Multiple imputation for longitudinal data using Bayesian lasso imputation model

Multiple imputation is a promising approach to handle missing data and is widely used in analysis of longitudinal clinical studies. A key consideration in the implementation of multiple imputation is to obtain accurate imputed values by specifying an imputation model that incorporates auxiliary variables potentially associated with missing variables. The use of informative auxiliary variables is known to be beneficial to make the missing at random assumption more plausible and help to reduce uncertainty of the imputations; however, it is not straightforward to pre-specify them in many cases. We propose a data-driven specification of the imputation model using Bayesian lasso in the context of longitudinal clinical study, and develop a built-in function of the Bayesian lasso imputation model which is performed within the framework of multiple imputation using chained equations. A simulation study suggested that the Bayesian lasso imputation model worked well in a variety of longitudinal study settings, providing unbiased treatment effect estimates with well-controlled type I error rates and coverage probabilities of the confidence interval; in contrast, ignorance of the informative auxiliary variables led to serious bias and inflation of type I error rate. Moreover, the Bayesian lasso imputation model offered higher statistical powers compared with conventional imputation methods. In our simulation study, the gains in statistical power were remarkable when the sample size was small relative to the number of auxiliary variables. An illustration through a real example also suggested that the Bayesian lasso imputation model could give smaller standard errors of the treatment effect estimate.