Controlling for Differential Regression-To-The-Mean via Propensity Scores: A Simulation Study

Regression-to-the-mean (RTM) is a statistical phenomenon that may occur in epidemiologic studies where inclusion in the study cohort is contingent upon experiencing a laboratory/clinical measurement beyond a defined threshold. When differential across treatment groups, RTM could bias the final study estimate. This poses substantial challenges in observational studies that index patients upon experiencing extreme laboratory or clinical values. Our objective was to investigate propensity score-based methods as a tool for mitigating this source of bias via simulation.

We simulated a noninterventional comparative effectiveness study, comparing treatment with romiplostim to standard-of-care therapies for immune thrombocytopenia (ITP), a disease characterized by low platelet counts. Platelet counts were generated from normal distributions according to the underlying ITP severity, a strong confounder of treatment and outcome. Patients were assigned treatment probabilities based upon ITP severity, which created varied levels of differential and non-differential RTM. Treatments were compared via the difference in median platelet counts during 23 weeks of follow-up. We calculated four summary metrics of the platelet counts measured prior to cohort entry and built six propensity score models to adjust for those variables. We adjusted for these summary metrics using inverse probability of treatment weights.

Across all simulated scenarios, propensity score adjustment reduced bias and increased precision of the treatment effect estimator. Adjusting for combinations of the summary metrics was most effective at reducing bias. Adjusting for the mean of prior platelet counts or the difference between the cohort-qualifying platelet count and the largest prior count eliminated the most bias when assessed individually.

These results suggest that differential RTM could be reasonably addressed by propensity score models with summaries of historical laboratory values. This approach can be easily applied to any comparative effectiveness or safety study, though investigators should carefully consider the best summary metric for their data.