Characterizing Heterogeneity Bias in Cohort-Based Models

Purpose: Previous research using numerical methods suggested that use of a cohort-based model instead of an individual-based model can result in significant heterogeneity bias. However, the direction of the bias is not known a priori. We characterized mathematically the conditions that lead to upward or downward bias. Method: We used a standard three-state disease progression model to evaluate the cost effectiveness of a hypothetical intervention. We solved the model analytically and derived expressions for life expectancy, discounted quality-adjusted life years (QALYs), discounted lifetime costs and incremental net monetary benefits (INMB). An outcome was calculated using the mean of the input under the cohort-based approach and the whole input distribution for all persons under the individual-based approach. We investigated the impact of heterogeneity on outcomes by varying one parameter at a time while keeping all others constant. We evaluated the curvature of outcome functions and used Jensen’s inequality to determine the direction of the bias. Results: Both life expectancy and QALYs were underestimated by the cohort-based approach. If there was heterogeneity only in disease progression, total costs were overestimated, whereas QALYs gained, incremental costs and INMB were under- or overestimated, depending on the progression rate. INMB was underestimated when only efficacy was heterogeneous. Both approaches yielded the same outcome when the heterogeneity was only in cost or utilities. Conclusion: A cohort-based approach that does not adjust for heterogeneity underestimates life expectancy and may underestimate or overestimate other outcomes. Characterizing the bias is useful for comparative assessment of models and informing decision making.