Imputation method adjusted for covariates for nonrespondents in instruments with applications

In clinical research, measurement instruments (or questionnaires) consisting of a number of items (questions) are often used to assess treatment effect, e.g., quality-of-life assessment, and clinical disease activity index. In many situations, instead of an individual component, it is of interest to provide an assessment of the treatment effect in some overall measures, e.g., subscale or total score. In practice, these types of data often suffer from incompleteness. A common method is to simply ignore all the item nonrespondents from the analysis. Although this method is statistically valid under the assumption of missing completely at random (MCAR), it suffers from decreasing power/efficiency. In this paper, we propose a regression imputation approach adjusted for covariates with item nonrespondents in the instrument. The proposed method provides consistent estimators, which are asymptotically normal. A bootstrap procedure is also proposed to estimate the asymptotic variance of the derived estimators. A simulation study was conducted to study the finite samples performance of the derived estimators. It is also shown that the estimators based on the imputed data set are more efficient than the estimators based on the completers only. The proposed methodology was illustrated through two applications in observational studies.