The positivity assumption and marginal structural models: the example of warfarin use and risk of bleeding

Estimates of the average causal effect (ACE) of warfarin on the risk of bleeding may be confounded by indication as patients at high risk of bleeding are unlikely to be prescribed warfarin. One approach to estimating the ACE is inverse probability of treatment weighting (IPTW). This study was designed to examine the use of IPTW in this setting, and to demonstrate problems with the violation of the positivity assumption. We analyzed a case-control study on 4,028 cases of gastro-intestinal bleeding and 79,239 controls set in the United Kingdom's General Practice Research Database. Warfarin exposure was defined as a prescription issued in the 90 days before the index date. Secondary analyses were conducted restricted to patients more likely to receive warfarin and with a truncated weight distribution, to exclude subjects highly unlikely to be treated. The estimated association between warfarin use and bleeding was stronger with IPTW [odds ratio (OR): 17.2; 95% confidence interval (CI): 6.5-37.7] than with a standard logistic regression model (OR: 2.1; 95% CI: 1.7-2.5). The presence of large weights (five subjects with stabilized weight > 500) indicated a potential violation of the positivity assumption. In the restricted analysis, both IPTW (OR: 2.0; 95% CI: 0.4-9.6) and standard regression (OR: 1.6; 95% CI: 1.3-2.0) were compatible with a meta-analysis of randomized trials inverse probability of treatment weighting is sensitive to the positivity assumption; however, such sensitivity may assist in diagnosing off-support inference.