Estimating the treatment effect for adherers using multiple imputation

The use of multiple imputation has increased markedly in recent years, and journal reviewers may expect to see multiple imputation used to handle missing data. However in randomized trials, where treatment group is always observed and independent of baseline covariates, other approaches may be preferable. Using data simulation we evaluated multiple imputation, performed both overall and separately by randomized group, across a range of commonly encountered scenarios. We considered both missing outcome and missing baseline data, with missing outcome data induced under missing at random mechanisms. Provided the analysis model was correctly specified, multiple imputation produced unbiased treatment effect estimates, but alternative unbiased approaches were often more efficient. When the analysis model overlooked an interaction effect involving randomized group, multiple imputation produced biased estimates of the average treatment effect when applied to missing outcome data, unless imputation was performed separately by randomized group. Based on these results, we conclude that multiple imputation should not be seen as the only acceptable way to handle missing data in randomized trials. In settings where multiple imputation is adopted, we recommend that imputation is carried out separately by randomized group.

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Propensity score analysis with partially observed covariates: How should multiple imputation be used?

Statistical Methods in Medical Research ◽

10.1177/0962280217713032 ◽

2017 ◽

Vol 28 (1) ◽

pp. 3-19 ◽

Cited By ~ 39

Author(s):

Clémence Leyrat ◽

Shaun R Seaman ◽

Ian R White ◽

Ian Douglas ◽

Liam Smeeth ◽

...

Keyword(s):

Propensity Score ◽

Multiple Imputation ◽

Treatment Effect ◽

Propensity Scores ◽

Propensity Score Analysis ◽

Imputation Model ◽

Complete Case ◽

Inverse Probability ◽

Score Analysis ◽

Partially Observed

Inverse probability of treatment weighting is a popular propensity score-based approach to estimate marginal treatment effects in observational studies at risk of confounding bias. A major issue when estimating the propensity score is the presence of partially observed covariates. Multiple imputation is a natural approach to handle missing data on covariates: covariates are imputed and a propensity score analysis is performed in each imputed dataset to estimate the treatment effect. The treatment effect estimates from each imputed dataset are then combined to obtain an overall estimate. We call this method MIte. However, an alternative approach has been proposed, in which the propensity scores are combined across the imputed datasets (MIps). Therefore, there are remaining uncertainties about how to implement multiple imputation for propensity score analysis: (a) should we apply Rubin’s rules to the inverse probability of treatment weighting treatment effect estimates or to the propensity score estimates themselves? (b) does the outcome have to be included in the imputation model? (c) how should we estimate the variance of the inverse probability of treatment weighting estimator after multiple imputation? We studied the consistency and balancing properties of the MIte and MIps estimators and performed a simulation study to empirically assess their performance for the analysis of a binary outcome. We also compared the performance of these methods to complete case analysis and the missingness pattern approach, which uses a different propensity score model for each pattern of missingness, and a third multiple imputation approach in which the propensity score parameters are combined rather than the propensity scores themselves (MIpar). Under a missing at random mechanism, complete case and missingness pattern analyses were biased in most cases for estimating the marginal treatment effect, whereas multiple imputation approaches were approximately unbiased as long as the outcome was included in the imputation model. Only MIte was unbiased in all the studied scenarios and Rubin’s rules provided good variance estimates for MIte. The propensity score estimated in the MIte approach showed good balancing properties. In conclusion, when using multiple imputation in the inverse probability of treatment weighting context, MIte with the outcome included in the imputation model is the preferred approach.

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The Effect of Partly Missing Covariates on Statistical Power in Randomized Controlled Trials With Discrete-Time Survival Endpoints

Methodology ◽

10.1027/1614-2241/a000121 ◽

2017 ◽

Vol 13 (2) ◽

pp. 41-60

Author(s):

Shahab Jolani ◽

Maryam Safarkhani

Keyword(s):

Randomized Controlled Trials ◽

Discrete Time ◽

Treatment Effect ◽

Survival Data ◽

Controlled Trials ◽

Missing Covariates ◽

Indicator Method ◽

Imputation Methods ◽

Randomized Controlled ◽

Baseline Covariates

Abstract. In randomized controlled trials (RCTs), a common strategy to increase power to detect a treatment effect is adjustment for baseline covariates. However, adjustment with partly missing covariates, where complete cases are only used, is inefficient. We consider different alternatives in trials with discrete-time survival data, where subjects are measured in discrete-time intervals while they may experience an event at any point in time. The results of a Monte Carlo simulation study, as well as a case study of randomized trials in smokers with attention deficit hyperactivity disorder (ADHD), indicated that single and multiple imputation methods outperform the other methods and increase precision in estimating the treatment effect. Missing indicator method, which uses a dummy variable in the statistical model to indicate whether the value for that variable is missing and sets the same value to all missing values, is comparable to imputation methods. Nevertheless, the power level to detect the treatment effect based on missing indicator method is marginally lower than the imputation methods, particularly when the missingness depends on the outcome. In conclusion, it appears that imputation of partly missing (baseline) covariates should be preferred in the analysis of discrete-time survival data.

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