Composite partial likelihood estimation under length-biased sampling, with application to a prevalent cohort study of Dementia

The Canadian Study of Health and Aging (CSHA) employed a prevalent cohort design to study survival after onset of dementia, where patients with dementia were sampled and the onset time of dementia was determined retrospectively. The prevalent cohort sampling scheme favors individuals who survive longer. Thus, the observed survival times are subject to length bias. In recent years, there has been a rising interest in developing estimation procedures for prevalent cohort survival data that not only ac count for length bias but also actually exploit the incidence distribution of the disease to improve efficiency. This article considers semi parametric estimation of the Cox model for the time from dementia onset to death under a stationary assumption with respect to the disease incidence. Under the stationery condition, the semi parametric maximum likelihood estimation is expected to be fully efficient yet difficult to perform for statistical practitioners, as the likelihood depends on the baseline hazard function in a complicated way. Moreover, the asymptotic properties of the semi parametric maximum likelihood estimator are not well-studied. Motivated by the composite likelihood method (Besag 1974), we develop a composite partial likelihood method that retains the simplicity of the popular partial likelihood estimator and can be easily performed using standard statistical software. When applied to the CSHA data, the proposed method estimates a significant difference in survival between the vascular dementia group and the possible Alzheimer's disease group, while the partial likelihood method for left-truncated and right-censored data yields a greater standard error and a 95% confidence interval covering 0, thus highlighting the practical value of employing a more efficient methodology. To check the assumption of stable disease for the CSHA data, we also present new graphical and numerical tests in the article. The R code used to obtain the maximum composite partial likelihood estimator for the CSHA data is available in the online Supplementary Material, posted on the journal web site.