RM3 A Comparison Between Markov Chains and System Dynamics Modeling for the Estimation of Metabolic Syndrome Costs in a Public Health Care Delivery Organization in MÉxico

Abstract

The objective of this study was to compare life-time costs for a population obtained through Markov chain (MC) and system dynamics (SD) methodologies. While both methodologies are based on the concepts of state and transition, the meanings of each differ. The importance of this study lies in the fact that in some cases information is available for one type of model or the other, and the possibility of using either tool for modeling a situation is of pragmatic interest. Models of increasing degrees of complexity were developed. At each level of complexity, a MC model and a SD model were developed and the differences in results obtained were compared. SD models were simulated with Vensim software and MC models with TreeAge Pro software. Data were drawn from an institutional survey and from literature. An important issue in this comparison is that Markov models are based on transition probabilities while system dynamic models rely on material flows. Also, simulation techniques differ in that Montecarlo methods move a patient trough the model until it exits before including another patient, while SD models treat all patients in the cohort simultaneously. Thus, transformations for the set of mathematical expressions in each modeling methodology may lead to similar numerical results while not being conceptually equivalent. The simplest models led to equivalent aggregate numerical results. In these cases, the probability of leaving state Sn (MC) is numerically equivalent to inverse residence time (SD). More complex models required adapting the structure of one to be equivalent to the other. Applications of each methodology overlap at a certain aggregation level. When a long period is studied and not much detail is required in each state, SD seems an appropriate tool. When more precision is needed for individual patients, MC analysis seems a better choice.