Survival and Reliability Models with High Dimensional Data

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This proposal deals with novel methods and models to describe time to event data. Areas of application include engineering reliability, medical statistics and others. For example, in medical statistics, models for clinical trial data, which include estimation of time to cure of patients with C.Difficile is of current interest. In engineering the time for a dominant crack to develop to a critical size resulting in failure due to metal fatigue is also of interest. I am particularly interested in failure or event time models, which are based on a plausible underlying model of the process, which actually produces failure. The most popular model for event time data is the Cox model. While this has been very useful, Cox himself has expressed doubts about its possible overuse (Statistical Science, Reid 1994). An important aspect of this model, and more general counting process models, is that they focus on purely empirical models of the hazard function. Earlier research, including some of my own, in the engineering reliability area, suggests that considerable subject matter knowledge in, for example, failure due to metal fatigue, is usually more convincing to applied scientists.I consider several models, which have an underlying process-based origin. The process may measure cumulative damage in an engineering context or a putative measure of human health in a medical context. The Birnbaum-Saunders fatigue life model arises from a stochastic model of the growth of a dominant crack eventually leading to catastrophic failure. It is related to a class of models referred to as First Hitting Time (FHT). The underlying process in this case may be a Wiener process (see Lee and Whitmore 2006). I propose to work with variants of Wiener process based models, as well as the Birnbaum-Saunders model. I will develop novel methods to deal with high-dimensional (HD) covariate data for both of these models; an example is microbiome data, in which the covariate space relates to very HD next generation sequencing data on clinical trial participants. Another issue I will study is random effects versions of these models.This can be used for clustered data or as an alternative to multiplicative frailty models for Cox PH. The latter model has flaws, in that the PH assumption may fail and also multiplicative frailty is not entirely convincing, Aalen et al (2008). I will develop novel methods for a variety of cure rate models based on FHTs. Similar models are very useful in engineering reliability. 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.