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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.

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The authors thank Stephen Cole for comments on an earlier version of this work. This study was funded by the Canadian Institutes of Health Research (CIHR) and the Canadian Foundation for Innovation. Robert Platt holds a Chercheur-boursier award from the Fonds de Recherche en Sante du Quebec (FRSQ) and is a member of the Research Institute of the McGill University Health Centre, which receives operating funds from the FRSQ.

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The authors declare no conflict of interest.

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Ethical review for this study was done by the Independent Scientific Advisory Committee for MHRA database research.

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Correspondence to Robert William Platt.

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Platt, R.W., Delaney, J.A.C. & Suissa, S. The positivity assumption and marginal structural models: the example of warfarin use and risk of bleeding. Eur J Epidemiol 27, 77–83 (2012).

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  • Causal modeling
  • Bias
  • Warfarin
  • Positivity assumption
  • Inverse probability weighting