1. Introduction
Knowledge of the intima-media (IMT) growth process is essential for decision making regarding statin therapy initiation and intensification. The purpose of our study is to assess whether the mathematical modeling of IMT growth, proposed in [
1,
2], can assist clinicians at crucial stages of the process.
Thickening of the intima-media complex, which is an undisputed symptom of atherosclerosis, is an inevitable consequence of the process of aging of the human vascular system. The age-related changes can be observed at both micro- and macro-levels. At the micro-level, cellular senescence manifests as reduced cell proliferation, an irreversible arrest of growth, apoptosis, DNA damage, etc. [
3]. At the macro-level, atherosclerotic plaques with calcium deposits can be detected by imaging examinations applied routinely in clinical practice; see [
4]. The deposits are of clinical significance, as they are the final stage of vascular degeneration.
Clearly, many factors contribute to atherosclerosis development; see e.g., [
5]. In particular, there are some inherited predisposing factors and other factors that may be modified by our lifestyle, which include diet; physical activity; and adherence to recommendations of optimal management of many atherosclerosis-modifying diseases, such as arterial hypertension, diabetes, and hyperlipidemia—see [
6].
According to our knowledge, it is very difficult, if at all possible, to regress atherosclerotic plaque development. However, in some cases, doctors are able to stabilize the plaque and, therefore, inhibit disease progression. This can happen if intensive treatment with high-dose statins is applied; see [
7].
However, doubts surrounding the dosage of statins and the therapy timing remain. A few years ago, a cohort study [
8] on the general UK population reported statin overuse in patients with low cardiovascular risk and underuse in patients with high cardiovascular risk. Furthermore, another study (see [
9]) points to possible adverse events, such as muscle and liver injury, cognitive impairment, new-onset diabetes mellitus, and even hemorrhagic stroke, as a result of long-term statin therapy. Moreover, there is no strong clinical evidence that the elderly would benefit from statin therapy; see [
10]. Statin therapy should be individualized and based on the patient’s risk profile. This study uses a model that may alleviate the above concerns.
The measurement of the carotid artery IMT can be achieved by the simple and noninvasive technique of measuring atherosclerotic burden [
11]. Consequently, IMT has been utilized as a reliable marker of drug efficiency and tested in clinical trials devoted to atherosclerosis treatment. Moreover, IMT is widely accepted as a screening tool that can be used together with the traditional risk factors assessment. The size and dynamics of IMT can help in determining optimal therapeutic interventions as well as in the application of other diagnostic tools; see [
12]. Although there are studies that have presented a discrepancy between carotid IMT changes, prognosis, and the course of cardiovascular pathologies [
13,
14], the overwhelming clinical data (see [
15,
16,
17,
18,
19]) strongly confirm that the IMT will continue to be used as a valuable tool in clinical research.
It was conjectured in [
1] that the IMT growth process follows an S-shape (i.e.,
logistic) curve. An application of a mathematical model based on this proposition to atherosclerosis management by statins was developed in [
2]. However, the number of observations in [
1] of the logistic model being calibrated was low (27); therefore, the quantitative reasoning based on that model was mainly of conceptual value rather than being immediately applicable to management of atherosclerosis. The recent availability of the large Cardio Poznan Database (122 observations) [
20] has created an opportunity for us to perform a new calibration of the logistic model from [
1] and provide some managerial advice.
In the next section, we describe briefly the Cardio Poznan Database, the source of our new data. Then,
Section 3 discusses the new data support for the S-shaped IMT growth. Subsequently, in
Section 4, we propose a procedure for inferring an optimal age to start statin treatment for a particular group of patients. The paper ends with brief Concluding Remarks and an Appendix, which contains a few summary statistics concerning the observations gathered in the database.
2. Cardio Poznan Data
The data collection project, see [
20], received a positive opinion (decision No. KB 341/21) of the Bioethics Committee of the Poznan University of Medical Sciences.
The data collection involved 122 consecutive patients: 78 males (63.9%) and 44 females (36.1%). Their mean age was 49.6 years, and the standard deviation was 15.6 years. These patients were treated in the Department of Hypertension and Angiology and Internal Medicine at the Poznan University of Medical Sciences in the first quarter of 2020. From this group, we selected the male subjects (n = 31) who had arterial hypertension-related cardiac disease, i.e., coronary artery disease (CAD) and/or vascular complications, such as peripheral vascular disease (PVD). This group of 31 male patients represents the observation sample for our study. These patients are referred to as severely sick men. They are split into two subgroups: (1) patients undergoing statin therapy, denoted as statin(+), and (2) patients not treated with statins, denoted as statin(-).
We provide a summary of the demographic and clinical data of the studied patients in
Appendix A,
Table A1. The findings of the laboratory tests and imaging examinations (carotid artery Doppler ultrasonography) are provided in
Table A2.
5. How to Infer an Optimal Age for Starting Statin Treatment
We have previously proposed that the optimal patient age for a specific group of patients to start statin treatment is when the curve is at its steepest. This seems the best locus on the S-curve to prevent it from rising or, in clinical terms, to prevent IMT from thickening.
Figure 1,
Figure 2,
Figure 3 and
Figure 4 can help to find such loci for a specific group of patients.
The patterns of the speed of plaque formation differ between the aggregate of the severely sick patients and the non-medicated patients. We can see these speeds in
Figure 5: the solid line represents the patient aggregate and the dash-dotted line the non-medicated patients. The dashed line indicates patients on statin; see the next section.
The maximum speed of the plaque formation for the non-medicated patients (a) is higher than the patients’ aggregate i.e., for the former and latter group and (b) occurs 17 years earlier for the former and latter groups.
We claimed in Proposition 2 that 38 years of age (see infl. point in
Table 2) is the right age to start statin treatment in the aggregated group. Our argument is that a decrease—induced by treatment—in the slope of the IMT logistic curve is most efficient when the curve is at its steepest, whereby the efficiency concerns lowering the future IMT levels. Beginning treatment of non-medicated patients at the young age of 21 years old (see infl. point in
Table 3) appears to be early. However, as judged by the logistic curve in
Figure 3, these patients do not need medication. Arguably, their own bodies manage to considerably slow down plaque growth at this age. Just after the inflection point, we can see in
Figure 5 that the dash-dotted (red) line quickly drops far below the other lines. The corresponding graph of the plaque formation in
Figure 3 flattens as if these non-medicated patients were submitted to treatment. In fact, one could claim that it is their own bodies that generate this plaque formation pattern.
Briefly, an analysis of IMT slopes can help in making decisions regarding the best patient age for commencing statin treatment. The steepest slope can be learned from the slope’s first derivative graph (see
Figure 5). The steepest slope is where the derivative attains a maximum.
6. Limitations and Strength of This Study
An important limitation of our study is that it concerns male patients only. The reason for this is that the female population was less represented in [
20]. Furthermore, the female patient population is less homogeneous than the male patient population in that their symptoms associated with cardiovascular pathologies are more variable and therefore more difficult to calibrate in the model than those of male patients.
Another limitation is related to the patient sample size in [
20]. Although significantly larger than that in [
1], our sample size is modest when compared with that of international studies; see e.g., the JUPITER trial [
23]. With more patients in the database, perhaps augmented by a population-based study, we would be able to attempt to model IMT growth in female patients.
Notwithstanding these limitations, we strongly believe that the male patient sample size we used in this study was sufficient to validate the model proposed and explained in [
1,
2]. The results of the biostatistical data analyzed in this paper should assure clinicians regarding our model’s usefulness.