Uniform confidence bands for hazard functions from censored prevalent cohort survival data

Prevalent cohort studies are commonly conducted in many areas of research when incident deemed infeasible due to logistic or other constraints. While such cost effective, it is known that survival data collected on prevalent cases do not form a representative sample from the target population. When incidence (e.g. onset disease) arise stationary Poisson process, allows developing more efficient methodology. stationarity assumption holds applications, best our knowledge, problem establishing uniform confidence bands using arisen settings has been addressed current literature. We devise method for obtaining cumulative hazard and function built their nonparametric maximum likelihood estimators (NPMLEs). To attain this objective, we first present results strong consistency, weak convergence asymptotic efficiency NPMLE function. Given intractable forms limiting processes case, idea numerically approximate functionals normalized NPMLEs. Our simulation reveal finite samples. The proposed procedures illustrated set real patients with dementia Canadian Study Health Aging.