound) drug in plasma (0 -1). Note that predictive models for %PPB and loga HSA are derived using GALAS (Global, Adjusted Locally Accord‐ ing to Similarity) modeling methodology consisting of global (baseline) statistical model (based on *PLS* with multiple bootstrapping, using a predefined set of fragmental descrip‐ tors), and local correction to baseline prediction (based on the analysis of model perform‐ ance for similar compounds from the training set = self-training library). Because of the percentage (*%PPB*) scale platform of the overall protein binding in plasma, values are linear‐ ized prior to modeling and converted to apparent serum affinity constants, *log Kapp,* the main parameter used in modeling. With this, final prediction can be converted back to *%PPB* us‐ ing the following expression (Bhal et al., 2007):

$$\%PPB = \frac{\log K\_{app}}{1 + \log K\_{app}} \ge 100\% \tag{4}$$

To illustrate the performance of *%PPB* and loga HSA models, validation set compounds within Model Applicability Domain (MAD) (*RI ≥ 0.3*) is taken from Bhal et al. (2012) and shown in figures 4. In equation (y), the local part of the model provides the basis for estimating relia‐ bility of prediction by means of calculated Reliability Index (*RI*) values that range from 0 – 1. 0 means unreliable prediction and 1 fully reliable or ideal prediction. The *RI* values can also be used for interpreting prediction results, for example in setting the cut-off point (*RI = 0.3*), meaning that if compound falls outside of the MAD, the respective prediction should be to‐ tally discarded from further analysis irrespective of *%PPB* and *loga HSA*.

**Figure 3.** Model applicability domain versus proprietary chemical space, predicted using ACD/Log*D* Suite (Bhal &

The development of *in silico* technologies or chemical informatics over the last 20 years has, thus, provided a more powerful and rapid ability to examine clinical decision-making and answers to critical public research health issues based on scientifically validated models from an un biased an empirical question based on a minimally biased appraisal of all the relevant empirical studies. This, in turn, has fostered the discussion of policy of drug discov‐ ery relevant to health issues as well as health services and planning, in conjunction with the use of clinical investigations and disease surveillance. Such reviews aim to improve ethically relevant decisions in public healthcare research or policy. With this in mind, identification of a lead compound or biochemical starting point for a drug discovery program has been high‐ lighted recently as a critically important activity, reflected by lead generation strategies be‐

For a more robust process, calculated quantitative parameters will provide further informa‐ tion though slightly different from the core predictive pharmacokinetic data. These parame‐ ters show great inter relation. Such parameters include the drug's affinity constants (*log*

*HSA*) to human serum albumin (the major carrier protein in plasma). Experimental data come from direct chromatographic determination of binding strength to that particular pro‐

> *L A* æ ö = ç ÷

Where [LA] is the concentration of ligand bound to albumin, [L] is that of free ligand, and [A] is the concentration of free albumin which, estimated at ~ 0.6 *mM* in human plasma.

è ø (3)

[ ] log log . [ [ ]]

*LA K*

ing widely implemented in the pharmaceutical industry (Jupertas, 2007).

tein. These parameters are usually calculated as follows (Bhal et al. 2007):

*HSA a*

Coworkers, 2007)

68 Current Topics in Public Health

*Ka*

**Figure 4.** Predicted *versus* observed *%PPB* and loga HSA values for validation set compounds (ACD/Log*D* Suite).

The *P* descriptor is a lipophilicity descriptor for neutral compounds, or where the com‐

For ionizable solutes, the compounds may exist as a variety of different species in each phase at a given pH. D, typically used in the logarithmic for (lo*D*) representing the distribu‐ tion coefficient which is the appropriate descriptor for ionizable compounds since it is a measure of the pH-dependent differential solubility of all species in the octanol/water sys‐

.

, meaning that,

+ = *MeN H*3

pKa Ionization centre

4.8 Pyridine 10.9 Piperidine

**Table 2.** pKa values of 5-Methoxy-2-(1-piperidin-4-ylpropyl)pyridine (Bhal et al., 2012)

*MeN H*3 + *water*

Bhal (2012) used methylamine to illustrate the difference between these two descriptors as

+ *oc*tan*ol*

To accurately predict a compound's lipophilicity based on predicted molecular physical properties, it was imperative that the author applied the correct descriptor in an appropriate manner. In this context, log*D* instead is used in lieu of log*P* as the use of the latter to address lipophilicity concerns by drug research and manufacturing companies in the past (around 1980's and 90's) had resulted in incorrect conclusions for ionizable compounds. A good ex‐ ample would be to reproduce data generated by the previous author employing ACD/Log*D* in his application to discuss the significance of applying log*D* instead of log*P* using drug discovery as an example where lipophilicity is correlated with *in vivo* permeability. Using the sample molecule in figure 6 (5-Methoxy-2-(1-piperidin-4-ylpropyl)pyridine), data pre‐

The pH dependence of log*D* for this sample molecule (5-Methoxy-2-(1-piperidin-4-ylprop‐ yl)pyridine) is shown in figure 7 showing a plot of log*D* versus pH, while figure 8 displays

Looking at the plot in figure 8, and according to Bhal el al. (2012), we can confirm that ioniza‐ tion of the compound greatly affects octanol-water partitioning and that lipophilicity cannot

and Log*P* = log10(Partition Coefficient)

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.. So, keeping the definition of D above in

+ *oc*tan*ol*

+ *water* .

*MeN Hwater* + *MeN H*3

pounds exist in a single form.

tem (Levin, 1980).

follows: MeNH3

= *MeN H*2 *oc*tan*ol MeN H*2 *water*

sented in table were calculated.

the changing ionic forms of molecule A.

*PMeN H*2

*Partition coefficient*, *p* = *Compound oc*tan*ol*

*Distribution coefficient*, *D* = ∑ *Microspecies oc*tan*ol*

+ ⇌ MeNH2 + H+

and/or *PMeN H*3

*Compund water*

Log*P* = 1 can be explained as a ratio of 10 :1 organic:aqueous phase.

∑ *Microspecies water*

mind, we can write the expression of D as:*D* = *MeN H*2 *oc*tan*ol* + *MeN H*3

**Figure 5.** Predicted *versus* experimental values of *logLD50* (with a very high *RI > 0.75*) *%PPB* and loga HSA values for vali‐ dation set compounds (Bhal et al., 2012).

In figures 5 and 6, both models produce highly accurate results, while even better statistical characteristics are observed if only predictions of moderate and high reliability index are considered.

In order to understand the behavior of drug compounds in the real world, Bhal et al. (2012) has used ACD/Predictors such as log*P*, log*D*, solubility, and pKa to evaluate and predict the likely behavior of 5-Methoxy-2-(1-piperidin-4-ylpropyl)pyridine (Fig. 7), a compound prior to its synthesis. Lipophilicity is represented by the descriptors log*P* (also known as Kow or Pow) and log*D*, and is used, for example, to help predict *in-vivo* permeability of active com‐ pounds in drug discovery and the behavior of compounds in many other areas of health re‐ lated research. The partition coefficient, P, is a measure of the differential solubility of a compound in two immiscible solvents and the most commonly used commonly used sol‐ vent system is octanol-1-ol/water.

**Figure 6.** Chemical structure of 5-Methoxy-2-(1-piperidin-4-ylpropyl)pyridine, A

The *P* descriptor is a lipophilicity descriptor for neutral compounds, or where the com‐ pounds exist in a single form.

$$\text{Partition coefficient}, \text{ } p = \frac{\text{Compound } \mathbf{J}\_{\text{actual}}}{\mathbf{Compound } \mathbf{J}\_{\text{water}}} \text{ and } \text{LogP} = \log\_{10}(\text{Partition Coefficient}).$$

Log*P* = 1 can be explained as a ratio of 10 :1 organic:aqueous phase.

For ionizable solutes, the compounds may exist as a variety of different species in each phase at a given pH. D, typically used in the logarithmic for (lo*D*) representing the distribu‐ tion coefficient which is the appropriate descriptor for ionizable compounds since it is a measure of the pH-dependent differential solubility of all species in the octanol/water sys‐ tem (Levin, 1980).

$$\text{Distribution coefficient} \; D = \frac{\sum \text{Microspecies} \; \mathbf{J}\_{\text{studor}}}{\sum \text{Microspecies} \; \mathbf{J}\_{\text{unter}}}.$$

**Figure 5.** Predicted *versus* experimental values of *logLD50* (with a very high *RI > 0.75*) *%PPB* and loga

In figures 5 and 6, both models produce highly accurate results, while even better statistical characteristics are observed if only predictions of moderate and high reliability index are

In order to understand the behavior of drug compounds in the real world, Bhal et al. (2012) has used ACD/Predictors such as log*P*, log*D*, solubility, and pKa to evaluate and predict the likely behavior of 5-Methoxy-2-(1-piperidin-4-ylpropyl)pyridine (Fig. 7), a compound prior to its synthesis. Lipophilicity is represented by the descriptors log*P* (also known as Kow or Pow) and log*D*, and is used, for example, to help predict *in-vivo* permeability of active com‐ pounds in drug discovery and the behavior of compounds in many other areas of health re‐ lated research. The partition coefficient, P, is a measure of the differential solubility of a compound in two immiscible solvents and the most commonly used commonly used sol‐

dation set compounds (Bhal et al., 2012).

70 Current Topics in Public Health

vent system is octanol-1-ol/water.

**Figure 6.** Chemical structure of 5-Methoxy-2-(1-piperidin-4-ylpropyl)pyridine, A

considered.

HSA values for vali‐

Bhal (2012) used methylamine to illustrate the difference between these two descriptors as follows: MeNH3 + ⇌ MeNH2 + H+ , meaning that,

$$P\_{\text{MeN}\,H\_{2}} = \frac{\left[\text{MeNH}\_{3}\right]\_{\text{causal}}}{\left[\text{MeNH}\_{2}\right]\_{\text{water}}} \text{ and/or } P\_{\text{MeN}\,H\_{3}} = \frac{\left[\text{MeNH}\_{3}\right]\_{\text{causal}}}{\left[\text{MeNH}\_{3}\right]\_{\text{water}}} \text{. So, keeping the definition of D above in terms of the form: }$$

$$\text{mind, we can write the expression of D as:}\\D = \frac{\left[\text{MeNH}\_{2}\right]\_{\text{causal}} + \left[\text{MeNH}\_{3}\right]\_{\text{causal}}}{\left[\text{MeNH}\_{2}\right]\_{\text{causal}} + \left[\text{MeNH}\_{3}\right]\_{\text{causal}} + \left[\text{MeN}\right]\_{\text{causal}}}.$$

*MeN Hwater* + *MeN H*3

+ *water*

To accurately predict a compound's lipophilicity based on predicted molecular physical properties, it was imperative that the author applied the correct descriptor in an appropriate manner. In this context, log*D* instead is used in lieu of log*P* as the use of the latter to address lipophilicity concerns by drug research and manufacturing companies in the past (around 1980's and 90's) had resulted in incorrect conclusions for ionizable compounds. A good ex‐ ample would be to reproduce data generated by the previous author employing ACD/Log*D* in his application to discuss the significance of applying log*D* instead of log*P* using drug discovery as an example where lipophilicity is correlated with *in vivo* permeability. Using the sample molecule in figure 6 (5-Methoxy-2-(1-piperidin-4-ylpropyl)pyridine), data pre‐ sented in table were calculated.

**Table 2.** pKa values of 5-Methoxy-2-(1-piperidin-4-ylpropyl)pyridine (Bhal et al., 2012)

The pH dependence of log*D* for this sample molecule (5-Methoxy-2-(1-piperidin-4-ylprop‐ yl)pyridine) is shown in figure 7 showing a plot of log*D* versus pH, while figure 8 displays the changing ionic forms of molecule A.

Looking at the plot in figure 8, and according to Bhal el al. (2012), we can confirm that ioniza‐ tion of the compound greatly affects octanol-water partitioning and that lipophilicity cannot be simplified to a constant. This is very so as lipophilicity of the compound is low below pH 12 when the majority of the compound exists in an ionized form. This would definitively be contradictory, of course, if log*P* was examined alone (Predicted log*P* is 2.7 ± 0.3 by author for comparison sake).

Figure 9 shows a schematic representation of the changing pH environments that an orally administered compound is likely to encounter in the gastrointestinal (GI) tract. From fig‐ ure 9, we can observe that there is, thus, no constant pH in the body and it is therefore es‐ sential that we consider an appropriate pH when predicting the *in vivo* behavior of a drug

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73

**Figure 9.** The pH environment of the human gastrointestinal tract (Bhal et al., 2012)

approaches and adequate reporting of data (Bouwmeester et al., 2011).

**4. Implications of analytical methods and** *in-silico* **techniques in public**

The outcomes from a global network on the development of standardized analytical meth‐ ods for the public and environmental health directly impacts on the quality of health of mankind worldwide. High quality data necessitates the development of harmonized study

Priority public health scale can only be based on well-characterized dose-response relations derived from a systematic study of the bio-kinetics and bio-interactions of drugs or druglike molecules at both organism and (sub)-cellular levels using validated analytical methods and pharmacokinetic studies. The ADME (absorption, distribution, metabolism and excre‐ tion) and toxicity effects is crucial to declare a particular molecule safe for the treatment of a particular disease and often clinical trials to arrive at a conclusive release of a new drug very costly, sometimes in the range of millions of dollars covering the cost of fundamental re‐ search through clinical trials or testing to manufacturing. Multiple content databases, data mining and predictive modeling algorithms, visualization tools, and high-throughput dataanalysis solutions are being integrated to form systems-ADME/Tox (Ekins et al., 2005). More so, Ekins and co-authors (2005) reported that the functional interpretation and relevance of

candidate.

**health**

**Figure 7.** The logD curve of 5-Methoxy-2-(1-piperidin-4-ylpropyl)pyridine (ACD/LoD Suite), Bhal et al., 2012)

The author concludes that the negative values of log*D* (-1.44 to 0) in the physiologically rele‐ vant pH range (pH 1–8) lead us to conclude that this compound would be more susceptible to higher aqueous solubility and of lower lipophilicity in the body. As a result we would expect membrane permeability to be poor. Also, it is true as seen from graph in figure 8 the neutral form of molecule A is almost non-existent at physiologically relevant pH (1–8). This neutral form possibly dominates at ~pH 13. Conclusively, compound A is highly associated with the lipid phase (>30 fold affinity for octanol over water), and thus will likely permeate biological membranes spontaneously.

**Figure 8.** A graph illustrating the changing ionic forms of 5-Methoxy-2-(1-piperidin-4-ylpropyl)pyridine with pH (Bhal et al., 2012)

Figure 9 shows a schematic representation of the changing pH environments that an orally administered compound is likely to encounter in the gastrointestinal (GI) tract. From fig‐ ure 9, we can observe that there is, thus, no constant pH in the body and it is therefore es‐ sential that we consider an appropriate pH when predicting the *in vivo* behavior of a drug candidate.

**Figure 9.** The pH environment of the human gastrointestinal tract (Bhal et al., 2012)

be simplified to a constant. This is very so as lipophilicity of the compound is low below pH 12 when the majority of the compound exists in an ionized form. This would definitively be contradictory, of course, if log*P* was examined alone (Predicted log*P* is 2.7 ± 0.3 by author for

**Figure 7.** The logD curve of 5-Methoxy-2-(1-piperidin-4-ylpropyl)pyridine (ACD/LoD Suite), Bhal et al., 2012)

The author concludes that the negative values of log*D* (-1.44 to 0) in the physiologically rele‐ vant pH range (pH 1–8) lead us to conclude that this compound would be more susceptible to higher aqueous solubility and of lower lipophilicity in the body. As a result we would expect membrane permeability to be poor. Also, it is true as seen from graph in figure 8 the neutral form of molecule A is almost non-existent at physiologically relevant pH (1–8). This neutral form possibly dominates at ~pH 13. Conclusively, compound A is highly associated with the lipid phase (>30 fold affinity for octanol over water), and thus will likely permeate

**Figure 8.** A graph illustrating the changing ionic forms of 5-Methoxy-2-(1-piperidin-4-ylpropyl)pyridine with pH (Bhal

comparison sake).

72 Current Topics in Public Health

biological membranes spontaneously.

et al., 2012)

### **4. Implications of analytical methods and** *in-silico* **techniques in public health**

The outcomes from a global network on the development of standardized analytical meth‐ ods for the public and environmental health directly impacts on the quality of health of mankind worldwide. High quality data necessitates the development of harmonized study approaches and adequate reporting of data (Bouwmeester et al., 2011).