Survival analysis and estimating functions

这个建议涉及适合于模拟和预测受明显随机变化影响的真实的物理现象的统计方法。应用领域包括工程可靠性、医学统计学和地质统计学。例如，在医学统计学中，考虑了临床试验数据的模型，其中包括对癌症等疾病治愈率的估计。我通过将个体的潜在健康状况建模为随机（随机）过程，开发了各种新颖的治愈率模型。当此过程达到临界阈值时，会发生故障。如果存在未达到阈值的正概率，则在群体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。这些阈值模型是一个令人兴奋的替代模型，如研究充分的考克斯模型，经常用于医疗统计，或加速失效时间模型，这是流行的工程可靠性。有很大的余地为新的方法的发展和应用这些新的模式，以真实的科学和技术问题。这是一个非常令人兴奋的替代范式更传统的建模方法。 我的建议的另一部分涉及预测推理。例如，在地统计学和空间 更一般地说，人们的兴趣往往集中在预测风险因素对疾病地理发生率的影响，或根据附近观察到的样本预测采矿区的矿石品位。我的部分建议涉及科学家如何最好地预测或绘制这种空间变化。强的模型假设往往会导致误导性的推论。我正在开发一种新的预测方法，这种方法假设较少，因此对这些假设的失败更具鲁棒性，但仍然可以导致可靠的推论。

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. Another part of my proposal deals with predictive inference. For example, in geostatistics, and spatial statistics, more generally, interest often centres on predicting, for example, the effect of risk factors on geographic incidence of disease or the prediction of ore grade in a mining block from observed samples in the vicinity. Part of my proposal deals with how scientists can best predict or map such spatial variation. Strong model assumptions are often made which may lead to misleading inferences. I am developing a novel approach to prediction which assumes less, and hence is more robust to failures in these assumptions, but which can nevertheless lead to reliable inferences.