Survival analysis and estimating functions

这一建议涉及的统计方法适用于模拟和预测实际的物理现象受到明显的随机变化。应用领域包括工程可靠性、医学统计和地质统计。例如，在医学统计中，考虑了包括癌症等疾病治愈率估计在内的临床试验数据模型。我通过将个体的潜在健康状态建模为随机过程，开发了各种新颖的治愈率模型。当这个过程达到一个临界阈值时，就会出现故障。如果未达到阈值的概率为正，则人群中存在免疫或治愈的个体。估计治愈比例并评估各种协变量对治愈比例的影响具有重要的科学意义。类似的模型在工程可靠性中也非常有用，当达到临界阈值时，一些累积损伤过程导致失效。这些阈值模型是一种令人兴奋的替代模型，如在医学统计中经常使用的研究充分的Cox模型，或在工程可靠性中流行的加速失效时间模型。新方法的发展和这些新模型在实际科学和技术问题上的应用有很大的空间。对于更传统的建模方法来说，这是一个非常令人兴奋的替代范例。

This proposal deals with statistical methods appropriate to model and predict real physical phenomena subject to appreciable random variation. Areas of application include engineering reliability, medical statistics and geostatistics. For example, in medical statistics, models for clinical trial data which include estimation of cure rates for diseases such as cancer are considered. I develop a variety of novel cure rate models by modeling the underlying health status of individuals as a stochastic (random) process. When this process reaches a critical threshold, failure ensues. If there is a positive probability that the threshold is not attained then there exist immune or cured individuals in the population. Estimating cure proportions and assessing the impact of various covariates on the proportion cured is of great scientific significance. Similar models are also very useful in engineering reliability where some cumulative damage process results in failure when a critical threshold is attained. These threshold models are an exciting alternative to models such as the well-studied Cox model, frequently used in medical statistics, or the accelerated failure time model which is popular in engineering reliability. There is great scope for new methodological development and applications of these new models to real scientific and technological problems. This is a very exciting alternative paradigm to more conventional modeling approaches.