**Jing Xu**

Jing Xu obtained her BS and MS degrees from Hainan University. Since 2006, she has carried out doctoral research with Professor Huashi Guan at the College of Medicine and Pharmaceutics, Ocean University of China. Since 2007, she has continued doctoral research in the group of Prof. Peter Proksch and received her PhD degree in 2010 at Heinrich-Heine-Universitat D ¨ usseldorf, Germany, ¨ where she sparked an interest in mangrove microbial natural products with a particular focus on bioactive molecules, which has continued to this day. She joined the faculty of Hainan University after her graduation, where she is currently a Professor on Pharmaceutical Chemistry. She undertook a postdoctoral appointment at Nanjing University simultaneously, with Prof. Renxiang Tan, during 2011–2014. She spent 2016 working with Prof. Dr. Peter Leadley at the University of Cambridge as visiting scholar.


**3. Results**

All of the 556 water samples were analyzed by culture and, overall, 151 (27.1%) were positive for Legionella, of which 65 (43%) grew on only GVPC, 85 (56.3%) grew on both GVPC and BCYE, and one (0.7%) grew on only BCYE. (Table 1). The difference of the results obtained analyzing the samples by the two media was significant (McNemar's test, *p* < 0.0001).

**Table 1.** Recovery of *Legionella* by using buffered charcoal yeast extract (BCYE) and glycine, vancomycin, polymyxin B, cycloheximide (GVPC) media.

McNemar'stest *p*-value <0.0001.

The sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV) of GVPC vs. BCYE media are shown in Table 2. GVPC demonstrated a greater sensitivity and a good specificity as compared with BCYE medium. The Cohen's Kappa coefficient calculated on these data provided a value of 0.65, indicating a good quality of agreement (*p* < 0.0001) (Table 2).

**Table 2.** GVPC vs. BCYE sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), concordance, Kappa value, and *p*-value.

CI, confidence interval; PPV, positive predictive value; NPV, negative predictive value.

Considering the 85 samples that were positive on both GVPC and BCYE media, 11 samples showed fewer colony forming units per liter (CFU/L) on GVPC than on BCYE (Table 3). However, the differences of CFU/L found between the two media were never higher than 1 log (*p*-value = 0.0388).

**Table 3.** *Legionella* CFU/L range detected on samples positive on both BCYE and GVPC media.

Figure 1 shows the distribution of *L. pneumophila* serogroups and *Legionella* species found on GVPC and BCYE agar plates. *Legionella* species were detected in 19 samples by GVPC and in 13 samples by BCYE. Considering the range of the colony forming unit (CFU)/L detected, the data proved that, among the 65 samples positive on only GVPC, there were 51 samples (78.4%) showing a range between 50 and 1000, highlighting the high efficiency of GVPC in isolating low bacterial counts. The calculated medians of CFU/L detected on BCYE and GVPC plates were equal to 2500 (interquartile range = 5500) on BCYE and 1350 (interquartile range = 3950) on GVPC, and the difference between the two media was significant (*p*-value < 0.0001).

**Figure 1.** Distribution of *Legionella pneumophila* serogroups and *Legionella* species (BCYE n = 86 vs. GVPC n = 150).


**8. Conclusions**

In summary, tubular stress test assessment using the FST is a rediscovered and promising new tool to stratify risk in different kidney diseases. Multi-center, prospective studies with large enough sample sizes, applying standardized furosemide dosage and timing and comparing the FST to other novel plasma and urinary biomarkers are necessary to adequately validate results and define the possible clinical applications of the test.

**Supplementary Materials:** Supplementary materials can be found at http://www.mdpi.com/1422-0067/21/9/3086/ s1.

**Author Contributions:** Development of the idea: A.C. and J.B.-M. Writing—Review and Editing: C.A., J.R.S. and A.L.V. Supervision: A.C., E.B.-M. and J.B.-M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.


**7. Research tools**

We asked the participants to describe one major dilemma that had actually occurred during their work as counselors. Each of the 15 participants described a social or moral dilemma. We asked them what type of dilemmas they frequently coped with during the course of their work. Each of them selected one particular dilemma. We were particularly interested in their approach to solving the dilemma and the factors they took into consideration in solving it.

We categorized the strategies used in solving the dilemma into two groups. The more open, democratic group, for example, presented the dilemma for discussion to the class, listened to the student responses, asked them what they considered to be the best way to approach the problem, and considered their responses in implementing solutions. More conservative strategies simply told the students how they should behave, solving the problem for them.


**5. Results**

Tables 7–18 compare the error values (when the error value was smaller than 10−8, the corresponding value was considered optimal) obtained by the original algorithms (SHADE, L-SHADE, and jSO) and their improved versions using turning-based mutation (Tb-SHADE, TbL-SHADE and Tb-jSO, respectively). The results of a comparison are showed in the last column of each table. If the performance of the original version was significantly better, uses the "−" sign; if the performance of the improved version was significantly better, uses the sign "+"; if their performances were similar, "=" is used. The better performance values are displayed in bold, and the last row of these tables shows the results of an overall comparison. Tables 19–22 provide the error values obtained by the advanced algorithms DISH, jDE100 and j2020 on CEC2020. All tables provide the best, mean and std (standard deviation) values of 30 independent repetitions of the experiments.

**Table 7.** SHADE vs. Tb-SHADE on CEC2020 in 5*D*.

**Table 8.** SHADE vs. Tb-SHADE on CEC2020 in 10*D*.

**Table 9.** SHADE vs. Tb-SHADE on CEC2020 in 15*D*.

**Table 10.** SHADE vs. Tb-SHADE on CEC2020 in 20*D*.

**Table 11.** L-SHADE vs. TbL-SHADE on CEC2020 in 5*D*.

**Table 12.** L-SHADE vs. TbL-SHADE on CEC2020 in 10*D*.

**Table 13.** L-SHADE vs. TbL-SHADE on CEC2020 in 15*D*.

**Table 14.** L-SHADE vs. TbL-SHADE on CEC2020 in 20*D*.

**Table 15.** jSO vs. Tb-jSO on CEC2020 in 5*D*.

**Table 16.** jSO vs. Tb-jSO on CEC2020 in 10*D*.

**Table 17.** jSO vs. Tb-jSO on CEC2020 in 15*D*.

**Table 18.** jSO vs. Tb-jSO on CEC2020 in 20*D*.

**Table 19.** DISH and jDE100 on CEC2020 in 5*D*.

**Table 20.** DISH and jDE100 on CEC2020 in 10*D*.

**Table 21.** DISH and jDE100 on CEC2020 in 15*D*.

**Table 22.** DISH and jDE100 on CEC2020 in 20*D*.

Convergence diagrams are shown in Figures 1–12. Figures 1–4 shows the convergence curves of SHADE and Tb-SHADE, respectively, for some test functions in 5*D*, 10*D*, 15*D*, and 20*D*, Figures 5–8 shows those of L-SHADE and TbL-SHADE for some test functions in 5*D*, 10*D*, 15*D*, and 20*D*. and Figures 9–12 shows those of the jSO and Tb-jSO, respectively, for some test functions in 5*D*, 10*D*, 15*D* and 20*D*. It is apparent that the red line of the turning-based mutation version of the algorithm was often slower to converge but attained better objective function values.

**Figure 1.** The selected average convergence of SHADE and Tb-SHADE on CEC2020 in 5*D* is compared. From left to right f3, f9 and f10.

**Figure 2.** The selected average convergence of SHADE and Tb-SHADE is compared on CEC2020 in 10*D*. From left to right f8, f9 and f10.

**Figure 3.** The selected average convergence of SHADE and Tb-SHADE is compared on CEC2020 in 15*D*. From left to right f8, f9 and f10.

**Figure 4.** The selected average convergence of SHADE and Tb-SHADE is compared on CEC2020 in 20*D*. From left to right f3, f5 and f9.

**Figure 5.** The selected average convergence of L-SHADE and TbL-SHADE is compared on CEC2020 in 5*D*. From left to right f3, f4 and f10.

**Figure 6.** The selected average convergence of L-SHADE and TbL-SHADE is compared on CEC2020 in 10*D*. From left to right f8, f9 and f10.

**Figure 7.** The selected average convergence of L-SHADE and TbL-SHADE is compared on CEC2020 in 15*D*. From left to right f8, f9 and f10.

**Figure 8.** The selected average convergence of L-SHADE and TbL-SHADE is compared on CEC2020 in 20*D*. From left to right f3, f5 and f9.

**Figure 9.** The selected average convergence of jSO and Tb-jSO is compared on CEC2020 in 5*D*. From left to right f3, f4 and f10.

**Figure 10.** The selected average convergence of jSO and Tb-jSO is compared on CEC2020 in 10*D*. From left to right f3, f8 and f9.

**Figure 11.** The selected average convergence of jSO and Tb-jSO is compared on CEC2020 in 15*D*. From left to right f3, f8 and f9.

**Figure 12.** The selected average convergence of jSO and Tb-jSO is compared on CEC2020 in 20*D*. From left to right f3, f4 and f10.

Tables 23–34 shows the number of runs (#runs) of population aggregation, the average generation (Mean CO) of the first cluster during these runs, and the average population diversity (Mean PD) of these generations.

**Table 23.** Clustering and population diversity of SHADE and Tb-SHADE on the CEC2020 in 5*D*.

**Table 24.** Clustering and population diversity of SHADE and Tb-SHADE on the CEC2020 in 10*D*.

**Table 25.** Clustering and population diversity of SHADE and Tb-SHADE on the CEC2020 in 15*D*.

**Table 26.** Clustering and population diversity of SHADE and Tb-SHADE on the CEC2020 in 20*D*.

**Table 27.** Clustering and population diversity of L-SHADE and TbL-SHADE on the CEC2020 in 5*D*.

**Table 28.** Clustering and population diversity of L-SHADE and TbL-SHADE on the CEC2020 in 10*D*.

**Table 29.** Clustering and population diversity of L-SHADE and TbL-SHADE on the CEC2020 in 15*D*.

**Table 30.** Clustering and population diversity of L-SHADE and TbL-SHADE on the CEC2020 in 20*D*.

**Table 31.** Clustering and population diversity of jSO and Tb-jSO on the CEC2020 in 5*D*.

**Table 32.** Clustering and population diversity of jSO and Tb-jSO on the CEC2020 in 10*D*.

**Table 33.** Clustering and population diversity of jSO and Tb-jSO on the CEC2020 in 15*D*.

**Table 34.** Clustering and population diversity of jSO and Tb-jSO on the CEC2020 in 20*D*.

The rankings of the Friedman test [52] were obtained by using the average value (Mean) of each algorithm on all 10 test functions in Tables 7–22, and are shown in Tables 35–38. The related statistical

values of the Friedman test are shown in Table 39. If the chi-square statistic was greater than the critical value, the null hypothesis was rejected. *p* represents the probability of the null hypothesis obtaining. The null hypothesis here was that there is no significant difference in performance among the nine algorithms considered here on CEC2020.

**Table 35.** The Friedman ranks of comparative algorithms on CEC2020 in 5*D*.

**Table 36.** The Friedman ranks of comparative algorithms on CEC2020 in 10*D*.

**Table 37.** The Friedman ranks of comparative algorithms on CEC2020 in 15*D*.

**Table 38.** The Friedman ranks of comparative algorithms on CEC2020 in 20*D*.

**Table 39.** Related statistical values obtained of Friedman test for α = 0.05.

#### **6. Results and Discussion**

The results on the CEC2020 benchmark sets are first discussed. As shown in Tables 7–18, the scores were two improvements against two instances of worsening (5*D*), four improvements and two instances of worsening (10*D*), five improvements and two instances of worsening (15*D*), and four improvements no instances of worsening (20*D*) in the case of SHADE; three improvements against zero instances of worsening (5*D*), four improvements and one worsening (10*D*), six improvements no worsening (15*D*), and five improvements and no worsening (20*D*) in the case of L-SHADE; and one improvement against no worsening (5*D*), four improvements and one worsening (10*D*), four improvements and one worsening (15*D*), and two improvements two instances of worsening (20*D*) in the case of jSO. In some test functions, the improved algorithm even escaped the local optimum and found the optimal value (if the error was smaller than 10−8, the relevant value was considered optimal). Examples are f3 in Tables 10 and 13, and Table 14, f8 in Tables 9, 13 and 16, and Table 17, f9 in Table 12, and f10 in Table 11. In most cases, the improved version was clearly better than the original algorithm except for Tb-SHADE (5*D*) and Tb-jSO (20*D*).

According to the convergence curves in Figures 1–12, in most cases, the improved algorithm showed similar convergence to the original in the early stage of the optimization process, but it clearly maintained a longer exploration phase and achieved better values of the objective function in the middle and late stages; in a few cases (such as *f* 4 in Figure 5), the improved algorithm had slower convergence but did not achieve a better objective function value than the original.

As the numerical analyses in Tables 23–34 show, in most cases, the improved algorithms exhibited fewer clusters (#runs), later clustering (mean CO), and higher population density (mean PD) than the original algorithm. But Tb-SHADE (5*D*) had a lower population density on *f* 6–*f* 9, as did TbL-SHADE (all dimensions) on *f* 2–*f* 7, where this might have been related to the linear decrease in the population size. Tb-jSO showed similar numbers of clusters in all dimensions and a lower population density on some test functions in 5*D*. Therefore, in most cases, the improved versions maintained the diversity of population and a longer exploration phase in the optimization process.

The significant improvements in Tables 7–18 and the clustering analysis in Tables 23 and 24 can be linked. The results in the former set of tables with the "+" symbol were always connected with the occurrence of later clustering, none at all, or fewer instances of clusters of 30 (for the last option, see, for example, column #runs in Tables 24–26, *f* 3). Consequently, the improvement in the performance effected by the updated version was related to the maintenance of population diversity and a longer exploration phase.

According to the Friedman ranking in Tables 35–38, Tb-SHADE, TbL-SHADE, and Tb-jSO were clearly better than the original algorithms and the advanced DISH and jDE100 in 10*D*, 15*D,* and 20*D*. But Tb-SHADE did not perform as well as SHADE in 5*D* and did not perform as well as DISH in 5*D*, 10*D* and 20*D*. In addition, the j2020 algorithm delivered the best performance and ranked first in 10*D*, 15*D* and 20*D* and one of the improved versions, TbL-SHADE, only delivered the best performance and ranked first in 5*D*. And jDE100 (winner of CEC2019), which ranks last in Tables 35–38, did not seem suitable for CEC2020. Table 39 shows that the null hypothesis was rejected in all dimensions, and thus the Friedman ranking was correct. All in all, the three improved algorithms obtained good optimization results in contrast to the original algorithm as well as the advanced DISH and jDE100 algorithms but were slightly worse than the advanced j2020 algorithm.


Demographic Analysis and the Decomposition of Social Change

*Parfait Eloundou-Enyegue, Sarah Giroux and Michel Tenikue*

#### **Abstract**

Social science has made great strides over the last half-century, with some of the most significant gains made in micro-level studies. However, analysts interested in broad societal change will not be satisfied with this micro-level detail alone. They will find the detail useful, but they still need to convert the micro-level relations into macro-level outcomes. Decomposition methods rooted in demography can help in those situations. This chapter discusses how these decomposition methods can build on other methods traditionally used in the social sciences. It specifies the kind of problems that are well suited for decomposition analysis, and it briefly reviews three basic types of decomposition approaches (demographic, regression, and mathematical). We illustrate, using mortality data as an example, and conclude with some suggestions for how this method might more broadly advance macrosocial research.

**Keywords:** decomposition, demographic methods, social change, secondary data, sustainable development

#### **1. Introduction**

Social science has made great strides over the last half-century, with some of the most significant gains made in micro-level studies. With advances in computing and communication technology, researchers can now collect, share, and process statistical data on millions of households and individuals. The combination of increased computing power and the expanded availability, size, and complexity of social science datasets has resulted in a "data gold rush," with the gold digging powerfully aided by remarkable advances in novel statistical methods [1]. With these methods, researchers can now explore in great detail the mix of factors shaping individual behaviors.

These methods can offer powerful insights into individual behavior. Yet, scientists and planners are primarily interested in societal rather than individual outcomes. For example, rather than how individual characteristics –such as education level– shape an individual's likelihood of smoking, we might also want to see the big picture: how would an educational expansion at the national level shape changes in smoking rates? While the former, microlevel question can be robustly addressed with existing micro-regressions, the latter cannot. This is unfortunate when the interest is in national-level outcomes.

Answering such societal questions is tricky on two fronts. First, as Robinson [2] argued 70 years ago, is the risk of ecological fallacy when one draws macro-level conclusions from micro-level analyses, or vice-versa. Thus, a researcher may find

highly educated individuals to be less likely to smoke, but it does not follow that highly educated *countries* will necessarily have lower smoking rates. Second, the same regression methods cannot robustly apply to countries as units of analysis. Even if we had adequate data for every country in the world (an optimistic scenario), we would still have a relatively small sample of about 200 cases. Such a small sample cannot support robust statistical analyses, especially if one begins to consider many covariates [3, 4]. Despite being widely used in development economics in the 1990s, cross-country regressions have fallen out of favor. Yet, the broad questions about societal transformations remain.

Researchers thus need alternative approaches to link micro-data and macroissues, building on the detail and robustness of microlevel statistics as they aggregate them to inform macro-level questions. Decomposition methods, a broad set of tools that emerged from the field of demography, present a useful set of options [5–11]. Researchers interested in studying social transformations (spontaneous or induced changes in the structure or performance of a large community or state) can leverage various decomposition approaches to examine issues where the unit of analysis is not the individual but the community.

These methods can be used when the study outcome meets three critical criteria; namely, it is 1) quantifiable, 2) aggregate, and 3) the result of a gradual change. A *quantifiable* outcome is one that can be captured as an absolute number, a percentage, a ratio, or an average. This is the case for outcomes such as rates of smoking or marriage, or average incomes. Second, the phenomenon studied must reflect an *aggregation of individual behaviors*, rather than being an intrinsic/indivisible feature of an entire society. Thus, an outcome such as a country's migration laws (an intrinsic feature with no micro-level correlate) would be excluded. However, one could very well study migration rates among different groups since this is an aggregated measure of individual behaviors. Last, the outcome must be a phenomenon that *changes gradually over time*- such as changes in the ratio of male to female wages. These methods are not suited to sudden changes or rare events (i.e., deaths from Hurricane Katrina) but rather to processes that unfold gradually.

#### **1.1 Limitations and advantages of decomposition methods**

Decomposition methods are accounting tools. Thus, while excellent at describing the processes, sectors, or groups driving change, they say little about causation. Thus, in examining changes in smoking rates, decomposition methods could reveal the extent to which different education groups (i.e., no schooling, primary, secondary, higher) contributed to declines in smoking rates. Still, they cannot say *why* education caused smoking rates to change. This is a sizable shortcoming, as causal understanding remains the holy grail for scholars and policymakers seeking to develop better-informed theory and policy. However, understanding the proximate drivers of change is still a useful guide in policy development.

Additionally, decomposition methods have four key advantages over other forms of data analysis: they are 1) easy to interpret; 2) transparent; 3) compatible with other research methods, and 4) efficient. The findings from decomposition methods are easily applied and interpreted because they use basic analyses that do not rely on complex statistics or software. For instance, one standard output from decomposition is to show the percentage of social change accounted for by a given process or group. Such an output (a percentage) is easily digestible compared to outputs from regression analyses such as beta coefficients or odds ratios. The method is transparent because the results of a decomposition analysis are easy to replicate, and the accuracy of the results is easy to check: the sum of all groups' contributions is 100%. The efficiency of decomposition methods reflects its

#### *Demographic Analysis and the Decomposition of Social Change DOI: http://dx.doi.org/10.5772/intechopen.96350*

flexibility and the tradeoff between data requirement, analytical technicity, and the type of findings. Its basic forms can be modified and support more complex combinations to suit the researcher's individual needs. Also, decomposition methods are not very data intensive. In the field of global development, for instance, one can conduct insightful decomposition analyses by relying on tabulations and data sources that are widely available online.

As the examples in this contribution will show, the method and results are quite transparent. First, the input data and sources can be easily checked online by other scholars. Second, unlike multivariate statistics, where results can vary heavily depending on the model specification and individual coding details, decomposition results do not depend on the vagaries of individual modeling choices. Finally, the output from complex regression analysis often seems to be spewed from an impenetrable black box, and it must be taken at face value, with the reader often unable to detect an odd result from, say, a programming mistake. Such is not the case with decomposition: the decomposition findings are presented in a way that allows the reader to immediately assess the internal coherence, credibility, and accuracy of the results.

A third strength is that the decomposition approach can be leveraged and combined with other methods of analysis. In our previous work, we combined a micro-level regression examining the associations between the number of siblings a child has and their educational outcomes, with a decomposition analysis [12]. By combining these two approaches, one can aggregate the robust micro-level findings and answer the macro-level question of how fertility transitions (a country level phenomenon) impact educational attainment at the national level. This integration of methods bypassed the standard limitations of cross-country regression, while also drawing upon the robust micro-level regression findings. The decomposition method is also compatible with many other methods, including qualitative analysis. By quantifying the key behavioral and compositional changes and stratifying across groups and processes, decomposition methods can serve to direct the qualitative research. Essentially, this series of methods does not replace or compete with other methods but, rather, it complements them and expands our toolkit in innovative ways.

Last but not least, decomposition methods efficiently leverage existing information. While some parts of the world are indeed experiencing a "data gold rush," researchers and policymakers in many parts of the global South often operate with a paucity of data [1, 13]. Despite recommendations by the International Monetary Fund's (IMF) General Data Dissemination System (GDDS) that countries conduct censuses every ten years, 66 countries currently fail to meet the standard [14]. Many researchers in these settings turn to publicly available nationally representative living standards (e.g., the Living Standards Measurement Surveys) or health surveys (e.g., the Demographic Health Surveys or Multiple Indicator Cluster Surveys). These sources can generate robust micro-level data, but they do not occur at regular intervals and are spotty or unavailable for numerous countries. For instance, from 2002 to 2011, 57 countries had either zero or a single poverty estimate [15]. Thus, decomposition methods are an ideal tool that allows scholars to leverage limited data in creative ways.

#### **2. Decomposition basic types**

Decomposition is not a single method but a set of related methods. It is used across different fields, but its variants are insufficiently integrated. Most researchers know only the variants that directly apply to their issues of interest, such as life expectancy [8, 16], job discrimination [6, 17], and poverty or inequality [18, 19]. Yet all these variants can fit into the general taxonomy presented here. Their commonality is in using accounting-based approaches to describe patterns of change. However, they vary in the functional relationship between independent and dependent variables, as shown in **Table 1**.

For each of these relationships, decomposition analysis allows us to examine how a change in the dependent variable is driven by changes in each independent variable (reflecting a group or a process).

### **2.1 Demographic decomposition**

In a demographic decomposition, the main accounting question is about the contribution of 'composition' or group-specific size versus 'group-specific behavior.' Thus, a researcher might be interested in documenting how much the change in the national rate of smoking between 2000 and 2020 was driven by changes in the distribution of the national population across different education levels

*X indicates the independent variable.*

*Y indicates dependent variable for the entire country.*

*w refers to the demographic weight of an individual subgroup.*

t *= time;*

*Δ = indicates the historical change.*

α *= intercept or baseline value.*

β *= the marginal change in Y associated with a one-unit change in X.*

e *= error term.*

#### **Table 1.**

*Three basic types of relationships in Decomposition1 .* *Demographic Analysis and the Decomposition of Social Change DOI: http://dx.doi.org/10.5772/intechopen.96350*

(compositional effect) versus changes in the smoking rates of each education group (behavioral effect).

Formally, the national rate of smoking rate (Y) is expressed as a weighted average (by wj ) of smoking rates in subpopulations groups defined by educational categories (yj).

$$\mathbf{Y}\_t = \sum \mathbf{w}\_{jt} \* \mathbf{y}\_{jt} \tag{1}$$

In this formula, a national change in the smoking rate can be broken down into two components:

$$
\Delta Y = \begin{array}{c|c}
\Sigma \overline{\mathbf{y}}\_f \ast \Delta \mathbf{w}\_f + \Sigma \,\overline{\mathbf{w}}\_f \ast \Delta \mathbf{y}\_f \\
\hline \parallel \\
\hline \vphantom{\begin{array}{c}
\text{Compposition} \\
\text{effect}
\end{array}}
\end{array}
\begin{array}{c|c}
\Delta \mathbf{y}\_f \\
\hline \parallel \\
\hline \end{array}
\tag{2}
$$

Formula (2) thus allows the analyst to apportion change into two conceptually compelling components- the compositional (P*yj* ∗Δ*wj*Þ and behavioral ( P*wj* ∗Δ*yj* Þ effect. The compositional effect is change that is driven by changes in the relative size of each subgroup. The compositional changes are relatively mechanical, as they simply reflect a change in how much each subpopulation is weighted when calculating the national average. The second component of change reflects changes in the behaviors of each subgroup. While the decomposition does not highlight the reasons for change, it does allow the researcher to understand how much of a total change is driven by a meaningful shift in group-specific behavior.

#### **2.2 Regression decomposition**

Simple regression analysis tends to model an outcome (Y) as a function of a baseline outcome or intercept (α), a regression coefficient (β), and the value of a predictor variable (X). For instance, one may predict the performance of a well-trained athlete (Y) by knowing the basic performance of a 'couch-potato' who has never set foot in a gym (α) and the payoff from each hour of being at the gym (β) multiplied by the number of hours one spends at the gym (X). In that case, if you randomly picked two people in the world, say one from Senegal and the other from Turkey, the difference in their athletic performance (ΔY) can entirely be explained by three factors including:

Similarly, a researcher might use a regression decomposition to document how much of the variation in men and women earnings was driven either by the differences in education levels or by the differences in returns to education, suggesting that the gap is driven by discrimination processes. In other words, the researcher would like to know the contribution of (1) the male-female difference in the average level of education, (2) the male-female difference in return to education to male–female wage differences, and (3) the differences in baseline wages between men and women. These three possibilities are explored below. The formal analysis consists of writing the earning equations for males (m) and females (f) and then taking the difference between these two equations.

$$\mathbf{Y\_m} = \alpha\_\mathbf{m} + \beta\_\mathbf{m} \mathbf{X\_m} \tag{3}$$

$$\mathbf{Y\_{f}} = \mathbf{a\_{f}} + \mathfrak{B\_{f}X\_{f}} \tag{4}$$

The decomposition seeks to explain the difference in wages based on the change in the various parameters of the regression equation. This change is expressed as follows

ð5Þ

In Eq. (5), the term with upper bar represents the average *x* ¼ *xm*þ*x f* 2*:*

Eq. (5) expresses how much of the pay gap is driven by differences in base salaries (Δα) versus differences in the levels of schooling (ΔX) and differences in return to education (Δβ).

Note that the same procedure can apply to both cross-sectional analysis (the difference between two groups in a given year) and longitudinal analysis (the change experienced by one group between years). The approach is the same; only the interpretations differ.

#### **2.3 Mathematical decomposition**

In some cases, an outcome of interest is a function of a set of other variables. For instance, a country's GDP per capita (Y) is measured as the size of the economy divided by the total population. Thus, change in GDP (ΔY) between two time periods can be decomposed into two pieces-the amount of change driven by the growth or contraction in the economy (ΔG) and the change in the total population size (ΔP) or precisely change in the inverse of the population (Δ(1/P)).

$$Y = \mathbb{G}\!/\!/\!/ \text{ is differentiated as}$$

$$\Delta Y = \left(\overline{\mathbf{G}} \* \Delta(\mathbf{1}/P)\right) + \left(\left(\overline{\mathbf{1}/P}\right) \* \Delta G\right) \tag{6}$$

This first decomposition is not very informative. However, one can transform the initial equation into a formula that is slightly longer but conceptually richer:

$$Y = \frac{G}{P} = \frac{G}{A} \ast \frac{A}{P} \text{ where A is the working-age population.}$$

With this transformation, G/A represents the economic productivity of the adult population (or π). This is a conceptually important factor in theories of economic growth. The same is true for the new term A/P (or α), which reflects the ratio of the working-age population to the total population, a core variable in the analysis of demographic dividends. Thus, we now have two theoretically interesting variables (π and α) and can decompose national income in terms of these two variables.

*Demographic Analysis and the Decomposition of Social Change DOI: http://dx.doi.org/10.5772/intechopen.96350*

$$
\Delta Y = (\overline{\pi} \ast \Delta a) + (\overline{a} \ast \Delta \pi) \tag{7}
$$

Now, any historical change in GDP (ΔY) can be decomposed into the change in productivity (π) versus the change in the share of the working population (α).

#### **3. Demographic decomposition: a deeper dive**

While offering readers a review of different decomposition approaches, we wanted to focus in some detail on demographic decomposition. As noted above, demographic decomposition applies to national outcomes (Y) that are an aggregated result of the outcomes of several subpopulations (yj), each weighted by its relative size (wj). Formally:

$$Y\_t = \sum w\_{\text{jt}} \* \mathcal{Y}\_{\text{jt}} \tag{8}$$

For example, the mortality rate of a country (*Yt*) is the weighted average of rates (*wjt*) in different regions or socioeconomic groups. In this formulation, Y, the dependent variable, is quantifiable and the independent variable X is measured nominally and captured by a set of categories (j). For the demographic decomposition to work, the independent variable must meet four critical criteria: *exhaustiveness*, *distribution*, *variability,* and *relevance*.

Exhaustiveness simply means that each member of the population belongs to one, and only one, of the categories within the independent variable. The set of categories must cover the entire population, and the categories have to be mutually exclusive. Distribution refers to the concept that the number of categories cannot be too few (>2) nor too many. If there are too few categories, as in a variable like a dichotomy, the analysis will not be detailed enough to be informative. Yet, with too many categories (i.e., age in single years), the data will end up spread too thinly.

It is also crucial that the independent variable change over time, i.e., the size of the individual categories comprising the independent variable (the wj ) must fluctuate over time. Without such variation, the compositional effect in the decomposition analysis will always remain zero. Because of this, an independent variable like gender is often not ideal, as sex-ratios in a national population rarely change dramatically over time. Similarly, annual income with set threshold cut-offs (i.e., less than \$20,000; \$20,000–\$40,000; \$40,000- \$60,000; more than \$60,000) could be appropriate, but income quartiles would not, since, by definition, there is no change in the size of each quartile over time.

Lastly, a good independent classification variable should be conceptually relevant to the outcome of interest. Thus, for many phenomena, a strong classification variable might be "region of country" if there has been 1) changes in the size of the population within each region and 2) variation in the Y variable by region. This would be especially appropriate if the variation in Y reflects a scenario where programs and policies are designed at the regional level.

#### **3.1 Two patterns of change: a visual representation**

Demographic decomposition allows the analyst to document how much of a particular change is driven by 1) changes in the behavior of different social groups vs. 2) changes in the demographic size of these social groups.

Both compositional and behavioral factors can drive a range of important changes in national social, economic, and health outcomes. **Figure 1** below

#### **Figure 1.**

*Patterns of change: Vertical versus horizontal convergence in infant mortality.*

illustrates a basic decomposition using the example of infant mortality. This topic is especially relevant for sub-Saharan African policymakers working to achieve Target 3.2 of the Sustainable Development Goals (SDGs), aiming to reduce the levels of child mortality to no more than 25 deaths per 1,000 live births by 2030 [20]. In 2019, Sub-Saharan Africa had the highest neonatal mortality rate at 27 deaths per 1,000 live births [21].  However, this fact masks considerable variation within African countries, including severe differences by parental wealth and maternal education [22]. Having a better understanding of the internal variation in these trends can be critical for developing effective policies.

**Figure 1** provides a visual description of how the same national-level change can stem from very different subnational patterns. On the left-hand side of **Figure 1** (Frame A: Macro-Level Change) are five squares that represent the trend in child mortality for the country as a whole, with darker colors indicating lower levels of mortality. The chart shows a steady regression at the national level from lower levels of child mortality (the white square on the far left) to higher mortality levels (the black square on the far right). Given these trends, one crucial question is how this evolution occurred, specifically, how various socioeconomic classes contributed to it.

On the right side of the diagram (Frame B) are two possible, and fundamentally opposite, scenarios of how this change can unfold. The first, (B1), highlight a case of horizontal change, where the child mortality rates decline at the same rate for all income groups. Conversely, in Frame B2, we see a vertical change, with the mortality declines beginning with the country's highest income group before gradually spreading to the rest. In year 2, it was only the highest SES group that was

experiencing any decline in child mortality—the other income groups remained unchanged. If we were to ask about the groups that drive the change, we would get different answers from the two scenarios: in the first case, all groups evolved simultaneously, while in the second case, the change occurred first in the higher SES groups. Understanding how this national trend unfolds has key implications for resource allocation and policy targeting.

### **3.2 Compositional vs. behavioral change**

The example above shows how the same national-level change in mortality can emerge from a single group (i.e., entirely driven by mortality declines among the highest SES group) or be something that occurs as the result of a widespread change throughout the population (i.e., all groups experience a decline, but the declines are quantitatively smaller for each group). However, a full decomposition allows the analyst to identify the groups driving the change (referred to here as the compositional effect) and *also* consider how changes in the behavior of each group mattered (referred to here as the behavioral effect).

**Figure 2** presents a hypothetical case where a researcher is trying to understand changes in average monthly income. The figure's left portion shows Time 1, where the average monthly income for all individuals is \$142.50. The classification variable is economic class, ranging from richest to poorest1 , and income is the weighted average of incomes across all of the economic classes making up the national population. On the right-hand side of the figure are two different scenarios, with the average monthly income rising to \$159.20 in both cases. Yet while the two scenarios reflect an identical aggregate change, they are qualitatively quite different.

In scenario 1, the average income of each economic group remains exactly the same between time 1 and time 2. The only factor that changes is the percentage of the population in each economic class. The percentage of the population in the second-highest economic group rose from 15% to 20%, while the poor's share of the population declined. Thus, the change in scenario one is entirely *compositional*. No individual group became richer, but more individuals moved to higher economic classes. Conversely, in scenario 2, we see the same aggregate gains but no

#### **Figure 2.** *Decomposing change in child mortality, Cameroon 1991–2011.*

1 For this example, these are not quintiles but based on dollar cutoff values that remain the same between time one and time two.

compositional change. Instead, all of the gains are driven by an increase in the average income among some groups. The wealthiest group became even richer, jumping from \$350 in year 1 to \$400 in year 2.

This example presents an extreme contract, where social change entirely (100%) stems from a change in either composition (Scenario 1) or behavior (Scenario 2). While useful for pedological purposes, it's perhaps unsurprising that reality is usually less extreme. In most cases, change is driven by some combination of the two effects. For example, compositional change might explain 30% of the change, while behavior accounts for the rest. Demographic decomposition allows the analyst to piece apart these different drivers of change (**Figure 3**).

#### **3.3 Demographic decomposition: the mathematical formulation**

In this first case, we focus on a national average; Y will be expressed as a weighted average (by wj ) of the values of individual subpopulations (yj).

$$\mathbf{Y}\_t = \sum \mathbf{w}\_{\mathbf{j}t} \* \mathbf{y}\_{\mathbf{j}t} \tag{9}$$

In this formula, a national change can be broken down into two components:

$$
\Delta \mathbf{Y} = \sum \overline{\mathbf{y}}\_{\text{j}} \* \Delta w\_{\text{j}} + \sum \overline{w}\_{\text{j}} \* \Delta \mathbf{y}\_{\text{j}} \tag{10}
$$

As noted above, decomposition methods apportion change into two key components. The compositional effect captures the amount of change driven by changes in each population subgroup's relative size. As seen in the last example, national income may go up simply because the number of individuals in the highest economic class increases, thus increasing the group's demographic weight. Conversely, the behavioral effect captures change that was driven by an actual change in the group's behavior. In our last example, this was reflected by actual gains in income among the lowest economic groups.

**Figure 3.** *Compositional vs. behavioral change: An extreme case.*

*Demographic Analysis and the Decomposition of Social Change DOI: http://dx.doi.org/10.5772/intechopen.96350*

In the case of child mortality, declines can similarly be driven by compositional and behavioral effects. Mortality declines could result from an economic contraction whereby the relative size of the lower economic groups, already characterized by higher mortality levels, expands (i.e., their population weight, *w*, increases). This would reflect a compositionally driven change. Conversely, change can also be driven by changes in the behavior of groups. If one subgroup's mortality levels increase, all else equal, the national mortality will increase. Thus, mortality reversals can also be driven by behavioral change. The researcher's task is to identify how much of the change is driven by each component.

#### **3.4 Key steps**

Regardless of the topic, a researcher using demographic decomposition needs to attend to four key tasks, as follows:

For our example, the analyst is trying to understand the extent to which changes in the composition of the population (here, changes in the relative size of each economic class) versus behavioral changes of economic groups (here, changes in the mean mortality rate of each economic group) drove the declining rates of infant mortality in Cameroon.

Column 1 highlights the social class categories used (Highest, Second Highest, Average, Second Lowest, Lowest). Columns 2–5 are where the analyst must insert their data (gathered elsewhere) on group size (*wjt*) and behavior (*yjt*). The spreadsheet is built to then calculate the national average for each year, here 143.6 in 1991 to 117.7 in 2011. The resulting difference reflects a decline in infant mortality of 25.9.

The last step is then to explain this 25.9 unit decline, using formula 10. As reflected in Column 6, the researcher can see that 17% of the decline was driven by compositional change. This is unsurprising, as the class composition of the population changed slightly during this period. The proportion of children living in low-income families declined (from 18% to 15%) while there was a slight rise in the proportion of children living in rich families (19 to 21%). As poorer families exhibit higher infant mortality rates, mortality rates will mechanically go down if their representation in the population shrinks. Column 7 displays the amount of change due to behavioral changes, which was the larger contributor to change, at 83%. A glance at Columns 2 and 5 (showing mortality rates by economic class in 1991 and 2011) confirms that mortality rates did indeed decline across all social classes during this period, including the poorest.

4.*Presentation of findings.* **Figure 2** is easily presentable to most scientific audiences, requiring little explanation. Moreover, the researcher can not only highlight the leading processes- i.e., how much of the change was driven by compositional (Column 6) vs. behavioral (Column 7) forces- but can also explore leading groups. The percentages in column 9 are simply the result of adding the behavioral and compositional contributions of each socioeconomic class and dividing by the total change. The second-lowest economic group's contribution was the largest, with the total change equal to the sum of its composition effects (4.85) and behavior (5.79) for a total of 10.65, or 41% of the total change. The lowest economic group made the next largest contribution to the mortality decline (37%), followed by the second highest (16%), average (3%), and highest (3%) groups.

As is evident from **Figure 2**, the sum of all contributions in a decomposition reflects the total change- thus, the values in columns 6 and 7 sum to 25.9, the total decline in mortality. As a percentage, the sum of all contributions must equal 100%. One important note is that some contributions can be negative (less than 0%) or greater than 100%. Conceptually, a negative value reflects a contribution that worked in the opposite direction of the observed change. In our case, a negative percentage would reflect a change in either the composition or behavior of a group that worked to increase mortality. Percentages larger than 100% signal that the overall change would have been even greater, if it was not hampered by the effects of opposite influences from other groups.

While relatively easy to digest, decomposition findings are easy to present to nontechnical audiences as a graph rather than a table. Pie charts, such as the one on the left side of **Figure 2**, can cleanly show how much of the total change was driven by compositional vs. behavioral factors. Similarly, stacked histograms can efficiently summarize the results and identify the dominant social groups driving change.

#### **4. Policy implications**

Even if decomposition is not a causal method, it can guide policy. For instance, if a planner observes that much of recent national change is derived from

#### *Demographic Analysis and the Decomposition of Social Change DOI: http://dx.doi.org/10.5772/intechopen.96350*

compositional changes, then s/he gains insights into future changes. In a country where education levels are rising, having a positive compositional effect (having more educated people leads to progress), then one can anticipate further gains if national levels of education continue to grow. Likewise, if child mortality is declining mostly via a compositional effect (fewer high-parity births), then one expects child mortality to continue to decline if fertility does. In some cases, the planner may have reason to expect the composition changes to continue largely on their own, as is the case of mortality, educational, fertility transitions. In some instances, s/he must proactively induce compositional change through policy.

If mortality is driven by a behavioral effect, the appropriate response is to target either the leading group or the lagging group. One would target the leading groups if one is not worried about inequalities and one does not expect further growth in this top group to be curtailed by a ceiling effect. One has further justification for investing in this leading group if one expects the example set by this vanguard group to trickle down and promote change among the following groups. Some development theorists might argue that in the early stages of development, it can make sense to build up some pioneers who would set the pace and pull the rest of the population [23]. On the other hand, one may favor the lagging group if one assumes that leading already has a momentum on their own and will continue to progress even if unaided. One may further favor the lagging groups out of concern for inequality.

This application of decomposition to policy requires a nuanced theoretical understanding of processes of change and the diffusion of innovations in the general population. In diffusion theory, change may accelerate among the lagging groups after reaching a critical mass in preceding groups [24, 25]. In other ways, change proceeds in a domino pattern and, to the extent that decomposition analysis helps identify the next group in that domino line, it can speed the process.

### **5. Conclusion**

Students of social change need robust methods to inform policy reliably. With the significant advances in data and computing technology achieved over the last forty years, they are in a better position to study micro-level processes, including the causes of individual behavior. However, this microlevel expertise is not sufficient to account for social change, where the focus is on aggregate (not individual) outcomes. Applying the existing micro-methods methods to understand aggregate social problems amounts to "barking up the wrong tree" or—to stay with this canine metaphor- "letting the methodological tail wag the dog." Decomposition methods can help address this micro–macro conundrum by making it possible to aggregate evidence from smaller units to understand the big picture.

Given that the big picture, rather than individual-level detail, is the focus of most socioeconomic planning, decomposition methods are quite relevant to policy. The methods are ideal for studying many of the social transformations underway across the globe. In particular, they can inform the study of critical components in the United Nations' Sustainable Development Goals (SDG), including poverty, health, inequality, and schooling. Many countries are working hard to achieve these goals face with severely limited data and resources. A fuller understanding of the drivers of socioeconomic change and the unevenness of change in these rapidly changing and diverse societies can allow policymakers to target policies more effectively. To this end, decomposition methods can help.


**6. Six quick wins in risk management**

After analyzing the root causes of the economic downturn and the main mistakes, it is time to provide some tips that have proven to be successful for a leading European Bank that, despite the challenging environment, has managed to excel in performance and obtain the 2011 Best Bank Award.

For this player, the quality in risk management is one if its core identity signs and thus, a top 1 line of action. For over 150 years, The Bank has combined prudency in risk management and advanced risk management techniques which have fostered recurrent and healthy turnover and value creation for its stakeholders.

The balance between The Bank's appetite for risk vs. risk control is driven by its business model and core principles:

All these principles are the main levers of The Bank's risk management guidelines. These can be summarized in six quick wins that for other industry players have turned into best practices (Figure 5):

1. Independent Risk Management Function

risk, which entitles:

2011 Best Bank Award.

model and core principles:

profits and financial results.

instrumental subsidiaries.

and in a standard format

practices (Figure 5):

aligned with its strategic objectives.

1. Independent Risk Management Function

margin to react and launch mitigation actions.

**6. Six quick wins in risk management**

healthy turnover and value creation for its stakeholders.

1. An organizational culture funded on prudent risk management 2. Prudent and anti-cyclic policies as concerns to provisions

special emphasis on risk admission and monitoring processes

they considered was more complete and consequently in difficult times they have had more

Having said this, the key to overcome such mistakes is based upon prudent management of

3. Proactive risk management initiatives covering the whole credit life cycle; putting

After analyzing the root causes of the economic downturn and the main mistakes, it is time to provide some tips that have proven to be successful for a leading European Bank that, despite the challenging environment, has managed to excel in performance and obtain the

For this player, the quality in risk management is one if its core identity signs and thus, a top 1 line of action. For over 150 years, The Bank has combined prudency in risk management and advanced risk management techniques which have fostered recurrent and

The balance between The Bank's appetite for risk vs. risk control is driven by its business

 The Retail Business is the bulk of The Bank's activity. The Bank is present worldwide and has significant market share (>10%) in all the main markets in which it operates.

 The Bank formalizes its presence through autonomous subsidiaries, both in terms of capital and liquidity, compatible with a common corporate control model. The shareholders' structure looks to be simple, minimizing the number of non-operative or

 The Bank relies on a powerful and advanced technology infrastructure and corporate tools – which enable an agile compilation and processing of the information – timely

The Bank's activity is framed within its social and reputational commitment, fully

All these principles are the main levers of The Bank's risk management guidelines. These can be summarized in six quick wins that for other industry players have turned into best

The Global Business practice is mainly developed in The Bank's core markets. Based upon strong capital and liquidity, The Bank's business model enables recurrent

**Figure 5.** Quickwins in Risk Management

### **6.1. Independent risk management function**

The Risk Management function has to be separated from daily operations. In this sense, The Bank counts on a Risks Management Unit, with its own Head of Department reporting directly to the Executive Board. Such Unit is responsible for risk admission and monitoring processes and acts on an autonomous way and thinking Global.

### **6.2. Heavily involved executive board**

The Senior Management of The Bank is aware of the importance of Risk Management and thus, inspires such culture and principles to the rest of the organization.


3.1. Classifying blood cells with deep convolutional neural networks

An important part of the data acquired by blood tests is the number of white blood cells (WBCs) or leukocytes, usually differentiated into total and differential WBC count, where the latter describes the absolute and relative numbers of WBC subtypes (neutrophils, lymphocytes, basophils, eosinophils, and monocytes) in the sample. The amount of WBCs in the sample provides information on the state of the patient's innate and adaptive immune system, e.g., a significant changes in the WBC count relative to the patient's baseline is evidence that their body is being affected by an antigen, whereas variations in the specific WBC subtypes can correlate with specific types of antigens or different pathways of immune and inflammatory reaction. Therefore, detailed measurement and understanding of the WBC counts is an important part of the quantitative picture of health and the organism's general condition.

the high accuracy of 98.6%. While the presently used model performs less well (accuracy of 86%) when classifying WBCs into multiple individual type categories as opposed to binary classification, given the high performance and simplicity of this purely software-based approach, Athelas team plans to extend it to more complex problems, including datasets containing other cell types, which could enable faster improvement cycles, increased accessibility, and

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During the last decade, human ageing research has received an increasing amount of mainstream interdisciplinary attention [19, 20], with an emerging tendency to approach various

Insilico team developed a DL system designed to predict human chronological age from biochemical data obtained from a basic blood test [21], narrowing an extensive set of potential ageing-related biomarkers to a limited subset of the most salient ones. A dataset of > 6 � 104 records was used, with each record consisting of a patient's age, sex, and 46 blood biochemical markers. The dataset was preprocessed, normalising all blood marker values to 0–1 range, and

An ensemble of 21 feed-forward deep neural networks (DNNs) was created as the ML model, with a range of values assigned to DNN parameters such as the number of hidden layers, the number of processing units per layer, activation function, and optimization and regularisation methods. The permutation feature importance method [22] was used to evaluate the relative importance of the various biochemical markers with regard to ensemble accuracy. Batch normalisation [23] was used to reduce the effects of overfitting and increase the stability of

The best results were obtained from a DNN with five hidden layers, using regularised mean squared error (MSE) function as the loss function, parametric rectified linear unit (PReLU) [24] activation function in each layer, and AdaGrad [25] optimiser of the loss function. The highestscoring DNN performed with 82% ε-prediction accuracy at ε ¼ 10 (i.e., considering the sample as correctly recognised if the predicted age is �10 years of the true age), out-performing several classes of competing ML models. Multiple models for combining individual DNNs into an ensemble (stacking) were evaluated, with the best being the elastic net model [26]. The most important blood markers were discovered to be albumin, glucose, alkaline phosphatase,

Insilico team created an online service (http://www.aging.ai) to make the DNN ensemble available to the general public, allowing patients to use their blood test data to evaluate the age prediction system and serving as a proof of concept for estimating ageing-related variables using readily available biochemical data. Additional data sources, including transcriptomic and metabolomic markers from liquid and individual organ biopsies, as well as imaging data, are being considered. Insilico team suggests that similar systems could also be developed for model organisms in order to perform cross-species analysis of individual biological markers

and their importance in predicting both chronological and biological age.

better patient outcomes, compared to previously used methods of cell count analysis.

3.2. Using deep neural networks for detection of ageing-related biomarkers

aspects of the natural ageing process as potentially treatable conditions.

then split into training and test datasets with ratio 90:10.

convergence of the models.

urea, and erythrocyte count.

Traditional methods of estimating the WBC count generally fall into one of two categories manual and automated. The historical manual inspection of the blood sample involved counting the number of cells in a blood sample under a microscope and extrapolating under the assumption of uniform cell distribution across the entire bloodstream. Automated methods involve specialised equipment such as Coulter counters [14] or laser flow cytometers [15] which can provide accurate results and good performance [16] but are generally expensive and require specialised training to operate.

In this light, the ML-based approach provides a potential improvement over the aforementioned techniques due to several reasons. First, it requires far less expensive equipment due to being built around simple imaging solutions. Furthermore, unlike earlier methods, it is able to provide almost instantaneous results after the initial training stage. Finally, its performance can be expected to improve over time, in proportion to growing dataset sizes and, being mostly software-based, it can be expanded and advanced continually and "over the air", without requiring extensive changes in the underlying infrastructure.

We illustrate this approach using an example problem provided by Athelas team [17], namely, binary classification of a stained image of a WBC as either polymorphonuclear or mononuclear.1 The training dataset consisted of hand-labelled images of stained WBCs of all given types in various proportions. Before the dataset could be used, several preprocessing steps were taken, including removing images with multiple cells and using transformations such as flips and rotations in order to increase the size and variability of the training dataset. By using transformed versions of the images, the training dataset size was increased from approximately 350 to 104 .

For the ML model, Athelas team used the LeNet-5 [18] convolutional neural network (CNN) [3, 4, 9] due to its simplicity and availability. The model was tested against a test dataset of 71 images (20% of the original training set and 0.7% of the training set after transformations), with

1 Eosinophils, basophils, and neutrophils are polymorphonuclear, while lymphocytes and monocytes are mononuclear.

the high accuracy of 98.6%. While the presently used model performs less well (accuracy of 86%) when classifying WBCs into multiple individual type categories as opposed to binary classification, given the high performance and simplicity of this purely software-based approach, Athelas team plans to extend it to more complex problems, including datasets containing other cell types, which could enable faster improvement cycles, increased accessibility, and better patient outcomes, compared to previously used methods of cell count analysis.

### 3.2. Using deep neural networks for detection of ageing-related biomarkers

3. Using machine learning techniques in blood tests

and require specialised training to operate.

mately 350 to 104

52 Liquid Biopsy

1

.

requiring extensive changes in the underlying infrastructure.

3.1. Classifying blood cells with deep convolutional neural networks

An important part of the data acquired by blood tests is the number of white blood cells (WBCs) or leukocytes, usually differentiated into total and differential WBC count, where the latter describes the absolute and relative numbers of WBC subtypes (neutrophils, lymphocytes, basophils, eosinophils, and monocytes) in the sample. The amount of WBCs in the sample provides information on the state of the patient's innate and adaptive immune system, e.g., a significant changes in the WBC count relative to the patient's baseline is evidence that their body is being affected by an antigen, whereas variations in the specific WBC subtypes can correlate with specific types of antigens or different pathways of immune and inflammatory reaction. Therefore, detailed measurement and understanding of the WBC counts is an impor-

tant part of the quantitative picture of health and the organism's general condition.

Traditional methods of estimating the WBC count generally fall into one of two categories manual and automated. The historical manual inspection of the blood sample involved counting the number of cells in a blood sample under a microscope and extrapolating under the assumption of uniform cell distribution across the entire bloodstream. Automated methods involve specialised equipment such as Coulter counters [14] or laser flow cytometers [15] which can provide accurate results and good performance [16] but are generally expensive

In this light, the ML-based approach provides a potential improvement over the aforementioned techniques due to several reasons. First, it requires far less expensive equipment due to being built around simple imaging solutions. Furthermore, unlike earlier methods, it is able to provide almost instantaneous results after the initial training stage. Finally, its performance can be expected to improve over time, in proportion to growing dataset sizes and, being mostly software-based, it can be expanded and advanced continually and "over the air", without

We illustrate this approach using an example problem provided by Athelas team [17], namely, binary classification of a stained image of a WBC as either polymorphonuclear or mononuclear.1 The training dataset consisted of hand-labelled images of stained WBCs of all given types in various proportions. Before the dataset could be used, several preprocessing steps were taken, including removing images with multiple cells and using transformations such as flips and rotations in order to increase the size and variability of the training dataset. By using transformed versions of the images, the training dataset size was increased from approxi-

For the ML model, Athelas team used the LeNet-5 [18] convolutional neural network (CNN) [3, 4, 9] due to its simplicity and availability. The model was tested against a test dataset of 71 images (20% of the original training set and 0.7% of the training set after transformations), with

Eosinophils, basophils, and neutrophils are polymorphonuclear, while lymphocytes and monocytes are mononuclear.

During the last decade, human ageing research has received an increasing amount of mainstream interdisciplinary attention [19, 20], with an emerging tendency to approach various aspects of the natural ageing process as potentially treatable conditions.

Insilico team developed a DL system designed to predict human chronological age from biochemical data obtained from a basic blood test [21], narrowing an extensive set of potential ageing-related biomarkers to a limited subset of the most salient ones. A dataset of > 6 � 104 records was used, with each record consisting of a patient's age, sex, and 46 blood biochemical markers. The dataset was preprocessed, normalising all blood marker values to 0–1 range, and then split into training and test datasets with ratio 90:10.

An ensemble of 21 feed-forward deep neural networks (DNNs) was created as the ML model, with a range of values assigned to DNN parameters such as the number of hidden layers, the number of processing units per layer, activation function, and optimization and regularisation methods. The permutation feature importance method [22] was used to evaluate the relative importance of the various biochemical markers with regard to ensemble accuracy. Batch normalisation [23] was used to reduce the effects of overfitting and increase the stability of convergence of the models.

The best results were obtained from a DNN with five hidden layers, using regularised mean squared error (MSE) function as the loss function, parametric rectified linear unit (PReLU) [24] activation function in each layer, and AdaGrad [25] optimiser of the loss function. The highestscoring DNN performed with 82% ε-prediction accuracy at ε ¼ 10 (i.e., considering the sample as correctly recognised if the predicted age is �10 years of the true age), out-performing several classes of competing ML models. Multiple models for combining individual DNNs into an ensemble (stacking) were evaluated, with the best being the elastic net model [26]. The most important blood markers were discovered to be albumin, glucose, alkaline phosphatase, urea, and erythrocyte count.

Insilico team created an online service (http://www.aging.ai) to make the DNN ensemble available to the general public, allowing patients to use their blood test data to evaluate the age prediction system and serving as a proof of concept for estimating ageing-related variables using readily available biochemical data. Additional data sources, including transcriptomic and metabolomic markers from liquid and individual organ biopsies, as well as imaging data, are being considered. Insilico team suggests that similar systems could also be developed for model organisms in order to perform cross-species analysis of individual biological markers and their importance in predicting both chronological and biological age.

## 3.3. Machine learning-based approach to Alzheimer disease biomarker discovery

In their study, Smalheiser team has developed [27] a ML-based model for predicting Alzheimer disease (AD) status of individual samples with high accuracy, using miRNAs and other small RNAs extracted from circulating exosomes obtained from liquid biopsy (blood plasma) samples.

The CNN received normalised 40 � 40 pixel images as input. They were passed to a layer of 6 convolutional filters with the size of 5 � 5, followed by a max-pooling layer in order to extract

where ð Þ p; q —pixel coordinates, y—input map, z—output map. This layer was followed by another convolutional filter layer, consisting of 12 filters, and, subsequently, by another maxpooling layer. The last layer was fully connected to the output layer by way of dot product between the weight and input vectors, passed to the sigmoid function which maps the values to the ½ � �1; 1 range. The filter parameters, network bias terms, and weight matrices were

Mao team compared their CNN-based classifier to a simpler, SVM-based method that depended on hand-crafted feature sets. Using the F-score (harmonic mean of precision and recall scores) as the comparison metric, they found that, after two rounds of five iterations, the F-score of the CNN-based classifier was 0.97, by 18.6 points exceeding the F-score (0.784) of the SVM-based classifier and hand-crafted feature set. They concluded that the CNN-based classifier presents a promising development towards automated CTC detection in images taken from blood samples, and that the technique could be adapted for use with microfluidics-

2�pþm,2�qþn

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the local signal in every 2 � 2 pixel region, defined by the max-pooling function,

0 ≤ m, n ≤ 2 yi

p, q ¼ max

automatically adjusted by backpropagation with learning rate set to 0:1.

based liquid biopsy platforms for early diagnosis and monitoring.

methods

dient (SCG)) [38].

2

respectively.

4. Cancer detection and monitoring using neural network-based

4.1. Using artificial neural networks for lung cancer detection and diagnosis

Goryński team describes [36] an artificial neural network (ANN)-based model class used for early detection and diagnosis of lung cancer. In their study, a dataset consisting of a wide range of biochemical parameters obtained from blood samples, as well as results from medical interviews (48 values in total) from 193 patients of mixed age and sex was used to train a family of 10 multilayer perceptron network (MLP) [3, 4] architectures, using a range of activation functions (linear, logistic, and tanh) for both hidden and output layers, as well as varying number of processing units ("neurons") in the hidden layer and different training algorithms (gradient descent, Broyden-Fletcher-Goldfarb-Shanno (BFGS) [37], and scaled conjugate gra-

Goryński team found that two of the trained models, named MLP 48–9-22 (trained using BFGS algorithm and using linear and tanh activation functions for hidden and output layers, respectively) and MLP 48–15-2 (SCG algorithm, logistic and tanh activation functions) gave highly

The naming scheme represents the number of "neurons" in the input, hidden, and output layers of the MLP model,

zi

A sample set of N ¼ 70 was used to construct the training dataset consisting of normalised miRNA expression data across 465 loci. Cross-validation was used in feature selection to evaluate the impact of values from specific loci as features. The samples were randomly divided into 7 partitions of 5 positive and 5 negative samples each and cross-validation was performed on these partitions, using 6 partitions for training and 1 for evaluation. The random partitioning was repeated 10 times in order to acquire 70 estimate points of the performance measures of interest, one for each sample in the set. These values were averaged and their relative performance was assessed using area under the curve of the receiver operating curve (ROC), Matthews correlation coefficient (MCC) [28], and F1 score.

Smalheiser team evaluated three different ML classifier algorithms—C4.5 decision trees [29] (using the J48 implementation), support vector machines (SVMs) [30], and adaptive boosting (AdaBoost) [31]. After selecting 50 most significant features, as per Mann-Whitney U test [32], the C4.5 classifier produced the best results, based on which it was selected as the feature selection method. The feature significance was measured by the number of times the given miRNA locus was used as a node in the decision tree over the 70 runs. The 18 highest-scoring features were selected to move on to the next step. AdaBoost algorithm was used for the final feature selection from the set of 18 features, producing an optimised set of 7 features which were then used with all 70 data samples to produce the final dataset.

The best model used by Smalheiser team was able to correctly classify, on average, 29 out of 35 samples from the AD group and 31 out of 35 samples from the control group, yielding accuracy in the range of 83–89%. Smalheiser team concluded that ML-based classifiers are able to produce highly accurate predictions of AD occurrence, using a dataset of only 7 miRNAs and that integrating exosome miRNA data with other data is likely to further increase performance of these models.

## 3.4. Detection and classification of circulating tumour cells using machine learning methods

The presence of circulating tumour cells (CTCs) in blood samples indicates the tumour response to chemotherapeutic drugs and contributes to the mechanism for subsequent growth of derived tumours (metastasisation) in distant tissues. Evaluation of CTCs can yield the diagnosis or help to follow the tumour response to chemotherapeutic drugs.

Mao team designed a deep (six layers) CNN for image-based circulating tumour cell detection with automatically learned network parameters [33]. They used a dataset of 45 phase contrast microscopy [34, 35] images, of which 35 randomly selected images were used for training and the remaining 10 for testing the network. The experiment was repeated 5 times in order to minimise network bias.

The CNN received normalised 40 � 40 pixel images as input. They were passed to a layer of 6 convolutional filters with the size of 5 � 5, followed by a max-pooling layer in order to extract the local signal in every 2 � 2 pixel region, defined by the max-pooling function,

3.3. Machine learning-based approach to Alzheimer disease biomarker discovery

(ROC), Matthews correlation coefficient (MCC) [28], and F1 score.

were then used with all 70 data samples to produce the final dataset.

samples.

54 Liquid Biopsy

mance of these models.

minimise network bias.

methods

In their study, Smalheiser team has developed [27] a ML-based model for predicting Alzheimer disease (AD) status of individual samples with high accuracy, using miRNAs and other small RNAs extracted from circulating exosomes obtained from liquid biopsy (blood plasma)

A sample set of N ¼ 70 was used to construct the training dataset consisting of normalised miRNA expression data across 465 loci. Cross-validation was used in feature selection to evaluate the impact of values from specific loci as features. The samples were randomly divided into 7 partitions of 5 positive and 5 negative samples each and cross-validation was performed on these partitions, using 6 partitions for training and 1 for evaluation. The random partitioning was repeated 10 times in order to acquire 70 estimate points of the performance measures of interest, one for each sample in the set. These values were averaged and their relative performance was assessed using area under the curve of the receiver operating curve

Smalheiser team evaluated three different ML classifier algorithms—C4.5 decision trees [29] (using the J48 implementation), support vector machines (SVMs) [30], and adaptive boosting (AdaBoost) [31]. After selecting 50 most significant features, as per Mann-Whitney U test [32], the C4.5 classifier produced the best results, based on which it was selected as the feature selection method. The feature significance was measured by the number of times the given miRNA locus was used as a node in the decision tree over the 70 runs. The 18 highest-scoring features were selected to move on to the next step. AdaBoost algorithm was used for the final feature selection from the set of 18 features, producing an optimised set of 7 features which

The best model used by Smalheiser team was able to correctly classify, on average, 29 out of 35 samples from the AD group and 31 out of 35 samples from the control group, yielding accuracy in the range of 83–89%. Smalheiser team concluded that ML-based classifiers are able to produce highly accurate predictions of AD occurrence, using a dataset of only 7 miRNAs and that integrating exosome miRNA data with other data is likely to further increase perfor-

3.4. Detection and classification of circulating tumour cells using machine learning

diagnosis or help to follow the tumour response to chemotherapeutic drugs.

The presence of circulating tumour cells (CTCs) in blood samples indicates the tumour response to chemotherapeutic drugs and contributes to the mechanism for subsequent growth of derived tumours (metastasisation) in distant tissues. Evaluation of CTCs can yield the

Mao team designed a deep (six layers) CNN for image-based circulating tumour cell detection with automatically learned network parameters [33]. They used a dataset of 45 phase contrast microscopy [34, 35] images, of which 35 randomly selected images were used for training and the remaining 10 for testing the network. The experiment was repeated 5 times in order to

$$\mathbf{z}\_{p,q}^i = \max\_{0 \le m\_\nu \le 2} \left\{ y\_{2 \times p + m, 2 \times q + n}^i \right\} \tag{1}$$

where ð Þ p; q —pixel coordinates, y—input map, z—output map. This layer was followed by another convolutional filter layer, consisting of 12 filters, and, subsequently, by another maxpooling layer. The last layer was fully connected to the output layer by way of dot product between the weight and input vectors, passed to the sigmoid function which maps the values to the ½ � �1; 1 range. The filter parameters, network bias terms, and weight matrices were automatically adjusted by backpropagation with learning rate set to 0:1.

Mao team compared their CNN-based classifier to a simpler, SVM-based method that depended on hand-crafted feature sets. Using the F-score (harmonic mean of precision and recall scores) as the comparison metric, they found that, after two rounds of five iterations, the F-score of the CNN-based classifier was 0.97, by 18.6 points exceeding the F-score (0.784) of the SVM-based classifier and hand-crafted feature set. They concluded that the CNN-based classifier presents a promising development towards automated CTC detection in images taken from blood samples, and that the technique could be adapted for use with microfluidicsbased liquid biopsy platforms for early diagnosis and monitoring.