Indeed, Morgan and Todd ( 2008) warn that applying the propensity score methods without due attention to the underlying assumptions, under the justification that these models are more advanced than the unweighted analysis (dubbed naïve henceforth), may provide a worse biased estimate. It has been suspected that the IPSW lacks robustness against the misspecification of these assumptions (Rubin 2004). The second is known as the overlap assumption (Hernán and Robins 2020), which indicates that after IPSW rebalance, the distributions of the baseline covariates are comparable between the treated and control groups (McDonald et al. The first one is the ignorability restriction, which implies that there is no unobserved covariate that affects both the outcome and treatment simultaneously (Rosenbaum and Rubin 1983 Joffe et al. Specifically, the performance of IPSW critically depends on the ‘strongly ignorable treatment assignment’ condition, which requires the validity of two main assumptions. In practice, however, the approach requires strong assumptions in order to successfully balance baseline covariate differences and allow estimation of the treatment effect with reduced selection bias (Rosenbaum and Rubin 1983 Frölich 2007). The use of IPSW is theoretically appealing as it intends to make the groups comparable (Kovesdy et al. IPSW uses weights based on the propensity score to balance baseline covariates between the treated and control groups so that the two groups are similar in terms of pre-treatment covariates (Joffe et al. In particular, the inverse propensity score weighting, under the potential outcomes approach, has been widely used to address the selection bias of the estimated average treatment effect. These include from the simple model adjustment to g-computation (Hernán and Robins 2020), propensity score-based matching and stratification (Austin and Small 2014 Imbens and Rubin 2015), and doubly robust estimators (Saarela et al. Several methods have been used to account for baseline differences between treated and untreated subjects. This treatment selection bias is commonly known as confounding bias or non-exchangeability problem (Hernán and Robins 2020). The observational nature of the study introduces a selection bias into the estimated average treatment effect as the lack of randomization can cause the treated and control groups to be different in terms of baseline characteristics (Lunceford and Davidian 2004). The present work is inspired by an observational study, where the objective was to explore the potential of oral anticoagulant treatment (OAT) in reducing the risk of mortality due to atrial fibrillation in patients with end-stage renal disease (ESRD) (Genovesi et al. Due to various reasons, including costs, ethicality, and the growing easiness of access to registers and large follow-up data, observational studies are increasingly used for the evaluation of treatment effect differences between groups of individuals (Austin 2019). When the goal is to establish the causal effects of treatments, randomized controlled trials (RCTs) are the gold standard (Kovesdy et al. Further, we showed that IPSW is still useful to account for the lack of treatment randomization, but its advantages are stringently linked to the satisfaction of ignorability, indicating that the existence of relevant though unmeasured or unused covariates can worsen the selection bias. Using extensive simulations, we show that BC-IPSW substantially reduced the bias due to the misspecification of the ignorability and overlap assumptions. The benefit of the treatment to enhance survival was demonstrated the suggested BC-IPSW method indicated a statistically significant reduction in mortality for patients receiving the treatment. The approach was motivated by a real observational study to explore the potential of anticoagulant treatment for reducing mortality in patients with end-stage renal disease. We present a bootstrap bias correction of IPSW (BC-IPSW) to improve the performance of propensity score in dealing with treatment selection bias in the presence of failure to the ignorability and overlap assumptions. However, IPSW requires strong assumptions whose misspecifications and strategies to correct the misspecifications were rarely studied. The inverse propensity score weight (IPSW) is often used to deal with such bias. When observational studies are used to establish the causal effects of treatments, the estimated effect is affected by treatment selection bias.
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