Time-dependent propensity score and collider-stratification bias: Inhaled beta2-agonist and risk of coronary heart disease

Background: In observational studies of time-varying exposure and confounders, the use of propensity score (PS) is limited to assigning weights as in marginal structural models (MSMs). 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. Objectives: We explored collider-stratification and confounding bias due to conditioning or stratifying on timedependent PS in a clinical example on the effect of inhaled short and long-acting beta2-agonist use (SABA and LABA, respectively) on coronary heart disease (CHD). Methods: A cohort of patients with an indication for SABA and/or LABA use was extracted from the Netherlands University Medical Center Utrecht General Practitioner Research Network. Information from 1995 to 2005 was used. SABA and LABA use and potential confounders were ascertained on 3 month intervals. Follow-up began the first day of diagnosis of bronchitis, asthma, or COPD and ended at the occurrence of CHD, death, unregistration with the GP, or end of the study, whichever occurred first. HR were estimated using PS stratification as well as covariate adjustment and compared with those of MSMs in both SABA and LABA separately. In MSMs, censoring was accounted for by including inverse probability of censoring weights. Results: 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, 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. Conclusions: Results were similar for different PS methods, but systematically higher than those of MSMs. When treatment and confounders vary during follow-up, conditioning or stratification on time-dependent PS may induce substantial collider-stratification or confounding bias. Hence, the use of methods such as MSMs is recommended.