These oscillation increases can occur because of a decrease in the corrective torque generated by the insole to control the oscillations and body velocity and because of an increase in the time required to feel the presence of the insole, transmit and process a response, and activate the muscles. Figure 9 illustrates the velocity amplitude changes caused.

**Figure 9.** Comparison of average single-foot velocity with and without the insole.

A correlation exists between the displacement average velocity values VAvg (cm/s): an increased displacement velocity—that is, a higher speed in perceiving imbalance and attempt‐ ing to stabilize the pressure center—decreases the imbalance. This may be because wearing the insole: i) reduces the ground reaction force; ii) reduces the resulting vector amplitude, and iii) generates greater body stability through greater velocity to control these oscillations. Figure 10 shows the velocity variation for each collection captured.

The circular area that corresponds to the area that best fits the trajectory of the pressure center is shown in Figure 11.

When we analyze the response variation data in the time domain, we obtain useful informa‐ tion, but to supplement the analysis. For a system without shock absorbers, the antiresonance corresponds to the absence of movement in all coordinates where the response is considered. Peaks in this frequency response occur in the time part of the diagram where the maximum response was observed because of entry excitation represented by the ground reaction force on the foot. We note that the vibration amplitude changes when we modify the oscillation frequency of the applied force. This result also shows that by varying the oscillation frequency of the force, both increases and decreases in vibration amplitude occur at different points on Use of Natural Latex as a Biomaterial for the Treatment of Diabetic Foot — A New Approach to Treating Symptoms… http://dx.doi.org/10.5772/59135 235

&?>collection<\$%&?>captured.

A<\$%&?>correlation<\$%&?>exists<\$%&?>between<\$%&?>the<\$%&?>displacement<\$%&?>average<\$%&?>velocity<\$%

that<\$%&?>is,<\$%&?>a<\$%&?>higher<\$%&?>speed<\$%&?>in<\$%&?>perceiving<\$%&?>imbalance<\$%&?>and<\$%&?>at

decreases<\$%&?>the<\$%&?>imbalance.<\$%&?>This<\$%&?>may<\$%&?>be<\$%&?>because<\$%&?>wearing<\$%&?>the<\$ %&?>insole:<\$%&?>i)<\$%&?>reduces<\$%&?>the<\$%&?>ground<\$%&?>reaction<\$%&?>force;<\$%&?>ii)<\$%&?>reduces< \$%&?>the<\$%&?>resulting<\$%&?>vector<\$%&?>amplitude,<\$%&?>and<\$%&?>iii)<\$%&?>generates<\$%&?>greater<\$% &?>body<\$%&?>stability<\$%&?>through<\$%&?>greater<\$%&?>velocity<\$%&?>to<\$%&?>control<\$%&?>these<\$%&?>os cillations.<\$%&?>Figure<\$%&?>10<\$%&?>shows<\$%&?>the<\$%&?>velocity<\$%&?>variation<\$%&?>for<\$%&?>each<\$%

>stability<\$%&?>region<\$%&?>with<\$%&?>the<\$%&?>insole<\$%&?>was<\$%&?>increased<\$%&?>by<\$%&?>increasing<\$%&?>the<\$% &?>limits.<\$%&?>The<\$%&?>red<\$%&?>line<\$%&?>indicates<\$%&?>the<\$%&?>area<\$%&?>with<\$%&?>the<\$%&?>insole,<\$%&?>and

When<\$%&?>we<\$%&?>analyze<\$%&?>the<\$%&?>response<\$%&?>variation<\$%&?>data<\$%&?>in<\$%&?>the<\$%&?>ti me<\$%&?>domain,<\$%&?>we<\$%&?>obtain<\$%&?>useful<\$%&?>information,<\$%&?>but<\$%&?>to<\$%&?>supplement <\$%&?>the<\$%&?>analysis.<\$%&?>For<\$%&?>a<\$%&?>system<\$%&?>without<\$%&?>shock<\$%&?>absorbers,<\$%&?>t he<\$%&?>antiresonance<\$%&?>corresponds<\$%&?>to<\$%&?>the<\$%&?>absence<\$%&?>of<\$%&?>movement<\$%&?>in <\$%&?>all<\$%&?>coordinates<\$%&?>where<\$%&?>the<\$%&?>response<\$%&?>is<\$%&?>considered.<\$%&?>Peaks<\$% &?>in<\$%&?>this<\$%&?>frequency<\$%&?>response<\$%&?>occur<\$%&?>in<\$%&?>the<\$%&?>time<\$%&?>part<\$%&?>

<\$%&?>the<\$%&?>blue<\$%&?>line<\$%&?>indicates<\$%&?>the<\$%&?>area<\$%&?>without<\$%&?>the<\$%&?>insole.

&?>values<\$%&?>VAvg<\$%&?>(cm/s):<\$%&?>an<\$%&?>increased<\$%&?>displacement<\$%&?>velocity—

tempting<\$%&?>to<\$%&?>stabilize<\$%&?>the<\$%&?>pressure<\$%&?>center—

**Figure 10.** Comparison of the variation in velocity with and without the insole. %&?>in<\$%&?>Figure<\$%&?>11.

These oscillation increases can occur because of a decrease in the corrective torque generated by the insole to control the oscillations and body velocity and because of an increase in the time required to feel the presence of the insole, transmit and process a response, and activate

VAvg compare VAvgp

Vxwithout insole Vxwith insole latex

1 1.5 2 2.5 3 3.5 4 4.5 5

sample

A correlation exists between the displacement average velocity values VAvg (cm/s): an increased displacement velocity—that is, a higher speed in perceiving imbalance and attempt‐ ing to stabilize the pressure center—decreases the imbalance. This may be because wearing the insole: i) reduces the ground reaction force; ii) reduces the resulting vector amplitude, and iii) generates greater body stability through greater velocity to control these oscillations. Figure

The circular area that corresponds to the area that best fits the trajectory of the pressure center

When we analyze the response variation data in the time domain, we obtain useful informa‐ tion, but to supplement the analysis. For a system without shock absorbers, the antiresonance corresponds to the absence of movement in all coordinates where the response is considered. Peaks in this frequency response occur in the time part of the diagram where the maximum response was observed because of entry excitation represented by the ground reaction force on the foot. We note that the vibration amplitude changes when we modify the oscillation frequency of the applied force. This result also shows that by varying the oscillation frequency of the force, both increases and decreases in vibration amplitude occur at different points on

the muscles. Figure 9 illustrates the velocity amplitude changes caused.

6

is shown in Figure 11.

**Figure 9.** Comparison of average single-foot velocity with and without the insole.

10 shows the velocity variation for each collection captured.

8

10

12

14

average displacement speed (cm/s)

16

18

20

22

234 Topics in Public Health

Figure 11. A<\$%&?>graph<\$%&?>generated<\$%&?>in<\$%&?>radar<\$%&?>format<\$%&?>to<\$%&?>show<\$%&?>that<\$%&?>the<\$%&? **Figure 11.** A graph generated in radar format to show that the stability region with the insole was increased by increas‐ ing the limits. The red line indicates the area with the insole, and the blue line indicates the area without the insole.

the time scale. In the time domain, there are natural frequencies and respective modal forms associated with these frequencies, which are inherent in each insole structure designed. These are basically characteristics that depend on inertia and rigidity. The introduction of shock absorbers with viscosity and mass characteristics and softness and flexibility features affect the response of the foot structure when it is excited by a force of some type.

### **5. Healing insole**

The healing insole is disposable and sterile. The same preparation process used for the latex biomaterial centrifuged to 60% was used for the insole. In the process of preparing the insole, latex was placed in acrylic molds that were previously cleaned and dried. The latex biomaterial was spread out until it formed a thin layer covering the surface. Rather than resting the latex in the oven horizontally, it was rested completely upright so that all excess latex drained. This contributed to the insole becoming clearer. An oven was not used for the insole polymerization; it was polymerized at room temperature, which also promoted transparency. This process was repeated 6 times to reach a final insole thickness of 0.5 mm. The latex insoles were sterilized in ethylene oxide. Some small holes, approximately 2 mm in diameter, were made in the insoles so that during use, exudation (secretion) could be eliminated from the wound. This research examined an innovative method of tissue regeneration for diabetic ulcers consisting of the combined and simultaneous action of the latex biomaterial and low-intensity red LED light. The tissue regeneration electronic circuit is formed by a signal-emitting cell that is based on the tissue neoformation principle involving the use of LEDs. The LED cells are placed only on ulcerated regions of the foot. The cells are placed outside the insole and are covered with a sheet of latex. They emit radiation with a fluency of 25 J/cm². Figures 12 and 13 refer to patient 6. This patient is 62 years old and 8 years of diagnosis of DM, her profession is housework. The ulcer 1 (Figure 12) is situated in the region 7 (instep) the existence of time to approximately 7 months already told before amputation. The ulcer appeared through a bruised evolving dramatically with infection coming to osteomyelitis, not to provide answers to antibiotic treatment was necessary amputation of the second to the fifth toe. Then his picture of infection and osteomyelitis have not healed completely and reached the 1st toe (hallux), which was necessary to perform a further amputation. Thus, the present research, to heal these surgeries amputations, applied the treatment with silver foam during the patient's stay in the GC and then the inductor system tissue formation while in the GE.

The ulcer 2 (Figure 13) due to complications arose from the first, and also by mechanical trauma, caused by lack of rest. The wound is situated in area 3, the existence of time to approximately 5 months. As already mentioned, ulcers 1 and 2 (Figures 12 and 13) were followed for 1 month in the GC. Then, in an attempt to accelerate the healing process, the wounds were also accompanied in GE using the inductor system tissue formation. Figures 14 and 15 show the results. This patient already had three ulcers from diagnosis of DM and two amputations.

Use of Natural Latex as a Biomaterial for the Treatment of Diabetic Foot — A New Approach to Treating Symptoms… http://dx.doi.org/10.5772/59135 237

the time scale. In the time domain, there are natural frequencies and respective modal forms associated with these frequencies, which are inherent in each insole structure designed. These are basically characteristics that depend on inertia and rigidity. The introduction of shock absorbers with viscosity and mass characteristics and softness and flexibility features affect

The healing insole is disposable and sterile. The same preparation process used for the latex biomaterial centrifuged to 60% was used for the insole. In the process of preparing the insole, latex was placed in acrylic molds that were previously cleaned and dried. The latex biomaterial was spread out until it formed a thin layer covering the surface. Rather than resting the latex in the oven horizontally, it was rested completely upright so that all excess latex drained. This contributed to the insole becoming clearer. An oven was not used for the insole polymerization; it was polymerized at room temperature, which also promoted transparency. This process was repeated 6 times to reach a final insole thickness of 0.5 mm. The latex insoles were sterilized in ethylene oxide. Some small holes, approximately 2 mm in diameter, were made in the insoles so that during use, exudation (secretion) could be eliminated from the wound. This research examined an innovative method of tissue regeneration for diabetic ulcers consisting of the combined and simultaneous action of the latex biomaterial and low-intensity red LED light. The tissue regeneration electronic circuit is formed by a signal-emitting cell that is based on the tissue neoformation principle involving the use of LEDs. The LED cells are placed only on ulcerated regions of the foot. The cells are placed outside the insole and are covered with a sheet of latex. They emit radiation with a fluency of 25 J/cm². Figures 12 and 13 refer to patient 6. This patient is 62 years old and 8 years of diagnosis of DM, her profession is housework. The ulcer 1 (Figure 12) is situated in the region 7 (instep) the existence of time to approximately 7 months already told before amputation. The ulcer appeared through a bruised evolving dramatically with infection coming to osteomyelitis, not to provide answers to antibiotic treatment was necessary amputation of the second to the fifth toe. Then his picture of infection and osteomyelitis have not healed completely and reached the 1st toe (hallux), which was necessary to perform a further amputation. Thus, the present research, to heal these surgeries amputations, applied the treatment with silver foam during the patient's stay in the GC and

The ulcer 2 (Figure 13) due to complications arose from the first, and also by mechanical trauma, caused by lack of rest. The wound is situated in area 3, the existence of time to approximately 5 months. As already mentioned, ulcers 1 and 2 (Figures 12 and 13) were followed for 1 month in the GC. Then, in an attempt to accelerate the healing process, the wounds were also accompanied in GE using the inductor system tissue formation. Figures 14 and 15 show the results. This patient already had three ulcers from diagnosis of DM and two

the response of the foot structure when it is excited by a force of some type.

then the inductor system tissue formation while in the GE.

**5. Healing insole**

236 Topics in Public Health

amputations.

**Figure 12.** Clinical photo follow-up Patient 6 (1 ulcer)-GC: a) the ulcerated foot region; b) pre-treatment (initial); c) post-treatment (1 week); d) two weeks; and) 3 weeks; f) 4 weeks.

The two figures (Figure 14 and Figure 15) pertain to the patient 6, pictured in the preceding Figure 12 and Figure 13. In each ulcer in this patient, it was evaluated the behavior of two different methods of healing: foam with silver (GC) and system inducing tissue formation (GE). Because of the location of the ulcer 1 this patient, ulcers on both 1 and 2 were applied only to

**Figure 13.** Clinical photo follow-up. Patient 6 (2 ulcer)-GC: a) region of the ulcerated foot; b) pre-treatment (initial); c) post-treatment (1 week); d) two weeks; and) 3 weeks; f) 4 weeks.

slide latex and electronic circuitry for tissue regeneration. Again being demonstrated that within the inductor tissue formation system can be used only blade latex and LED light to induce healing. Comparing the images in Figure 12 (GC) and Figure 14 (GE), one observes a faster ulcer healing 1 while in the GE. It is also noticed that the GE ulcer 1 showed better color, higher and more debridement of granulation tissue and reepithelialization. The same assess‐

Use of Natural Latex as a Biomaterial for the Treatment of Diabetic Foot — A New Approach to Treating Symptoms… http://dx.doi.org/10.5772/59135 239

**Figure 14.** Clinical photo follow-up. Patient 6 (1 ulcer)-Experimental Group: a) early (before the inductor system tissue formation); b) post-treatment (after using the inductor system tissue formation)-1 week; c) two weeks; d) 3 weeks; e) 4 weeks f) 6 weeks g) 8 weeks.

ment can be made between Figures 13 and 14, which displays the ulcer healing was also second fastest while in the GE. Both this patient's ulcers were followed up at 6 GE for 8 weeks. Figures 14 and 15, it was observed that after 8 weeks of treatment with the inducer system for tissue formation, both ulcer decreased significantly in size.

slide latex and electronic circuitry for tissue regeneration. Again being demonstrated that within the inductor tissue formation system can be used only blade latex and LED light to induce healing. Comparing the images in Figure 12 (GC) and Figure 14 (GE), one observes a faster ulcer healing 1 while in the GE. It is also noticed that the GE ulcer 1 showed better color, higher and more debridement of granulation tissue and reepithelialization. The same assess‐

**Figure 13.** Clinical photo follow-up. Patient 6 (2 ulcer)-GC: a) region of the ulcerated foot; b) pre-treatment (initial); c)

post-treatment (1 week); d) two weeks; and) 3 weeks; f) 4 weeks.

238 Topics in Public Health

An analysis of the progression of healing of ulcers, conducted by the patient's medical staff, showed full reepithelialization in eight weeks, as illustrated in Figure 16.

**Figure 15.** Clinical photo follow-up. Patient 6 (2 ulcer)-Experimental Group: a) early (before the inductor system tissue formation); b) post-treatment (after using the inductor system tissue formation)-1 week; c) two weeks; d) 3 weeks; e) 4 weeks f) 6 weeks g) 8 weeks.

The wounds were photographed on a weekly basis using a digital Sony DSC-H70 camera with 16.1-megapixel resolution. The images were taken with the patient positioned lying down in a chair, with the camera mounted on a tripod parallel to the wounds, and with a focal length of 15 centimeters. A metric ruler was placed alongside the wound for subse‐ quent computational analysis. The digital images obtained were analyzed using the ImageJ® software to quantify the total area of the ulcers. The latex and LED light action gradually favored contraction around the edge of the wound. The coloring of the wound also improved considerably over the course of the 9 weeks. After a week of treatment, the wound appeared more reddish in color. Furthermore, there was a significant increase in granula‐ tion tissue. At the beginning of treatment, the wound had a slight depth, and over the course of the 9 weeks of treatment, new tissue gradually formed, making the lesion appear to be filling and healing. In order for low-intensity LED therapy to have positive effects, a protocol of application is essential. The biological effects of this type of therapy depend on the irradiation parameters, such as the wavelength, fluence, irradiation time, and emis‐ sion mode. A rating of this study was to compare the behavior of two different methods of healing in the same patient. This fact refers to the patient 1, in which the silver foam (GC) of the right foot ulcer (metatarsal area) and tissue formation-inducing system (GE) to the ulcer of the left foot (the heel area) was applied. Comparing the ICU in both cases in the 2nd, 4th, 6th and 8th week, patient 1 showed better results in GE. This means that the system inducing tissue formation favoring the evolution of healing better than the foam with silver.

The wounds were photographed on a weekly basis using a digital Sony DSC-H70 camera with 16.1-megapixel resolution. The images were taken with the patient positioned lying down in a chair, with the camera mounted on a tripod parallel to the wounds, and with a focal length of 15 centimeters. A metric ruler was placed alongside the wound for subse‐ quent computational analysis. The digital images obtained were analyzed using the ImageJ® software to quantify the total area of the ulcers. The latex and LED light action gradually favored contraction around the edge of the wound. The coloring of the wound also improved considerably over the course of the 9 weeks. After a week of treatment, the wound appeared more reddish in color. Furthermore, there was a significant increase in granula‐ tion tissue. At the beginning of treatment, the wound had a slight depth, and over the course of the 9 weeks of treatment, new tissue gradually formed, making the lesion appear to be filling and healing. In order for low-intensity LED therapy to have positive effects, a protocol of application is essential. The biological effects of this type of therapy depend on the irradiation parameters, such as the wavelength, fluence, irradiation time, and emis‐ sion mode. A rating of this study was to compare the behavior of two different methods of healing in the same patient. This fact refers to the patient 1, in which the silver foam

**Figure 15.** Clinical photo follow-up. Patient 6 (2 ulcer)-Experimental Group: a) early (before the inductor system tissue formation); b) post-treatment (after using the inductor system tissue formation)-1 week; c) two weeks; d) 3 weeks; e) 4

weeks f) 6 weeks g) 8 weeks.

240 Topics in Public Health

**Figure 16.** Clinical photo follow-up. Patient 1 – a) ulcerated foot region, b) pre-treatment (initial treatment), c) posttreatment (1 week), d) 2 weeks, e) 3 weeks, f) 4 weeks, g) 5 weeks, h) 6 weeks, i) 7 weeks, j) 8 weeks, l) 9 weeks.

### **6. Conclusions and contributions**

Diabetes mellitus is a chronic disease and is characterized by a variety of complications, including diabetic foot stands, considered a serious and often devastating consequences on the results of ulcerations problem. The formation of sores that become infected and poorly healing can lead to gangrene and even amputation of toes, feet or legs. The essence of this study is intended, under the etiological-mechanical approach, to the intersection of an external element (latex-derived insole – the passive control) with diabetic passive stride. There is impact on the variation of some key variables such as change in mass and contact with soil. Then, we also analyze the parameter sensibility/robustness of the dynamical model obtained, and the effect of the addition of the insole controller in this sensibility. This study showed that the modeling of the diabetic gait is a challenging task, having previous researches already presented contributions which must be added to those brought up by this study. This parametric study's results provide the first steps towards the discovery of tendencies, aiming to obtain new perspectives with regard to this complex disease. Thus this research considers the disease's main etiology and parameters related to the patient's gait, anthropometry and social reality, for he/she might perform certain roles that require their feet to bear different loads – for instance, hairdressers and teachers. This must influence the design process of future insoles, which will function as controllers derived biomateri‐ als acting directly on the dynamics of the gait. The center of pressure of the human foot is displaced in carriers of diabetes, which attests the necessity of a study of the patient's gait prior to the manufacturing of the insole. Second, presented in this study will be an intellectual preparation for the emergence of a new concept, proposed with the idea of controllers derived biomaterials. This methodology will be critical to the creation of a "bioinspired" theory in the field of Biomedical Engineering, which will further assist in the construction of the concept (which says what the thing is) called controlling derived biomaterial (this study insole latex). Based on the literature, it was observed that the introduction of assistive devices is common for changing the stride. But this study presented, that element was characterized and analyzed as a controller that, through qualitative and quantitative changes in the charges applied to the foot, proved possible to correct the diabetic stride. Finally, a search for a new possibility for the treatment of diabetic foot. Accordingly, an inductor system for new tissue formation novel diabetic foot with light emitting circuit LEDs and use of natural latex has been developed. This system consists of a healing insole and an electronic circuit for tissue regeneration. Cicatrizing insole is derived from the rubber tree latex brasiliensis and made a personalized and individual‐ ized. This innovative method of healing diabetic foot ulcers consists of the joint and simultaneous action of biomaterial latex and light irradiation of low intensity LEDs. The clinical findings were analyzed qualitatively and quantitatively, which showed that the results obtained by the experimental test suggests that the inducing tissue neoformation system is characterizing.

### **Author details**

**6. Conclusions and contributions**

242 Topics in Public Health

system is characterizing.

Diabetes mellitus is a chronic disease and is characterized by a variety of complications, including diabetic foot stands, considered a serious and often devastating consequences on the results of ulcerations problem. The formation of sores that become infected and poorly healing can lead to gangrene and even amputation of toes, feet or legs. The essence of this study is intended, under the etiological-mechanical approach, to the intersection of an external element (latex-derived insole – the passive control) with diabetic passive stride. There is impact on the variation of some key variables such as change in mass and contact with soil. Then, we also analyze the parameter sensibility/robustness of the dynamical model obtained, and the effect of the addition of the insole controller in this sensibility. This study showed that the modeling of the diabetic gait is a challenging task, having previous researches already presented contributions which must be added to those brought up by this study. This parametric study's results provide the first steps towards the discovery of tendencies, aiming to obtain new perspectives with regard to this complex disease. Thus this research considers the disease's main etiology and parameters related to the patient's gait, anthropometry and social reality, for he/she might perform certain roles that require their feet to bear different loads – for instance, hairdressers and teachers. This must influence the design process of future insoles, which will function as controllers derived biomateri‐ als acting directly on the dynamics of the gait. The center of pressure of the human foot is displaced in carriers of diabetes, which attests the necessity of a study of the patient's gait prior to the manufacturing of the insole. Second, presented in this study will be an intellectual preparation for the emergence of a new concept, proposed with the idea of controllers derived biomaterials. This methodology will be critical to the creation of a "bioinspired" theory in the field of Biomedical Engineering, which will further assist in the construction of the concept (which says what the thing is) called controlling derived biomaterial (this study insole latex). Based on the literature, it was observed that the introduction of assistive devices is common for changing the stride. But this study presented, that element was characterized and analyzed as a controller that, through qualitative and quantitative changes in the charges applied to the foot, proved possible to correct the diabetic stride. Finally, a search for a new possibility for the treatment of diabetic foot. Accordingly, an inductor system for new tissue formation novel diabetic foot with light emitting circuit LEDs and use of natural latex has been developed. This system consists of a healing insole and an electronic circuit for tissue regeneration. Cicatrizing insole is derived from the rubber tree latex brasiliensis and made a personalized and individual‐ ized. This innovative method of healing diabetic foot ulcers consists of the joint and simultaneous action of biomaterial latex and light irradiation of low intensity LEDs. The clinical findings were analyzed qualitatively and quantitatively, which showed that the results obtained by the experimental test suggests that the inducing tissue neoformation Suélia de Siqueira Rodrigues Fleury Rosa1\*, Maria do Carmo Reis1 , Mário Fabricio Fleury Rosa2 , Diego Cólon3 , Célia Aparecida dos Reis4 and José Manoel Balthazar5

\*Address all correspondence to<EMAIL_ADDRESS>
1 Engineering and Biomaterials Laboratory – BioEngLab®, Biomedical Engineering, University of Brasilia, Brasil

2 University of Brasilia-Post-Graduate Program of Sciences and Technology in Health, Brasil

3 University of São Paulo-Polytechnic School, Automation and Control Laboratory, Brasil

4 Estadual Paulista Júlio de Mesquita Filho, School of Sciences, Mathematics Department of Bauru, Brasil

5 Paulista State University Júlio de Mesquita Filho, Institute of Geosciences and Exact Sciences of Rio Claro, Brasil

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*2.2. Constant Twist Angle Control*

The principle of constant twist angle control is that it maintains a pre-set constant static twist angle of the PTTO [31]. This is ensured by a control system which adapts the overpressure of the gaseous medium in the PTTO to the static load torque in order to maintain the pre-set constant twist angle. Constant twist angle control is suitable for tuning mechanical systems with fan characteristics. The principle of operation is explained in more detail below [32].

The transmitted static load torque *Mstat* and dynamic stiffness *kdyn* [N·m·rad−1] of the PTTO by a given constant twist angle ϕ*const* (for simplicity neglecting the rubber shell torque *MG* which is relatively small compared to the total transmitted torque [13]) can be generally considered as proportional to the overpressure *pTC* in the compression space of the PTTO corresponding to the given constant twist angle (see Equation (1)).

Thus, the static load torque can be expressed as

$$M\_{\text{stat}} = \mathbf{a}\_{\left(q\_{\text{comst}}\right)} \cdot p\_{T\mathbb{C}} \tag{2}$$

and dynamic torsional stiffness as

$$k\_{dyn} = \mathbf{b}\_{(\varphi\_{count})} \cdot \mathcal{p}\_{T\mathcal{C}\_{\prime}} \tag{3}$$

where *a*(ϕ*const*) [N·m·Pa−1] and *b*(ϕ*const*) [N·m·rad−1·Pa−1] are factors whose values depend on the constant twist angle ϕ*const* only.

The transmitted static load torque corresponding to the fan characteristics (of the propeller) can be expressed as

$$M\_{\rm stat} = \mathfrak{c}\_f \cdot \omega^2,\tag{4}$$

where *cf* [N·m·rad−2·s2] is a constant and ω [rad·s−1] is the angular speed of the propeller shaft.

From the equality of Equations (2) and (4) for the static load torque *Mstat*, then expressing *pTC* and putting it into Equation (3), the dynamic torsional stiffness will be

$$k\_{dyn} = \mathbf{b}\_{(q\_{count})} \cdot \frac{c\_f}{\mathbf{a}\_{(q\_{count})}} \cdot a^2. \tag{5}$$

Considering a two-mass torsional oscillating mechanical system with dynamic torsional stiffness *kdyn* and equivalent mass moment of inertia *IRED* [kg·m2], the natural angular frequency of this system will be

$$
\Omega \bullet = \sqrt{\frac{k\_{\text{dyn}}}{I\_{RED}}} = \sqrt{\frac{\mathbf{b}\_{(\text{\text{\textquotedblleft}cond)} \cdot \mathbf{c}\_f}{\mathbf{a}\_{(\text{\textquotedblleft}cond)} \cdot I\_{RED}}}} \cdot \boldsymbol{\omega} = \mathbf{C}\_{(\text{\textquotedblleft}cond)} \cdot \boldsymbol{\omega} \tag{6}
$$

where *C*(ϕ*const*) [-] is a factor depending on the given constant twist angle ϕ*const* only. This means that the natural frequency of the mechanical system will be proportional to the angular speed of the propeller shaft, and the value of factor *C*(ϕ*const*) can be properly set by selecting a suitable constant twist angle ϕ*const*. This is illustrated with an interference diagram of a two-mass torsional oscillating mechanical system using the PTTO with linear characteristics in Figure 4, where ω is the angular speed of the shaft, ω*e1* and ω*e2* are the excitation frequencies resulting from the periodically alternating load torque and Ω*0(*ϕ*const1* ... *8)* are the natural frequencies corresponding to the pre-set constant twist angles ϕ*const1* < ϕ*const2* < ... < ϕ*const8*. The intersections of the excitation frequencies with the natural frequency represent resonances at which the transmitted load torque reaches its maximum value. The case of resonance should be avoided in the operating speed range, as it can be dangerous in terms of a high alternating load torque.

**Figure 4.** Interference diagram of a mechanical system with constant twist angle control.

According to Figure 4, the course of natural frequencies consists of three parts. The first part, the *sub-regulatory area*, is a horizontal line beginning at zero speed when the load torque is zero (resulting from the fan characteristics) and the PTTO is inflated to the minimum operating pressure. At a certain speed, the torque twists the PTTO to the selected constant twist angle, and this is the start of the second part representing the *regulatory area* of the PTTO. In the regulatory area, the pressure in the PTTO is regulated to a value where the PTTO has the desired constant twist angle. The regulatory area ends at a speed when the pressure reaches the maximum operating value. This point is the start of the *over-regulation area*. After this point, the pressure has its maximum operating value. In the presented case, the optimum constant twist angle is ϕ*const4*, where the torsional natural frequency is farthest from the excitation frequencies, i.e., farthest from the resonance in the regulatory area of the PTTO.

Results of theoretical analyses in marine propulsion mechanical systems using constant twist angle control presented, for example, in [31,33] show that this type of control ensures proper tuning in terms of torsional vibration and has considerable potential for future application.

Constant twist angle control can be ensured by a constant twist angle regulator which is a part of the PTTO [13,26], or ECTACS can be used.

### *2.3. Experimental Torsional Oscillating Mechanical System*

In order to verify the ability of our ECTACS to keep the twist angle of a PTTO at a pre-set constant value, the ECTACS was applied into an experimental torsional oscillating mechanical system.

The TOMS of the piston compressor drive (Figure 5) is made up of a 3-phase asynchronous electromotor, *Siemens 1LE10011DB234AF4-Z* (11 kW, 1500 RPM) *(1)*. Rotational speed of this electromotor is continuously vector-controlled by a frequency converter, *Sinamics G120C*. The electromotor drives a 3-cylinder piston compressor, *ORLIK 3JSK-75 (3)*, through a PTTO type *4-2*/*70-T-C (2)* (Figure 1). The compressor in this system acts as a load and torsional vibration exciter too. For proper tuning of the system, it is necessary to know the dynamic behavior under different operating conditions, which was experimentally investigated in [34].

Under standard conditions, the load torque of the system has no fan characteristics, and this means that this TOMS is not very suitable for tuning torsional vibrations with constant twist angle control, so our goal is not the tuning itself but only the verification of the ability to maintain the desired constant twist angle of the PTTO.

**Figure 5.** Experimental torsional oscillating mechanical system.

The whole drive is mounted on a rigid sprung frame. The compressed air from the compressor flows into an air pressure tank with a volume of 20 l. The air pressure in the tank is controlled by a throttling valve. So, the load of the TOMS can be adjusted. Maximum compressor output air overpressure is 800 kPa and its value is measured by a pressure sensor, *Danfoss MBS 3000*, with an overpressure measuring range of 0–1 MPa. The same type of pressure sensor is used for measuring the air pressure value in the compression space of the PTTO. The accuracy of the *MBS 3000* sensor with a metal membrane is 0.5% of its measuring range, i.e., 5 kPa (combined fault–nonlinearity, hysteresis and reproducibility). The supply of compressed air into the PTTO is ensured by a rotation supply *(4)*. The mechanical part of the experimental TOMS is described in more detail in [35].

The multifunctional electronic module (MFEM), marked with the number *(5)*, which is a part of an electronic constant twist angle control system, developed by us, has the following functions: Page: 7 Is the italics necessary?

### *2.4. Data Measuring and Processing*

The dynamic load torque transmitted by the PTTO causes mutual dynamic angular twisting of the driving and driven hubs of the PTTO. The measurement is based on determining the PTTO's twist angle time course. The PTTO is equipped with black–white tape, which is stuck to the circumference of the driving and driven hubs of the PTTO and they are scanned by a pair of optoelectronic sensors (Figure 6). According to our specific requirements, a pair of *Dewetron* optoelectronic sensors of type *SE-TACHO-PROBE-01* [36] (Figure 6) was used.

These sensors detect the reflection from the reflective black–white moving tape (Figure 6b). The sensors react to the edges between the black and white stripes. There is a distinct change of electrical output voltage at the moment the edge is crossed. These sensors can work with a maximum frequency of 10 kHz but the cleanness of the reflective tape, cleanness of the optical parts of the sensors and the sharpness of the edges between the black and white stripes must be excellent [36].

**Figure 6.** Optoelectronic sensors *Dewetron SE-TACHO-PROBE-01*: (**a**) sensor attached to a data cable; (**b**) pair of sensors mounted in the experimental torsional oscillating mechanical system.

The number of black and white stripe pairs for the driving and driven hubs should be equal and chosen with respect to the maximum twist angle of the PTTO and to the character of the transmitted load torque (especially its dynamic component). It is also important that the length of all the black and white stripes should be equal. The angle corresponding to length of a black and white stripe pair must be larger than the maximum twist angle of the PTTO. For the PTTO type *4-2*/*70-T-C*, the maximum twist angle is 11◦ which corresponds to a maximum of 32 pairs of stripes. Further, as the major harmonic component for a three-piston compressor is the 3rd harmonic component, it is advantageous to select the number of black and white stripe pairs as integer multiples of 3 to obtain the best results for the twist angle time course by the equal operation of all cylinders (theoretically "3 identical recorded curve portions in one revolution"). Therefore, 30 black–white stripe pairs for each hub of the PTTO have been selected. The edge-crossing times *ti* need to be measured, where the index *i* stands for the sample order number. In our case, only the black-to-white stripe edges are considered. The times *ti* are computed from the counted number of impulses from the counter of the MFEM microprocessor. One impulse represents a time of 1/14745600 s.

Considering the times *t1i* for the driving hub and the times *t2i* for the driven hub of the PTTO, the time delays Δ*ti* [s] can be computed using the following equation:

$$
\Delta t\_i = t\_{2i} - t\_{1i}.\tag{7}
$$

In the next step, the total twist angle ϕ*T* [rad] of the PTTO can be computed according to the following equation:

$$
\varphi\_{Ti} = \frac{\pi \cdot n \cdot \Delta t\_i}{30},
\tag{8}
$$

where *n* [min−1] is the immediate rotational speed of the mechanical system.

From the total twist angle of the PTTO ϕ*T*, its static component ϕ*stat* can be computed as the mean value:

$$
\varphi\_{stat} = \frac{\sum\_{i=1}^{k} \varphi\_{Ti}}{k},
\tag{9}
$$

where *k* [-] is the number of samples, which has to be an integer multiple of the black–white stripe pairs number on the hub. In practice, the floating average method is used for this computation.

The computations according to Equations (7)–(9) are performed by the software part of our ECTACS in PC in real time. This way, the controlled variable (ϕ*stat*) for the ECTACS can be computed. It is very advantageous because the torsional vibration does not directly affect the control device like in the case of regulators directly built into the PTTO.

### *2.5. Description of the Constant Twist Angle Control System Function*

The goal of constant twist angle control is to maintain a pre-set static (mean) value of the twist angle by any given static load torque *Mstat* resulting from the current operating mode. Although it is possible to use a closed-loop PID control system with a static twist angle as a controlled variable and overpressure as a manipulated variable, based on the fact that the mathematical and physical model of the PTTO (presented in Section 2.1.1) is well known, it was decided to use a model-based adaptive control system [37]. This approach allows us to reach the desired value of the static twist angle more quickly, which is very important in terms of passing through the resonance as quickly as possible.

The static load torque of the PTTO at a periodically alternating load torque can be computed as

$$M\_{\rm stat} = M\_{\rm G\left(\varphi\_{\rm stat}\right)} + p\_{T^\cdot}(S\_{\rm t}r)\_{\left(\varphi\_{\rm stat}\right)^\*} \tag{10}$$

where *pT* is the mean overpressure in the PTTO, and the values of the rubber shell torque *MG* and static moment of effective area *Se*·*r* are computed from the static twist angle ϕ*stat*. The value of the twist angle is continuously measured and its mean value is computed by the control system.

The rubber shell torque *MG(*ϕ*stat)* and the static moment of effective area *Se*·*r(*ϕ*stat)* are computed as fifth degree polynomials:

$$M\_{\rm G\left(\varphi\_{\rm stat}\right)} = \sum\_{i=0}^{5} a\_{i} \cdot \varphi\_{\rm stat'}^{i} \tag{11}$$

$$(S\_{\mathfrak{c}} \cdot r)\_{\left(\varphi\_{\text{stat}}\right)} = \sum\_{i=0}^{5} b\_{i} \cdot \varphi\_{\text{stat}}^{i} \,. \tag{12}$$

After computing the static load torque according to Equation (10), the value of overpressure *pTC* needed for obtaining the desired constant twist angle ϕ*const*, using Equations (11)–(12), where the desired constant twist angle ϕ*const* is set instead of the static twist angle ϕ*stat*, can be expressed as follows:

$$p\_{TC} = \frac{M\_{\text{stat}} - M\_{G\left(\varphi\_{\text{cnot}}\right)}}{\left(S\_{\text{t}} \cdot r\right)\_{\left(\varphi\_{\text{cnot}}\right)}}.\tag{13}$$

After setting the new value of overpressure according to Equation (13), the value of the actual static twist angle is measured. The difference between the actual static twist angle ϕ*stat* and the desired static twist angle ϕ*const* can be expressed as

$$
\Delta \boldsymbol{\varrho} = \boldsymbol{\varrho}\_{\text{const}} - \boldsymbol{\varrho}\_{\text{stat}}.\tag{14}
$$

In the case where the achieved value of the mean twist angle lies outside the insensitivity range ϕ*ins*, Δϕ > ϕ*ins*, but inside the fine tuning range ϕ*FT*, Δϕ ≤ ϕ*FT*, fine tuning is used. The value of the needed overpressure is then computed as

$$p\_{\rm TC} = p\_{\rm T} + X \cdot \Delta \boldsymbol{\varrho} \cdot \mathbf{c},\tag{15}$$

where *X* [Pa·rad−1] is a derivation of *pTC* according to Equation (13) by angle ϕ*const* and *c* [-] is a constant factor. The value of the constant factor *c* should be selected in the range (0; 1.

Derivation *X* is then computed as

$$X = -\frac{\sum\_{i=1}^{5} i \cdot a\_{i^\*} \cdot \varphi\_{\text{stat}}^{i-1}}{\left(S\_{\varepsilon} \cdot r\right)\_{\left(\varphi\_{\text{stat}}\right)}} - \frac{\left(M\_{\text{stat}} - M\_{G\left(\varphi\_{\text{stat}}\right)}\right) \cdot \sum\_{i=1}^{5} i \cdot b\_{i^\*} \cdot \varphi\_{\text{stat}}^{i-1}}{\left(\left(S\_{\varepsilon} \cdot r\right)\_{\left(\varphi\_{\text{stat}}\right)}\right)^2}. \tag{16}$$

The flowchart of the constant twist angle control algorithm is shown in Figure 7.

**Figure 7.** Flowchart of constant twist angle control algorithm.

The parameters of the algorithm can be set via the software graphic user interface of the ECTACS on a PC.


**2. Epidemiology**

with chronic HCV approaches 185 million. Until recently, the regimen of pegylated interferon (peg-IFN) and ribavirin (RBV) stood as the standard of care and is still commonly used as firstline therapy in some countries. This is rapidly changing. Direct acting antivirals (DAA) have altered the landscape dramatically. By understanding the genome of the HCV, scientists and researchers have been able to exploit its mechanism of transmission by creating inhibitors against several of the nonstructural proteins that are integral to HCV replication and function. Sustained virological response (SVR), which is commonly defined as a lack of HCV viral detection 12-24 weeks following treatment, with ribavirin and pegylated interferon alone, was marginal but has continued to improve. Despite the improvement, the introduction of DAAs has made the previously reported 50-70% SVR rates fall far short of rates achieved with DAAs.

> **Nucleos(t)ide NS5B Polymerase Inhibitors**

As it currently stands, four classes of DAA exist, which can be categorized according to the protein they inhibit. These four include inhibitors of the NS3/4 protease, NS5A polymerase, and NS5B polymerases (nucleoside and nonnucleoside). The approval of two NS3/4 protease inhibitors, telaprevir (TEL) and boceprevir (BOC), occurred in 2011 and marked the beginning of the age of DAAs. This was followed 2 years later by the approval of sofosbuvir (SOF), a nucleoside NS5B inhibitor, and simeprevir (SIM), an NS3/4 protease inhibitor, further ex‐ panded the available treatment options. In 2014, a combination of IFN-free regimen utilizing SOF and an NS5A inhibitor, ledipasvir (LED), was approved. Closely following this, the fourdrug combination pack of an NS5A inhibitor, NS3/4A inhibitor, and a nonnucleoside NS5B inhibitor of ombitasvir (OMB), paritaprevir (PARr), and dasabuvir (DAS), respectively, gained Food and Drug Administration (FDA) approval in the United States. In addition to the DAAs in the four-drug combination pack, ritonavir has been added due to its potent inhibition of

*Boceprevir* Daclatasvir Mericitabine *Dasabuvir Telaprevir* Elbasvir *Sofosbuvir* Deleobuvir *Simeprevir Ledipasvir* VX-135 Lomibuvir *Parotaprevir Ombitasvir* Tegobuvir Asunaprevir Samatasvir ABT-072 Faldaprevir ACH-2928 BMS-791325 Danoprevir BMS824393 GS-9669

Legend: Drugs in italics have received FDA approval as of January 2015

**Table 1.** FDA approved and investigated drugs by mechanism of action

**Nonnucleos(t)ide NS5B Polymerase Inhibitors**

**NS3/4 Protease Inhibitors NS5A Inhibitors**

58 Recent Advances in Liver Diseases and Surgery

Grazoprevir PPI-461 Sovaprevir PPI-668 Vedroprevir GS-5816

Adapted from www.hepatitis.va.gov

Vaniprevir IDX320

In the most recent National Health and Nutrition Examination Survey (NHANES), the estimated prevalence of HCV infection is approximately 3.6 million in the United States alone, with an estimated 2.7 of these having chronic infection. Worldwide, the World Health Organization (WHO) estimates that nearly 150 million people have chronic HCV infec‐ tion. In both the United States and worldwide, estimates likely fall significantly short given that nearly half of all infected patients have never been tested for HCV. Additionally, the incidence among prisoners and the homeless are not known and in less developed nations are often not recorded [1]. HCV is thought to be the causal factor of up to one-third of cases of cirrhosis worldwide [2, 3].

In a study done by Shepherd *et al.* [4], analysis of positive HCV seroprevalence throughout some of the most populous nations of the world revealed an overall worldly prevalence rate of 2%, or roughly 123 million people. Given the limitations that widespread detection and recording pose, one would expect the actual prevalence to be larger. Individual analysis of many nations including China, Pakistan, and Egypt revealed estimated HCV seroprevalence well above this range. Disease transmission patterns again reveal that the majority of trans‐ mission of HCV is thought to be from unscreened blood donation, injection drug use, unsafe therapeutic injection, or other health care-related procedures. As medical practices become safer and blood screening continues to occur, the rates of HCV transmission from injection drug use will become the predominant mode of transmission as it has in developed countries like Australia, England, and the United States. Despite its success in the United States, several barriers to improving the safety of blood transfusions have remained throughout nations across the world [4-6]. As it stands, the WHO's global database estimates that among the 97 of 164 countries that provided data, 89% of donated blood is being screened following basic quality procedures [7].

HCV cirrhosis remains the primary indication for liver transplant (LT) in the United States with over 15,000 patients currently listed on the United Network for Organ Sharing (UNOS) list [8]. In year 2013 alone, over 6,400 patients underwent LT in the United States, increasing steadily from 1,700 in 1988 [9]. The United States leads in amount of deceased donor liver transplantations followed by China, with roughly 2,000 in 2010 [10].


*Article* **A Novel Approach to Modeling and Forecasting Cancer Incidence and Mortality Rates through Web Queries and Automated Forecasting Algorithms: Evidence from Romania**

**Cristiana Tudor**

International Business and Economics Department, The Bucharest University of Economic Studies, 010374 Bucharest, Romania<EMAIL_ADDRESS>
**Simple Summary:** Cancer remains a global burden, currently causing nearly one in six deaths worldwide. Accurate projections of cancer incidence and mortality are needed for effective and efficient policymaking, accurate resource allocation, and to assess the impact of newly introduced policies and measures. However, the COVID-19 pandemic disrupted public health systems and caused a significant number of cancers to remain undiagnosed, thus affecting the quality of official statistics and their usefulness for health studies. This paper addresses this issue by proposing novel cancer incidence/cancer mortality models based on population web-search habits and historical links with official health variables. The models are empirically estimated using data from one of the most vulnerable European Union (EU) members, Romania, a country that consistently reports lower survival rates than the EU average, and are further used to forecast cancer incidence and mortality rates in the country. Research findings have important policy implications, and the novel framework, owing to its generalizability, can be applied to the same task in other countries. Overall, the results indicate a continuation of the increasing trends in cancer incidence and mortality in Romania and thus underline the urgency to change the status quo in the Romanian public-health system.

**Abstract:** Cancer remains a leading cause of worldwide mortality and is a growing, multifaceted global burden. As a result, cancer prevention and cancer mortality reduction are counted among the most pressing public health issues of the twenty-first century. In turn, accurate projections of cancer incidence and mortality rates are paramount for robust policymaking, aimed at creating efficient and inclusive public health systems and also for establishing a baseline to assess the impact of newly introduced public health measures. Within the European Union (EU), Romania consistently reports higher mortality from all types of cancer than the EU average, caused by an inefficient and underfinanced public health system and lower economic development that in turn have created the phenomenon of "oncotourism". This paper aims to develop novel cancer incidence/cancer mortality models based on historical links between incidence and mortality occurrence as reflected in official statistics and population web-search habits. Subsequently, it employs estimates of the web query index to produce forecasts of cancer incidence and mortality rates in Romania. Various statistical and machine-learning models—the autoregressive integrated moving average model (ARIMA), the Exponential Smoothing State Space Model with Box-Cox Transformation, ARMA Errors, Trend, and Seasonal Components (TBATS), and a feed-forward neural network nonlinear autoregression model, or NNAR—are estimated through automated algorithms to assess in-sample fit and out-of-sample forecasting accuracy for web-query volume data. Forecasts are produced with the overperforming model in the out-of-sample context (i.e., NNAR) and fed into the novel incidence/mortality models. Results indicate a continuation of the increasing trends in cancer incidence and mortality in Romania by 2026, with projected levels for the age-standardized total cancer incidence of 313.8 and the agestandardized mortality rate of 233.8 representing an increase of 2%, and, respectively, 3% relative to the 2019 levels. Research findings thus indicate that, under the no-change hypothesis, cancer will remain a significant burden in Romania and highlight the need and urgency to improve the status quo in the Romanian public health system.

**Citation:** Tudor, C. A Novel Approach to Modeling and Forecasting Cancer Incidence and Mortality Rates through Web Queries and Automated Forecasting Algorithms: Evidence from Romania. *Biology* **2022**, *11*, 857. https:// doi.org/10.3390/biology11060857

Academic Editors: Shibiao Wan, Yiping Fan, Chunjie Jiang and Shengli Li

Received: 9 April 2022 Accepted: 30 May 2022 Published: 3 June 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

**Keywords:** cancer; incidence; mortality; modeling; forecasting; Google Trends; Romania; ARIMA; TBATS; NNAR

#### **1. Introduction**

Cancer remains a primary cause of death worldwide [1] and acknowledged as a growing global burden [2]. Moreover, many healthcare systems in less developed countries are ill-equipped to adequately deal with this burden, and a huge percentage of cancer patients worldwide lack access to timely, high-quality diagnosis and treatment [3]. As of 2020, cancer accounted for approximately 10 million deaths worldwide, or nearly one in six deaths. Furthermore, cancer maintains its place as the second leading cause of death in many nations, trailing only cardiovascular disease [3–6]. Additionally, the number of cancer diagnoses and fatalities is expected to significantly increase over the next decade, with projections for 2030 indicating 26 million new cancer cases and 17 million cancer deaths per year [7].

Concurrently, cancer is one of the most critical economic and financial burdens that the globe faces today [8]. In the United States alone, national costs of cancer totaled USD 183 billion as of 2015, with projections that include only population growth indicating an increase of 34% by 2030, reaching USD 246 billion [9].

Consequently, with this escalating global burden, cancer prevention and cancer mortality reduction are counted among the most serious public health concerns of the twenty-first century [10]. In particular, the term "primary prevention" refers to measures to reduce the incidence of the disease, whereas "secondary prevention" refers to efforts to diagnose cancer early or to reduce second cancers among cancer survivors [11]. Accurate cancer projections for future time points are paramount for both primary and secondary prevention and are additionally critical for planning future services and resource allocation, as well as establishing and evaluating cancer control programs [12]. However, time series forecasting is a challenging task [13], whereas producing accurate estimates for the future rates of cancer incidence and mortality is additionally complicated due to the short time series available. For example, at the time of the study the Eurostat (i.e., the statistical office of the European Union) database provides statistics for cancer deaths at a European level spanning the period 2011–2018, whereas the World Development Indicators (WDI) database of the World Bank offers data on the mortality rate from cardiovascular disease, cancer, diabetes, or chronic respiratory disease, and thus does not individualize cancer. Additionally, with short series, out-of-sample forecasting accuracy is hard to assess, and time series cross-validation can be difficult to implement [14].

To solve such research obstacles, monitoring health-seeking behavior in the form of public interest indicated by online search queries has emerged as an essential technique for early identification of health problem occurrences throughout certain periods and geographies [15]. This in turn is based on the fact that the internet has grown in importance as a source of health information accessed by the world population [16,17]. As a direct result, Google Trends has become increasingly popular in health and medical research over the past decade [15,18].

Our data confirm the relevance of web searches for highlighting real occurrences of health problems. Thus, [1] indicates that the three most common types of cancer in 2020, in terms of new cases, were breast cancer with 2.26 million cases, lung cancer with 2.21 million cases, and colon and rectum cancer with 1.93 million cases. Concurrently, as reflected in Figure 1, these were the exact web queries related to the term "cancer" over recent years at the world level, confirming that Internet searches are an accurate reflection of health issue incidences.

**Figure 1.** Most common queries related to the search term "cancer": worldwide (April 2017– March 2022). Source of data: Google Trends. Estimation results using the "gtrendsR" package [19] in R software.

Moreover, a visualization of the global web-search interest reveals that most normalized searches emerged in countries that also reported the highest age-standardized cancer rates. Of note, to accurately comprehend the geography of search interest for a given keyword, the term should be searched across all the world's languages. However, Google Trends provides a specific tool capable of dealing with this issue, i.e., "Topics," which collects all related words, variant spellings, and names in other languages under a single label to help with comprehending topics in a multilingual setting. Topics can thus be particularly effective in combining translations into multiple languages under a single subject [20]. As such, we specified the topic "cancer" when sourcing Google Trends data. Thus, Figure 2 reflects the normalized number of internet searches over the most recent five years, confirming that the highest population interest in the topic "cancer" was encountered in countries including Australia, the US, and Ireland. On the other hand, WHO data confirm that Australia registered the world's highest age-standardized cancer rate at 452.4 cases per 100,000 people in 2020, followed by New Zealand (422.9), Ireland (372.8), and the United States (362.2).

**Figure 2.** Internet search interest for "cancer" at the world level: (April 2017–March 2022). Source of data: Google Trends. Map is based on estimation results and uses the packages "gtrendsR" [19] and "tmap" [21] in R software.

Additionally, studies increasingly confirm that many cancers remained undiagnosed as a result of healthcare system disruptions caused by the COVID-19 outbreak [22–24]. In this context, with official statistics failing to accurately capture the variation in incidence, people's search interest for specific symptomatology emerges as the most relevant indication of the health problem's occurrence.

In light of the above considerations, this study sourced Google Trends data to extract information on internet searches for the word "cancer" and employed it as a proxy to forecast cancer incidence rates. Google Trends (www.trends.google.com, accessed on 30 March 2022) is a web-based tool that shows the popularity of a search phrase in a certain location over time. It provides a time series index of the number of Google queries submitted in a given location. The query weight or share is calculated by dividing the overall query volume for a specific search term within a geographic region by the total number of searches in that region throughout the period in question. Following that, the result is scaled from 0 to 100. As a result, the maximum query share of a search phrase for a given period is normalized to 100, reflecting the point when the search was at its most popular. In conclusion, on a scale of 0–100, Google Trends calculates relative search interest (RSI), with 100 reflecting peak interest [25]. Ref. [26] explore the utility of Google Trends data to examine population web searches for cancer screening and conclude that web queries can capture awareness and interest in cancer screening. Thus, Google Trends data may complement traditional data collection and analysis about cancer screening and related interests, providing important scientific possibilities. However, given the aforementioned disruption of public health systems caused by COVID-19 that altered official statistics, we argue that Google Trends data can now be used as a substitute for traditional statistics, which further expands its scientific value.

Of note, among European countries, cancer survival is significantly lower in newer and less developed EU members from Central and Eastern Europe [27]. Higher death rates at the CEE level are caused by two main factors: delayed diagnosis and suboptimal treatment [28], which are in turn related to inefficient and underfinanced public health systems and lower overall economic development [29].The situation is particularly challenging in Romania, which continues to register a divergent trend in mortality rates relative to its EU counterparts, including in the CEE area [30]. Figure 3 shows that the age-standardized mortality rate from all cancers follows an increasing trend in Romania from 2011 to 2018, reflecting the inefficiency of the public healthcare system in the country, whereas most other CEE countries have managed to reverse the trend.

**Figure 3.** Trends in cancer mortality rates in selected CEE countries (2011–2018). Estimation results. Plot created in R software ("ggplots" function). Source of data: Eurostat.

Moreover, the excess mortality from the main types of cancer registered in Romania relative to the EU average is reflected by the difference in the five-year survival rates presented in Table 1. For example, whereas recent statistics show that the survival rate of breast cancer patients has rapidly increased over recent years, due to the availability of early diagnostic tools and treatment [31], Romania still reports significant health gaps, which is heavily influenced by the fact that there is no organized population screening for breast cancer in the country [30].

**Table 1.** The five-year survival rates from main types of cancer (Romania versus EU26).

Source of data: Romanian Ministry of Health (2021) [32].

A worrisome disaggregation also occurs between cancer incidence and mortality rates registered in Romania, which has not managed to reduce cancer mortality despite periods of decreased incidence and which further highlights the necessity and urgency of better policies aimed at providing an efficient and inclusive public health system (Figure 4, Panel a). Moreover, the implementation of join-point regression analysis, also known as changepoint regression or segmented regression analysis [33] to detect changing trends in cancer incidence (see for example [34–39]) further confirms that the incidence rate in Romania presents two join points in 2014 and 2017, leading to three periods with a different trend over the analysis period, as follows: a positive trend with a slope coefficient of 14.68 until 2014, a negative trend with a slope coefficient of −8.83 during 2014–2017, and a slightly increasing trend with a slope of 2.05 after 2017 (Figure 4, Panel b). Hence, whereas the incidence follows an increasing trend until the first join-point (i.e., 2014), a reversal is detected thereafter, and a decreasing trend is confirmed over the second segment (i.e., 2014–2017). However, the decreasing trend is reversed thereafter, as the incidence rate presents a subsequent rise. On the other hand, the join-point regression analysis found no join-point in the mortality rate, confirming the disaggregation between the two series.

Patient migration from CEE countries has grown with the implementation of a European Union Directive issued in 2011. According to this directive, European nationals are eligible to use European healthcare services in any of the European member states, and their treatments are covered (at least partially) by their home country's health insurance system [40]. As a result, a phenomenon called "oncotourism" or "cancer tourism" has emerged, whereas diagnosed patients move away from inefficient Eastern and Central European public healthcare systems, particularly from Romania, toward the private system or the healthcare systems of more developed EU countries [41].

**Figure 4.** *Cont*.

**Figure 4.** Trends in age-standardized cancer incidence and mortality rates in Romania (2010–2019) (panel **a**); join-points in cancer incidence rate (panel **b**). Source of data: Romanian Ministry of Health (2021) [32]. Chart in panel (**a**) is produced in Datawrapper. Chart in panel (**b**) is produced with the "ggplot" function in R software; join-point regression analysis is performed with the "segmented" package within R software.

Consequently, accurate predictions for cancer incidences are paramount for early detection and for issuing effective and more inclusive public health policies, especially in the most vulnerable EU members in the CEE area. Additionally, cancer incidence projections are also useful for planning health services and establishing a baseline for evaluating the impact of public health measures [42]. Thus, the main goal of this study is to develop cancer incidence/cancer mortality models, and subsequently to make use of websearch data extracted from Google Trends and its point estimates issued through an array of statistical and machine-learning models to ultimately produce accurate forecasts of cancer incidence and mortality rates, while taking a special focus on a vulnerable CEE country significantly plagued by this disease, i.e., Romania. From a methodological perspective, the robustness of results is assured through various approaches, such as: (i) the estimation of alternative predictive models (statistical and machine-learning); (ii) the assessment of the relative out-of-sample forecasting accuracy through the hold-out forecasting technique; (iii) the estimation of the Diebold-Mariano test for superior forecasting accuracy, and (iv) resampling Google Trends data and employing the sampling average for the webquery index.

Of note, the vast majority of previous research either employs one forecasting method or assesses the predictive ability of concurrent methods by estimating forecasting accuracy metrics. This study implements alternative predictive models, both statistical and machine learning, through automated forecasting algorithms. Moreover, the random sampling issue that arises from using Google Trends data is mitigated through resampling and averaging. Additionally, the forecasting results are defended against the Diebold-Mariano (DM) predictive accuracy test. Hence, various robustness checks confirm the reliability of current findings. Furthermore, the strand of literature on cancer research, particularly with a focus on Central and Eastern Europe, remains thin. Hence, whereas most related studies focus on developed countries, the current research contributes to filling the literature void and is thus concerned with a rather under-investigated EU member, Romania, a country that constitutes an interesting playing field for cancer research due to divergent trends relative to its EU counterparts and plagued by the worrisome phenomenon of "oncotourism". The proposed method is novel and carries the generalizability advantage, being suitable to further investigate other countries for which official statistics have been heavily affected by the coronavirus pandemic.

Thus, compared to previous studies, the contributions of the current research are threefold: (i) we develop two novel models to explain cancer incidence and cancer mortality rates that embed both official statistics and data on population health-seeking behavior as reflected in internet search habits, whereas most previous studies employ some version of the age-period-cohort model (APC) for the same task; (ii) we propose a robust and integrated approach for web query volume forecasting that includes statistical and machinelearning forecasting methods and assures the robustness of results through multiple model calibration on training and test datasets and estimation of multiple accuracy metrics; and (iii) we apply this novel framework to data from one of the most vulnerable EU members, Romania, a country increasingly defined by the phenomenon of "oncotourism", whereby diagnosed patients avoid the inefficient national public health system. We additionally provide evidence on the link between internet-seeking behavior and the incidence and mortality of the disease in Romania, thus contributing to the extent of infodemiological literature. Research findings have important policy implications, and the framework, owing to its generalizability, can be applied to the same task in other countries. The novel approach is particularly relevant in the aftermath of the COVID-19 pandemic, which has disrupted public health systems and caused a significant number of cancers to remain undiagnosed, thus affecting the quality of official statistics and their usefulness for health studies.

Results overall indicate a continuation of the increasing trends in cancer incidence and mortality in Romania, with a standardized cancer incidence rate of 313.8 by 2026 and a standardized cancer mortality rate of 233.8 by the same horizon, and thus underline the urgency to change the status quo in the Romanian public health system.

The paper continues as follows. Section 2 presents the data used in model development and explains the integrated method. Section 3 describes the empirical findings that emerge from implementing the novel-forecasting framework on the Romanian data. Section 4 discusses the main findings and, finally, Section 5 concludes the study.

#### **2. Materials and Methods**

In this study, we sourced annual data on Romanian cancer incidence and mortality rates spanning 2010–2019 from the Romanian Ministry of Health. Next, to develop a model capable of explaining and forecasting these relevant health indicators in the absence of reliable official statistics (which is a worldwide issue caused by the significant number of undetected cancer cases after the onset of the COVID-19 pandemic), we relied on previous infodemiological studies that acknowledge the population's internet search habits as a reliable proxy for the incidence of a health problem.

The Google Trends platform is a handy tool for determining the popularity of a specific search keyword among a particular demographic. In this study, we extracted the monthly volume of Google queries issued from Romania for "cancer" for the period spanning January 2005–March 2022. It should be acknowledged that Google Trends implements random sampling and uses only a fraction of the entire search data to construct a search index [43] Thus, to overcome the sample instability issue, multiple samples (i.e., 12) were sourced and the average of samples was used to construct the web-query index, instead of only one sample (see [44] for relevant details on the sample bias and its correction). However, it has also been recognized that the Google Trends sampling procedure produces reasonably precise estimates, and consequently, there is often no need to employ more than a single sample [45]. The web query time series contained 207 monthly observations.

The relationship between web searches and the health indicators of interest for Romania was assessed through the linear model given by Equation (1).

$$
\hat{y} = \mathbf{b}X + \mathbf{a} \tag{1}
$$

where *yˆ* is alternatively the cancer incidence rate, and subsequently the cancer mortality rate, and the independent variable is the web-query index.

Additionally, we used both linear and nonlinear statistical and machine-learning techniques, which allowed us to capture most of the properties of the web-query time series and further contributed to avoiding unreliable forecasts. Predictive models can be delineated into two main categories [46–48]: statistical and machine learning methods (self-learning systems that can learn from data and continuously increase performance), respectively. Thus, in this study, the autoregressive integrated moving average (ARIMA) model (Equation (2)), the Exponential Smoothing State Space Model with Box-Cox Transformation, ARMA Errors, Trend, and Seasonal Components (TBATS) given by Equation (3), and the neural network autoregression (NNAR) model reflected in Equation (4) were alternatively fitted.

An ARIMA(*p*,*d*,*q*)(*P*,*D*,*Q*)s model, first developed by [49], is given by:

$$\begin{pmatrix} (1 - \rho\_1 B - \dots - \rho\_p B^p)(1 - \Phi\_1 B^s - \dots - \Phi\_P B^{sP})(1 - B)^d(1 - B^s)^D Y\_l = \\ (1 - \theta\_1 B - \dots - \theta\_q B^q)(1 - \Theta\_1 B^s - \dots - \Theta\_P B^{sQ})\varepsilon\_l \end{pmatrix} \tag{2}$$

where *s* is the seasonal period, the lowercase and the capital letters represent nonseasonal and seasonal parameters, and *ε<sup>t</sup>* is a random variable with mean zero and the standard deviation *σ*.

A TBATS model [50] can accommodate complex seasonal behaviors of data [51] and is written as:

$$\text{TBATS}(\mathfrak{w}, p, q, \mathfrak{q}, \{\mathfrak{m}\_1, k\_1\}, \{\mathfrak{m}\_2, k\_2\}, \dots, \{\mathfrak{m}\_{\Gamma}, k\_{\Gamma}\}),\tag{3}$$

where ω is the Box-Cox transformation, *k* is the number of harmonics used for the seasonal trait, and *ϕ* is the dampening parameter.

Artificial neural networks (ANNs) are capable of simulating complicated real-world systems while properly accounting for nonlinearities [52]. Lagged values of time series are frequently utilized as inputs in an ANN structure when fitting time series data, which is then known as neural network autoregression (NNAR) [53] (Munim et al., 2019). As in [29,54], the NNAR model is written as:

$$Y = f(H) = f(\mathcal{W} \* X + B), \\ X = [y(t - 1), y(t - 2), \dots, y(t - p)] \tag{4}$$

where *Y* stands for the output vector, *f* is the activation function, *H* is the vector of n nodes in the hidden layer, *W* is the weight matrix between the input and hidden layers, *X* is the vector of inputs (i.e., the lagged values of the actual observations), and *B* is a bias vector.

All estimations are automated and performed in R software via dedicated algorithms included in the "forecast" package [55]. To implement the method robustly, the series of length N = 207 was first split into a training set (containing 187 observations) for insample fit purposes and a testing set (containing the last 20 observations) on which the models that reported the best fit on the training set were further estimated and their out-ofsample forecasting ability assessed. Lastly, we assessed the forecast accuracy of alternative predictive models by estimating both scale and scale-free accuracy metrics.

First, let us define the forecast error of a candidate model as:

$$e\_{T+h} = \mathcal{Y}\_{T+h} - \mathcal{Y}\_{T+h\mid T} \tag{5}$$

where {*y1*, . . . ,*yT*} is the training set data and {*yT*+*1*,*yT+2*, . . . } is the test-set data.

Then, the following forecasting accuracy metrics are computed as:

Mean absolute error:

$$MAE = \sqrt{\frac{1}{N} \sum\_{i=1}^{N} |y\_i - \mathcal{Y}\_l|} \tag{6}$$

Root mean squared error:

$$RMSE = \sqrt{\frac{1}{N} \sum\_{i=1}^{N} \left( y\_i - \hat{y}\_l \right)^2} \tag{7}$$

Mean absolute percentage error:

$$MAPE = mean(|p\_t|)\tag{8}$$

where: *p<sup>t</sup>* = 100*e<sup>t</sup> yt*

Mean absolute percentage error:

$$\text{MSE} = \text{mean}(|q\_j|) \tag{9}$$

where *qj* is given by as: *q<sup>j</sup>* = *et* 1 *N*−1 *N* ∑ *i*=2 |*yt*−*yt*−<sup>1</sup> | *f* when the series is non-seasonal and by: *et*

*q<sup>j</sup>* = 1 *N*−*m N* ∑ *i*=*m*+1 |*yt*−*yt*−*m*| when the time series is seasonal.

Lastly, all predictive models were fitted to the entire series of length N and point forecasts for the web query index for the following 4 years (i.e., a 48-month forecasting horizon) were produced by the overperforming method in the out-of-sample setting. Forecasted values were then fitted into the incidence/mortality models developed by estimating Equation (1), which then issued the expected values for standardized cancer incidence and mortality rates corresponding to the forecasting horizon. Figure 5 reflects the integrated method employed in this study and implemented in R software.

**Figure 5.** The integrated framework for modeling and forecasting cancer incidence and mortality rates.

#### **3. Results**

*3.1. Relationship between Related Web Queries and the Age-Standardized Cancer Incidence/Cancer Mortality Rate in Romania*

The best-fit linear model between the vector of web-query volume and the cancer incidence/cancer mortality rate is reflected in Figure 6, panels (a) and (b), respectively. Both representations highlight a positive link between the web-search interest and the variables reflecting the incidence and mortality of the disease. Additionally, both equations show a similar slope coefficient, equal to 0.47 in the incidence rate model, and equal to 0.46 in the mortality rate model.

**Figure 6.** The relationship (linear—blue line, polynomial—orange line) between related web queries and the age-standardized cancer incidence rate in Romania (panel **a**). The relationship (linear blue line, polynomial—orange line) between related web queries and the age-standardized cancer mortality rate in Romania (panel **b**). Source of data: Romanian Ministry of Health [32]. All estimations were performed in R software; plots were created in R software (i.e.,"ggplot" function).

#### *3.2. Results from Modeling and Forecasting the Web-Query Index*

Table 2 reports the estimated accuracy measures for the test-set data containing topic searches for "cancer" submitted in Romania that were issued through the statistical and machine-learning predictive models. Results indicate that NNAR has been able to accurately capture variations in data and thus provide the best forecast for the web query index over the testing window.

**Table 2.** Accuracy measures for the out-of-sample (test-set) forecasting performance.

To assess the forecasting superiority of the feed-forward neural network autoregression model, we estimated the Diebold-Mariano (DM) test [56,57] to examine any significant differences between forecasts produced by NNAR and the second best-performing model (ARIMA). The DM test result (estimated with the "dm.test" function within the "forecast" package in R software) confirmed that there was a significant difference between the distribution of errors from ARIMA and NNAR, thus ensuring the forecasting superiority of the machine-learning method.

We next employed the best-performing model in terms of out-of-sample forecasting accuracy (i.e., NNAR) to produce the expected web-query volume in Romania for the next 48 months (4 years), corresponding to the period spanning April 2022 to March 2026. Figure 7 reflects the estimation results, showing (in blue color) the point estimates produced by NNAR for April 2022–March 2026. Of note, estimations corresponding to the 48-month forecasting horizon indicated a continuation of the increasing trend in web searches related to "cancer" issued from Romania.

**Figure 7.** Forecasted trend over April 2022–March 2026 (48 months) for web queries for the term "cancer" in Romania issued with NNAR (12,6). Source: estimation results. Model information: average of 20 networks, each of which is a 12-6-1 network with 85 weight options.

## *3.3. Forecasts of Cancer Incidence and Cancer Mortality Rates in Romania over 2022–2026*

Lastly, we put together the linear relationship model estimated before and the point estimates produced by the neural network autoregression model (NNAR) to estimate the cancer incidence and cancer mortality rate for the next four years. It is important to underline that all estimations are based on the status quo hypothesis, implying that these projections are expected if no changes in public health policy are implemented. Projected values for the two health indicators are centralized in Table 3.

**Table 3.** Forecasted values for cancer incidence and cancer mortality rates.

We notice that estimations issued through the incidence and mortality models and based on NNAR projections of the related web-search index reflect a continuation of the increasing trends in cancer incidence and mortality in Romania, underlining the urgency to change the status quo in the Romanian public health system. Estimates thus indicate a standardized cancer incidence rate of 313.8 by 2026 and a standardized cancer mortality rate of 233.8 by the same horizon, increasing from levels of 307.7 and 227.1, respectively, registered in 2019.

#### **4. Discussion**

Approximately 10 million deaths have been attributed to cancer in 2020, or nearly one in six deaths. Concurrently, many cancer patients worldwide still lack access to timely, high-quality diagnosis and treatment. Within the EU, CEE countries consistently report higher mortality rates, mainly as a result of delayed diagnosis and suboptimal treatment. For Romania, statistics are particularly worrisome, with the country reporting significantly lower survival rates for all main types of cancer and also a divergent trend in mortality rates relative to its EU counterparts that have managed to reverse the increasing trend. Consequently, "oncotourism" is especially characteristic of Romania, as diagnosed patients move away from the inefficient public healthcare system toward the private system or the healthcare systems of more developed EU countries.

Consequently, accurate predictions of cancer incidence and mortality rates are keys to informing policymakers and assisting in the policymaking process. The main goal of this study is to develop a robust model capable of capturing the evolution of cancer incidence and mortality rates and forecasting their evolution. Concurrently, we build on [58] and acknowledge that over the past decade, the use of internet data has become an important aspect of health informatics, with online sources becoming more accessible and offering data that can be used to analyze and forecast human behavior. As a result, we also agree with [59] that data from tracking online information seekers' behavior is useful in public health surveillance and research.

Thus, in model development, the study made use of web-search data extracted from Google Trends, which was introduced as an independent variable in light of previous studies that acknowledge the population's internet search habits as a reliable proxy for health problem occurrence. Moreover, this approach overcomes the current issue of the unreliability of official statistics, caused on one hand by the numerous undiagnosed cases after the COVID-19 outbreak and, on the other hand, by the unavailability or tardiness of treatment for diagnosed patients, directly affecting the rate of incidence and mortality. Concurrently, point estimates for the web-query index were issued through the best performing predictive model over the test-set (i.e., out-of-sample), after an assessment of the in-sample fit and out-of-sample forecasting accuracy of various statistical and machine-learning models (ARIMA, TBATS, and NNAR) had been performed via several accuracy metrics (MAE, RMSE, MAPE, and MASE). Estimations indicated that NNAR was the most capable of capturing the time series characteristics and of producing the most accurate estimates. Consequently, estimations for the web-query index were automatically produced with the NNAR model and sourced into the incidence/mortality models that have been previously developed. Ultimately, forecasts of cancer incidence and mortality rates in Romania by 2026 were issued, indicating a continuation of the increasing trend for both variables. Our results are in line with projections of [32] the Romanian Ministry of Health (2021), confirming the ascendant trend, although our point estimates fall below the public ministry's predictions, indicating more conservative increasing rates.

Future predictions depend on multiple assumptions, most importantly on the status quo (i.e., no-change) hypothesis of the Romanian public health system. Similarly, forecasts do not consider the impact of relevant changes in impact factors, such as potential changes in smoking prevalence at the national level, changes in obesity, changes in alcohol consumption, changes in nutrition habits, increased funding of the public health system, increased screening, HPV vaccination, etc. As a result, we agree with [60] that it is critical to review predictions at regular intervals to incorporate the most recent trends in the data. However, similar to [42], we reason that current estimates do provide a useful baseline for the planning of cancer resources and for evaluating the impact of any changes produced in impact factors as a result of newly introduced public health policies and measures. Furthermore, as with most research, this study suffers from other limitations. Mostly, the use of Google Trends data does carry some vulnerabilities that should be acknowledged, including the construction of the search index itself [61]. As a consequence, the long-run stability of the time series is heavily dependent on the data's time frame and frequency. As per [61], this study used monthly data that was best able to accurately capture the long-term trend. Moreover, random sampling is an inherent bias in Google Trends data [44]. However, this issue is particularly troublesome in forecasting when dealing with topics that

are less frequently searched for, which is not the case in the current study. Additionally, the performed resampling further mitigated the bias. Nonetheless, it should be acknowledged that this approach merely minimizes the bias and does not eliminate it. Finally, it should be mentioned that results should be interpreted with care, considering that data reflect the search habits of the population that has Internet access, which in turn depends on income level and other socioeconomic factors. Overall, I argue that the popularity of the search topic, together with the resampling strategy and previous studies that reinforce the usefulness of web search data as a powerful predictive instrument [44] does allow for confidence in the current research findings.

In addition, it should also be mentioned that the link between cancer variables and the web-query index has been assessed through the classical regression model. However, it has been increasingly acknowledged that the neutrosophic regression model [62–65], which issues the parameters in the indeterminacy interval rage, can be more efficient in the uncertainty environment than the classical regression model [66]. Thus, the assessment of the historical link between cancer incidence/cancer mortality rates and the web search index through the neutrosophic regression model constitutes a good avenue for future research. The implementation of the proposed method on data specific to different gender and age groups, as well as to geographic regions of the country, could also reveal particularly vulnerable groups and/or areas and offer relevant information to policymakers.

From a policy perspective, the findings highlight that cancer will continue to be a significant burden for Romania, which should be carefully planned for. Complementarily, results indicate the need for better policies aimed at mitigating main risk factors such as smoking, alcohol consumption, obesity and overweight, unhealthy nutrition, lack of physical exercise, etc., and at increasing the financing and efficiency of the public health system by allocating future resources for cancer research, treatment, and prevention.

#### **5. Conclusions**

In conclusion, this study developed two novel cancer incidence/cancer mortality models based on population web-search habits and historical links with official health variables. The models were empirically estimated using data from one of the most vulnerable European Union (EU) members, Romania, and further used to forecast cancer incidence and mortality rates in the country by employing estimates for the web-search query index issued through the best performing out-of-sample forecasting method (NNAR). Research findings have important policy implications, and the novel framework, owing to its generalizability, can be applied to the same task in other countries. It provides the important advantage of overcoming a current issue related to the quality of official statistics in the aftermath of the COVID-19 pandemic that disrupted public health systems and caused a significant number of cancers to remain undiagnosed. Overall, the results indicate a continuation of the increasing trends in cancer incidence and mortality in Romania and thus underline the urgency to change the status quo in the Romanian public health system.

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

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Data employed in this study are publicly available from the Eurostat database, from Google Trends, and the Romanian Ministry of Health.

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

#### **References**