Abstract
Propensity score analysis is a popular method to control for confounding in observational studies. A challenge in propensity methods is missing values in confounders. Several strategies for handling missing values exist, but guidance in choosing the best method is needed. In this simulation study, we compared four strategies of handling missing covariate values in propensity matching and propensity weighting. These methods include: complete case analysis, missing indicator method, multiple imputation and combining multiple imputation and missing indicator method. Concurrently, we aimed to provide guidance in choosing the optimal strategy. Simulated scenarios varied regarding missing mechanism, presence of effect modification or unmeasured confounding. Additionally, we demonstrated how missingness graphs help clarifying the missing structure. When no effect modification existed, complete case analysis yielded valid causal treatment effects even when data were missing not at random. In some situations, complete case analysis was also able to partially correct for unmeasured confounding. Multiple imputation worked well if the data were missing (completely) at random, and if the imputation model was correctly specified. In the presence of effect modification, more complex imputation models than default options of commonly used statistical software were required. Multiple imputation may fail when data are missing not at random. Here, combining multiple imputation and the missing indicator method reduced the bias as the missing indicator variable can be a proxy for unobserved confounding. The optimal way to handle missing values in covariates of propensity score models depends on the missing data structure and the presence of effect modification. When effect modification is present, default settings of imputation methods may yield biased results even if data are missing at random.
Highlights
The optimal way to handle missing values in covariates of propensity score models depends on the missing data structure and the presence of effect modification
Missing values can occur by different mechanisms: values are missing completely at random (MCAR) when the probability that a value is missing is independent from observed and unobserved information, missing at random (MAR) where the probability of missing depends only on observed information, or missing not at random (MNAR) where the probability of missing depends on unobserved information
The optimal strategy depends on the missing data structure and whether there is effect modification or unmeasured confounding
Summary
Numerous studies provide illustrations and discussions on the performance of different propensity score approaches [3, 4, 6,7,8,9,10,11]. Observational studies often have missing values in covariates. It is difficult to decide on the type of missing mechanism, especially when distinguishing whether the data are missing at random or not at random [13, 14]. In routinely collected data, variables are often selectively measured based on a patient’s characteristics which are often not well-specified [15]. If those ill-defined characteristics are associated with the variable with missing values, data is missing not at random. External knowledge or assumptions about the clinical setting are required to distinguish whether the missing is at random or not at random
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