Mary Lena Bleile: Imputation of Counterfactual Tumor Volumes

Dropout is a statistical problem which occurs when an experimental unit that one is taking serial measurements from becomes unavailable for further measurements, prior to the end of the study. One common instance of dropout is found in tumor growth experiments performed on animal subjects: some animals are sacrificed when they are in too much pain, or bad condition. Unlike traditional missing data problems in time series data, this issue poses unique statistical problems due to the fact that the resultant dropout process results in a monotonic missingness pattern: if we observe missingness at a time t, then we necessarily have missingness at all timepoints t* >t. We introduce a novel method for imputation of tumor volume counterfactuals: we build a multivariate growth curve with random effects as inspired by Heitjan, et al (1993), and apply Bayesian methods in order to acquire a random sample for each parameter, in concordence with the literature on multiple imputation. One can then leverage conditional distribution theory to acquire a complete dataset from each of the random posterior samples. We additionally supply an R package for ease of execution of our method.