Bias Associated with Failing to Incorporate Dependence on Event History in Markov Models

Purpose. When using state-transition Markov models to simulate risk of recurrent events over time, incorporating dependence on higher numbers of prior episodes can increase model complexity, yet failing to capture this event history may bias model outcomes. This analysis assessed the tradeoffs between model bias and complexity when evaluating risks of recurrent events in Markov models. Methods. The authors developed a generic episode/relapse Markov cohort model, defining bias as the percentage change in events prevented with 2 hypothetical interventions (prevention and treatment) when incorporating 0 to 9 prior episodes in relapse risk versus a model with 10 such episodes. Magnitude and sign of bias were evaluated as a function of event and recovery risks, disease-specific mortality, and risk function. Results. Bias was positive in the base case for a prevention strategy, indicating that failing to fully incorporate dependence on event history overestimated the prevention’s predicted impact. For treatment, the bias was negative, indicating an underestimated benefit. Bias approached zero as the number of tracked prior episodes increased, and the average bias over 10 tracked episodes was greater with the exponential compared with linear functions of relapse risk and with treatment compared with prevention strategies. With linear and exponential risk functions, absolute bias reached 33% and 78%, respectively, in prevention and 52% and 85% in treatment. Conclusion. Failing to incorporate dependence on prior event history in subsequent relapse risk in Markov models can greatly affect model outcomes, overestimating the impact of prevention and treatment strategies by up to 85% and underestimating the impact in some treatment models by up to 20%. When at least 4 prior episodes are incorporated, bias does not exceed 26% in prevention or 11% in treatment.