Robust imputation in multivariate hierarchical data

In obtaining unbiased estimates of univariate quantities and multivariate relationships from complex surveys, missing data are commonly problematic. In some studies, missing data can be ignored and unbiased estimates can simply be computed from the complete cases. However, in a quality of life survey in a cancer clinical trial, for example, missingness may be related to patient frailty such that patients with declining health may be less likely to complete quality of life questionnaires. If frailty is related to quality of life, analysis of complete cases may result in biased survey estimates. One issue in handling missing data in complex surveys is accounting for the hierarchical structure of the data. This hierarchical structure introduces dependency among subjects where, say, patients within treatment centers are more similar than patients in different treatment centers. A second issue in handling missing data in complex surveys is outliers. Using nonrobust imputation methods can propagate the effect of outliers on estimates computed from imputed data. To handle multivariate hierarchical missing data in the presence of outliers, a method of single imputation is presented which incorporates the best prediction estimator of the missing data with robust estimates of parameters in the multivariate normal mixed model. Some properties of the imputation method are developed and results of a simulation study are presented. In the simulation, the imputation estimator allowed for approximately unbiased estimation of population means and within-group and between-group correlations in uncontaminated data. In contaminated data, the imputation estimator more accurately predicted missing values and allowed for more efficient estimation of population means and within-group and between-group correlations than several other common imputation estimators. Lastly, the imputation method is applied with an adjusted jackknife variance estimator to quality of life survey data in a North Central Cancer Treatment Group longitudinal clinical trial.