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Inverse probability of treatment weighting (IPTW) is a popular propensity score (PS)-based approach to estimate causal effects in observational studies at risk of confounding bias. A major issue when estimating the PS is the presence of partially observed covariates. Multiple imputation (MI) is a natural approach to handle missing data on covariates, but its use in the PS context raises three important questions: (i) should we apply Rubins rules to the IPTW treatment effect estimates or to the PS estimates themselves? (ii) does the outcome have to be included in the imputation model? (iii) how should we estimate the variance of the IPTW estimator after MI? We performed a simulation study focusing on the effect of a binary treatment on a binary outcome with three confounders (two of them partially observed). We used MI with chained equations to create complete datasets and compared three ways of combining the results: combining treatment effect estimates (MIte); combining the PS across the imputed datasets (MIps); or combining the PS parameters and estimating the PS of the average covariates across the imputed datasets (MIpar). We also compared the performance of these methods to complete case (CC) analysis and the missingness pattern (MP) approach, a method which uses a different PS model for each pattern of missingness. We also studied empirically the consistency of these 3 MI estimators. Under a missing at random (MAR) mechanism, CC and MP analyses were biased in most cases when estimating the marginal treatment effect, whereas MI approaches had good performance in reducing bias as long as the outcome was included in the imputation model. However, only MIte was unbiased in all the studied scenarios and Rubins rules provided good variance estimates for MIte.
Propensity score matching (PSM) has been widely used to mitigate confounding in observational studies, although complications arise when the covariates used to estimate the PS are only partially observed. Multiple imputation (MI) is a potential solut
Selective inference (post-selection inference) is a methodology that has attracted much attention in recent years in the fields of statistics and machine learning. Naive inference based on data that are also used for model selection tends to show an
Field-normalization of citations is bibliometric standard. Despite the observed differences in citation counts between fields, the question remains how strong fields influence citation rates beyond the effect of attributes or factors possibly influen
Researchers often impute continuous variables under an assumption of normality, yet many incomplete variables are skewed. We find that imputing skewed continuous variables under a normal model can lead to bias; the bias is usually mild for popular es
Understanding how treatment effects vary on individual characteristics is critical in the contexts of personalized medicine, personalized advertising and policy design. When the characteristics are of practical interest are only a subset of full cova