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

我提出的研究计划有两个主题：复杂模型简单估计器的开发和研究，以及生存时间的预测。这些方法在生物统计学中特别重要，并将对降雨建模、多发性硬化症和卵巢癌等主题产生影响。*关于第一个主题，我计划在降雨观测的时间序列的背景下工作，这些时间序列很难描述，因为它们既有连续的值，也有零值，并且随着时间的推移而相互关联。因此，估计影响降雨量的因素的影响可能是具有挑战性的。我打算研究一种假设观测结果实际上是不相关的估计器的性能。早期对计数数据的研究表明，这样的估计器可能比以前认为的估计器行为良好、效率高、计算更简单。我将评估这个估计器的性质，并将我的结果应用于估计时间趋势和海洋尼诺指数(“厄尔尼诺”)对哥斯达黎加降雨量的影响的问题。我还计划在多发性硬化症(MS)临床试验的背景下工作，该试验的结果是在研究过程中使用患者大脑的MRI扫描检测到的病变数量，并根据基线上的病变活动来选择患者(所谓的“浓缩”研究设计)。以前的作者提出了一个天真的治疗效果估计器，忽略了患者选择过程。我将研究另一种估计器的性能，这种估计器可以很容易地计算出来，但比单纯的估计器表现得更好。我的工作将允许在丰富的多发性硬化症试验中改进治疗效果的估计，并更好地规划样本量。随后，我将把我们的方法扩展到在丰富的试验中收集的其他类型的反应。*我的第二个主题是关于卵巢癌患者复发和死亡时间的预测。我们的初步工作表明，随机生存森林是预测复发或死亡时间的有用工具；我计划扩展这些方法，以允许它们同时预测。此外，我将制定生存时间的预测区间，以量化我们对预测的不确定性。一个挑战是，预测预期生存时间低的患者的生存时间本质上是一个比预测预期生存时间高的患者的生存时间更容易的问题。因此，我打算开发一种方法来识别可以计算出相对准确预测的患者亚群。最终，我和我的合作者希望开发一个在线决策支持工具，患者和他们的照顾者可以使用它来指导卵巢癌风险的管理。

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 Niño Index (“El Niño”) 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 naïve 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.