BIAS ASSOCIATED WITH EVENT-HISTORY HETEROGENEITY IN MARKOV MODELS

Purpose: To assess tradeoffs between model bias and complexity in Markov cohort models that represent lifetime patterns of chronic, episodic conditions – such as depression or substance abuse – by incorporating the effect of event history on relapse risk.

 Methods: We developed a generic Markov cohort model of hypothetical event risk, for which all subjects enter “well” and free of prior events. Each annual cycle, individuals face probabilities of event occurrence, recovery, relapse, and death from any cause. The outcome of interest is cumulative time in event (CTE) with versus without two hypothetical interventions (preventing vs. treating relapses). We ran the model while varying the number of event recovery/recurrence from 3 to 10, using 10 as the gold standard against which to compare results. We evaluated results given changes in five model parameters: baseline event risk; relapse risk as a function of number of prior events; intervention type; recovery rate; and event-specific mortality. Bias was defined as the percent change in benefit (difference in CTE) with the limited model vs. the gold-standard model.

 Results: Using reasonable input parameters, an intervention that prevented events by 10% reduced cumulative event time by 2 years, and treatment that increased recovery by 10% yielded a benefit of 0.2 years. The direction of bias associated with incorporating fewer than 10 relapse episodes in the prevention intervention depended on whether the last episode was allowed to recover or not. The bias was always negative – indicating underestimated benefit – for the treatment intervention. When relapse risk equaled baseline risk or increased as uniform or exponential functions of prior history, absolute bias with prevention reached 92%, 183%, and 123%, respectively, and 3%, 106%, and 54% for treatment. Bias was greatest for high recovery rates and low event-specific mortality in both interventions, as well as with low baseline-incidence for prevention and high baseline-incidence for treatment. With all parameter variations, absolute bias and benefit were greater with prevention compared with treatment.

Conclusions: Failing to incorporate adequate number of relapses and the full effects of event history on relapse risk in Markov modeling can substantially impact model outcomes. When incorporating fewer recovery/relapse episodes, the potential benefits of prevention programs may be wrong by up to 2-fold, and those of treatment programs may be underestimated by up to 50%.