Prevalent cohort studies are commonly conducted in many areas of research when incident cohort studies are deemed infeasible due to logistic or other constraints. While such studies are cost effective, it is known that survival data collected on prevalent cases do not form a representative sample from the target population. When the incidence (e.g. onset of disease) arise from a stationary Poisson process, it allows developing a more efficient methodology. While the stationarity assumption holds in many applications, to the best of our knowledge, the problem of establishing uniform confidence bands using data arisen in such settings has not been addressed in the current literature. We devise a method for obtaining uniform confidence bands for the cumulative hazard and the survival function built on their nonparametric maximum likelihood estimators (NPMLEs). To attain this objective, we first present results on uniform strong consistency, weak convergence and asymptotic efficiency of the NPMLE of the cumulative hazard function. Given the intractable forms of the limiting processes in this case, the idea is to numerically approximate the functionals of the asymptotic processes of the normalized NPMLEs. Our simulation studies reveal the efficiency of the estimators for finite samples. The proposed procedures are illustrated using a set of real data on patients with dementia from the Canadian Study of Health and Aging.
The authors would like to thank Professor Christina Wolfson for providing access to the CSHA data. Ali Shariati’s research was supported by iMQRES No. 20191178 (Macquarie University funded scholarship). A part of this research was done during Ali Shariati’s visit to McGill University. Masoud Asgharian’s research was supported by NSERC RGPIN-2018-05618. The CSHA was supported by the Seniors Independence Research Program, through the National Health Research and Development Program (NHRDP) of Health Canada (project 6606-3954-MC[S]). The progression of dementia project within the CSHA was supported by Pfizer Canada through the Health Activity Program of the Medical Research Council of Canada and the Pharmaceutical Manufacturers Association of Canada; by the NHRDP (project 6603-1417-302[R]); by Bayer; and by the British Columbia Health Research Foundation (projects 38 [93-2] and 34 [96-1]).
This article was first posted with the incomplete captions of the Figures 3–8. The captions were corrected on 11 December 2023.
The authors thank the Co-Editor-in-Chief, Professor Grace Y. Yi, and the anonymous referees for their insightful and constructive comments.
"Uniform confidence bands for hazard functions from censored prevalent cohort survival data." Electron. J. Statist. 17 (2) 1807 - 1847, 2023. https://doi.org/10.1214/23-EJS2133