Stochastic Trees

Abstract

This paper introduces stochastic trees, a new modeling approach for the class of medical decision problems in which risks of mortality and morbidity may extend over time. A stochastic tree may be regarded as a continuous-time version of a Markov-cycle tree, or alternately, as a multi-state DEALE model. Optimal decisions in stochastic trees can be determined by rollback, much in the same fashion as decision trees. The author discusses how age-dependent mortality rates and declining incidence rates may be modeled using stochastic trees. Concepts are illustrated using examples from the medical literature. It is argued that stochastic trees possess important advantages over Markov-cycle trees for medical decision modeling.