Markov Models, Applications to Medical Decision Making

The basic purpose of a decision model is to estimate the prognosis of a patient or a population of patients subsequent to each alternative choice of management strategy being compared. For practical reasons, the analysis must be restricted to a time frame, often referred to as the time horizon of the analysis. The time horizon may be finite (e.g., 5 years from the time of decision) or may be indefinite or defined in operational terms such as “for the remainder of the patient's life” or “until all patients in the population are dead.” The choice of time horizon is determined by many factors, including the time frame of events of interest, the availability of data, and the perspective of the analysis. When the time horizon is the remaining lifetime, then the model must represent the prognosis following each management strategy that incorporates all future events in the patients' lives.

There are various ways in which a decision analyst can assign values to these terminal nodes of the decision tree. In some cases, the outcome measure is a simple life expectancy. One method for estimating life expectancy is the declining exponential approximation of life expectancy (DEALE), which calculates a patient-specific mortality rate for a given combination of patient characteristics and comorbid diseases. Life expectancies may also be obtained from Gompertz models. In the reference case recommended by the Panel on Cost-Effectiveness Analysis, prognosis is modeled as quality-adjusted life expectancy, in which the prognosis incorporates both quantity and quality of life. For health economic analyses, economic costs must also be assigned to each strategy being compared.

Various modeling techniques can be used to estimate prognosis. This entry introduces the Markov model as an alternative to simple decision tree models and discusses the assumptions inherent in Markov models, how they are evaluated, and how they are used in decision models to determine prognosis.