Abstract
BackgroundCausal effect estimation with observational data is subject to bias due to confounding, which is often controlled for using propensity scores. One unresolved issue in propensity score estimation is how to handle missing values in covariates.MethodSeveral approaches have been proposed for handling covariate missingness, including multiple imputation (MI), multiple imputation with missingness pattern (MIMP), and treatment mean imputation. However, there are other potentially useful approaches that have not been evaluated, including single imputation (SI) + prediction error (PE), SI + PE + parameter uncertainty (PU), and Generalized Boosted Modeling (GBM), which is a nonparametric approach for estimating propensity scores in which missing values are automatically handled in the estimation using a surrogate split method. To evaluate the performance of these approaches, a simulation study was conducted.ResultsResults suggested that SI + PE, SI + PE + PU, MI, and MIMP perform almost equally well and better than treatment mean imputation and GBM in terms of bias; however, MI and MIMP account for the additional uncertainty of imputing the missingness.ConclusionsApplying GBM to the incomplete data and relying on the surrogate split approach resulted in substantial bias. Imputation prior to implementing GBM is recommended.
Highlights
Causal effect estimation with observational data is subject to bias due to confounding, which is often controlled for using propensity scores
When only true confounders were used as covariates for propensity score estimation, there was no bias associated with single imputation (SI) + prediction error (PE), SI + PE + parameter uncertainty (PU), multiple imputation (MI), and multiple imputation with missingness pattern (MIMP) under all missingness mechanisms, and the bias was comparable to that obtained prior to introducing missing data
In summary, the results suggest that missing values in the covariates should be imputed before fitting the propensity score model to obtain unbiased causal effect estimates
Summary
Causal effect estimation with observational data is subject to bias due to confounding, which is often controlled for using propensity scores. A major challenge facing observational studies is that the treatment or exposure is not randomized and the estimate of the effect of the exposure on an outcome may be due to confounders, variables associated with both the exposure and outcome. If GBM works well in the presence of missing data, using it would circumvent the issues that arise when using MI with propensity score analysis [4,5,6]. The goal of this paper is to examine the performance of GBM vs other approaches through a simulation study in order to provide guidance to analysts when implementing propensity score analysis in the presence of missingness on the covariates
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