A Novel Approach for Minimizing Immortal Time Bias in Observational Studies

OBJECTIVES: To describe a novel and innovative approach that uses propensity scores to minimize immortal time bias.

METHODS: Immortal time arises when the determination of a patient’s treatment status involves a waiting period. A bias is introduced when this period is unaccounted for in the assessment of treatment effectiveness and/or safety. We classified treatment status at cohort entry (ie, time=t₀) based on whether or not the patient initiated treatment at any time during the study period, with actual treatment initiation time as t₁ (ie, t₁≥t₀). We simulated data for multiple scenarios with fixed treatment effects in three hazard ratio (HR) settings (HR=0.5, 1, and 3), that included the following variables (with varying values): waiting period (1-24 months), proportion of treated patients (10-50%), and two independent covariates. We derived two sets of propensity scores on each patient. Firstly, PS₀ at t₀ to construct blocks of comparable patients. For each treated patient, the closest untreated patient on PS₀ among those who survived up to t₁ was selected by 1:1 greedy matching. Secondly, with t₁ as start of follow-up for the treated and untreated patients in that block, we derived PS₁ and used inverse probability treatment weighting (IPTW) to address confounding. The percentages of residual bias were compared to those from three approaches: unadjusted (crude), landmark with IPTW (LMK), and time-dependent Cox with covariates adjustment (TDC).

RESULTS: Our approach yielded the lowest median percentage of residual bias across all scenarios (HR=0.5: 2.8% vs 82.4% for crude, 12.4% for LMK, 10.6% for TDC; HR=1: 4.0% vs 83.2% for crude, 4.6% for LMK, 12.1% for TDC; HR=3: 4.2% vs 73.7% for crude, 36.7% for LMK, 14.8% for TDC).

CONCLUSIONS: Our results suggest that the propensity score is an effective design tool for minimizing immortal time bias.