Using multiple imputation to estimate cumulative distribution functions in longitudinal data analysis with data missing at random.

In longitudinal clinical studies, after randomization at baseline, subjects are followed for a period of time for development of symptoms. The interested inference could be the mean change from baseline to a particular visit in some lab values, the proportion of responders to some threshold category at a particular visit post baseline, or the time to some important event. However, in some applications, the interest may be in estimating the cumulative distribution function (CDF) at a fixed time point post baseline. When the data are fully observed, the CDF can be estimated by the empirical CDF. When patients discontinue prematurely during the course of the study, the empirical CDF cannot be directly used. In this paper, we use multiple imputation as a way to estimate the CDF in longitudinal studies when data are missing at random. The validity of the method is assessed on the basis of the bias and the Kolmogorov-Smirnov distance. The results suggest that multiple imputation yields less bias and less variability than the often used last observation carried forward method.