Time-dependent propensity score and collider-stratification bias: an example of beta₂-agonist use and the risk of coronary heart disease

Stratification and conditioning on time-varying cofounders which are also intermediates can induce collider-stratification bias and adjust-away the (indirect) effect of exposure. Similar bias could be expected when one conditions on time-dependent PS. We explored collider-stratification and confounding bias due to conditioning or stratifying on time-dependent PS using a clinical example on the effect of inhaled short- and long-acting beta₂-agonist use (SABA and LABA, respectively) on coronary heart disease (CHD). In an electronic general practice database we selected a cohort of patients with an indication for SABA and/or LABA use and ascertained potential confounders and SABA/LABA use per three month intervals. Hazard ratios (HR) were estimated using PS stratification as well as covariate adjustment and compared with those of Marginal Structural Models (MSMs) in both SABA and LABA use separately. In MSMs, censoring was accounted for by including inverse probability of censoring weights.The crude HR of CHD was 0.90 [95 % CI: 0.63, 1.28] and 1.55 [95 % CI: 1.06, 2.62] in SABA and LABA users respectively. When PS stratification, covariate adjustment using PS, and MSMs were used, the HRs were 1.09 [95 % CI: 0.74, 1.61], 1.07 [95 % CI: 0.72, 1.60], and 0.86 [95 % CI: 0.55, 1.34] for SABA, and 1.09 [95 % CI: 0.74, 1.62], 1.13 [95 % CI: 0.76, 1.67], 0.77 [95 % CI: 0.45, 1.33] for LABA, respectively. Results were similar for different PS methods, but higher than those of MSMs. When treatment and confounders vary during follow-up, conditioning or stratification on time-dependent PS could induce substantial collider-stratification or confounding bias; hence, other methods such as MSMs are recommended.