Incidence regression, variable selection and conditional density estimation from prevalent cohort survival data under stochastic constraints

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Identifying important risk factors of dementia and quantifying the effect of age-at-onset on survival with dementia are among the questions of prime interest to researchers in dementia. The incident cohort study, in which disease-free individuals are recruited and followed until death, loss to follow-up or study termination, is considered to be the gold standard for addressing such questions. Logistic or other constraints may however preclude the possibility of conducting an incident cohort study. Thus data are often collected from the more feasible prevalent cohort study, whereby diseased individuals are recruited through a cross-sectional survey, determining their onset time retrospectively and following them until death or loss to follow-up. This design is often easier to conduct and cost effective, but the data it generates incorporate systematic bias that if ignored can lead to incorrect conclusions. In particular, individuals with longer disease duration times are overrepresented by the sampling scheme. When such duration times are subject to right censoring, the censoring is informative. It is also known that such sampling scheme induces covariate bias.******To measure the effect of different covariates on the incidence rates using data from follow-up studies on prevalent cases, one should develop a model for incidence rate through modelling the prevalence rate and the distribution of the duration times as functions of covariates. One needs then use the connection between incidence and prevalence rates while accounting for informative censoring and covariate bias. There is a complicating factor in estimation of the effect of some covariates when modelling distribution of the duration times. For instance, overall, the greater the age-at-onset, the shorter the survival with dementia. This information imposes a stochastic ordering on survival with the disease according to the age-at-onset which, in turn, imposes a constraint when measuring the effect of different covariates on the incidence rate.******Although the motivation for my study comes from the Canadian Study of Health and Aging (CSHA), but the methodology that I want to develop applies equally to any other prevalent cohort study with similar structure. Non- and semi-parametric estimation of conditional densities from prevalent cohort survival data under stochastic ordering is of independent interest on its own. First, I plan to extend the work of Park et al. (2012, Biometrika) when the data form a biased sample from the target population, extending the work to handle continuous covariates in the second step and then attack the incidence regression. Addressing issues like variable selection, goodness--of--fit tests and influential diagnostics, among others, while accounting for informative censoring, covariate bias and stochastic ordering require development of new models and methodologies.