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Mathematical models are able to reflect biological processes and to capture epidemiologic data. Thus, they may help elucidate roles of risk factors in disease progression. We propose to account for smoking, hypertension, and dyslipidemia in a previously published process-oriented model that describes the development of atherosclerotic lesions resulting in myocardial infarction (MI). The model is sex-specific and incorporates individual heterogeneity. It was applied to population-based individual risk factors and MI rates (Cooperative Health Research in the Region of Augsburg (KORA) study) together with subclinical atherosclerotic lesion data (Pathobiological Determinants of Atherosclerosis in Youth (PDAY) study). Different model variants were evaluated, testing the association of risk factors with different disease processes. Best fits were obtained for smoking affecting a late-stage disease process, suggesting a thrombogenic role. Hypertension was mainly related to complicated, vulnerable lesions. Dyslipidemia was consistent with increasing the number of initial lesions. By accounting for heterogeneity, individual hazard ratios differ from the population average. The mean individual hazard ratio for smoking was twice the population-based hazard ratio for men and even more for women. Atherosclerotic lesion progression and MI incidence data can be related in a mathematical model to illuminate how risk factors affect different phases of this pathological process., (© The Author(s) 2022. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health.)

Analyzing epidemiological data with simplified mathematical models of disease development provides a link between the time-course of incidence and the underlying biological processes. Here we point out that considerable modeling flexibility is gained if the model is solved by simulation only. To this aim, a model of atherosclerosis is proposed: a Markov Chain with continuous state space which represents the coronary artery intimal surface area involved with atherosclerotic lesions of increasing severity. Myocardial infarction rates are assumed to be proportional to the area of most severe lesions. The model can be fitted simultaneously to infarction incidence rates observed in the KORA registry, and to the age-dependent prevalence and extent of atherosclerotic lesions in the PDAY study. Moreover, the simulation approach allows for non-linear transition rates, and to consider at the same time randomness and inter-individual heterogeneity. Interestingly, the fit revealed significant age dependence of parameters in females around the age of menopause, qualitatively reproducing the known vascular effects of female sex hormones. For males, the incidence curve flattens for higher ages. According to the model, frailty explains this flattening only partially, and saturation of the disease process plays also an important role. This study shows the feasibility of simulating subclinical and epidemiological data with the same mathematical model. The approach is very general and may be extended to investigate the effects of risk factors or interventions. Moreover, it offers an interface to integrate quantitative individual health data as assessed, for example, by imaging., (© 2021 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.)

We propose a stochastic model for use in epidemiological analysis, describing the age-dependent development of atherosclerosis with adequate simplification. The model features the uptake of monocytes into the arterial wall, their proliferation and transition into foam cells. The number of foam cells is assumed to determine the health risk for clinically relevant events such as stroke. In a simulation study, the model was checked against the age-dependent prevalence of atherosclerotic lesions. Next, the model was applied to incidence of atherosclerotic stroke in the cohort of male workers from the Mayak nuclear facility in the Southern Urals. It describes the data as well as standard epidemiological models. Based on goodness-of-fit criteria the risk factors smoking, hypertension and radiation exposure were tested for their effect on disease development. Hypertension was identified to affect disease progression mainly in the late stage of atherosclerosis. Fitting mechanistic models to incidence data allows to integrate biological evidence on disease progression into epidemiological studies. The mechanistic approach adds to an understanding of pathogenic processes, whereas standard epidemiological methods mainly explore the statistical association between risk factors and disease outcome. Due to a more comprehensive scientific foundation, risk estimates from mechanistic models can be deemed more reliable. To the best of our knowledge, such models are applied to epidemiological data on cardiovascular diseases for the first time.