Advances in Biostatistics: Estimators Based on Misspecified Models and Predictions of Survival Times

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My proposed research program has two themes: The development and study of simple estimators of complex models, and the prediction of survival times. Such methods are of particular importance in biostatistics, and will have impact on subject areas including rainfall modelling, multiple sclerosis, and ovarian cancer.With respect to the first theme, I plan to work in the context of time series of rainfall observations, which are complicated to describe because they take on both continuous and zero values, and are correlated over time. Estimation of the effects of factors that influence rainfall can thus be challenging. I intend to investigate the performance of an estimator that assumes that the observations are, in fact, uncorrelated. Earlier work with count data suggests that such an estimator could be well-behaved, efficient, and simpler to compute than previously considered estimators. I will evaluate the properties of this estimator, and will apply my results to the problem of estimating time trends and the Oceanic Nio Index (“El Nio”) effect on rainfall in Costa Rica. I also plan to work in the context of multiple sclerosis (MS) clinical trials where the outcome is the number of lesions detected using MRI scans of patients' brains over the course of the study period, and where patients were selected for lesion activity at baseline (a so-called “enrichment” study design). Previous authors propose a naive estimator of the effect of treatment that ignores the patient selection process. I will study the performance of an alternative estimator that can be computed with little effort, yet performs better than the nave estimator. My work will allow for improved estimation of the treatment effect and for better planning of sample sizes in enriched MS trials. I will subsequently extend our methods to other types of responses collected in enriched trials.My second theme concerns the prediction of recurrence and death times of ovarian cancer patients. Our initial work has shown that random survival forests are a useful tool for predicting either recurrence or death times; I plan to extend these methods to allow for their simultaneous prediction. In addition, I will develop prediction intervals for survival times that allow the quantification of our uncertainty about our predictions. One challenge is that the prediction of the survival time of a patient with a low expected survival time is inherently an easier problem than the prediction of the survival time of a patient with a high expected survival time. I thus intend to develop methods for identifying subgroups of patients for whom relatively precise predictions can be computed. Ultimately, my collaborators and I hope to develop an online decision support tool that patients and their caregivers can use to guide the management of ovarian cancer risks.