Imputing Censored Covariates and Evaluating Predictive Models: Applications to Huntington Disease

In longitudinal studies of Huntington disease, many patients are not diagnosed during follow-up. This phenomenon, known as random right censoring, creates challenges for both estimation and prediction. This dissertation contributes new statistical methods and empirical evaluations to address right-censored data and applies these tools to observational studies of Huntington disease. The first chapter strengthens a recent method for right-censored covariates, known as Cox-based conditional mean imputation (CMI). We derive the correct form of the conditional mean, correcting errors in recent publications and strengthening the method’s theoretical foundation. To support practical implementation, we also provide an open-source R package for Cox-based CMI. In the second chapter, we propose a nonparametric CMI method based on the generalized Kaplan-Meier estimator. This estimator allows us to impute the conditional mean of a censored covariate, without assuming a specific distribution or proportional hazards. We prove the consistency of this estimator when used in linear regression, and empirically demonstrate its improved performance over Cox-based CMI under heavy censoring. We apply this method to data from an observational study of Huntington disease to better understand how patients' apathy scores evolve over time. The final chapter compares four existing models that predict time to clinical diagnosis of Huntington disease. We assess each model’s ability to stratify patients by risk using censoring-appropriate metrics, doing so with both published parameters and new estimates obtained via cross-validation. This analysis highlights a clear trade-off between model complexity and predictive performance. Finally, we demonstrate how these models can be used to selectively recruit patients for a preventative clinical trial, and estimate sample sizes for varying effect sizes and trial durations.