Estimation of Survival with a Combination of Prevalent and Incident Cases in the Presence of Length Bias

Abstract

In studying natural history of a disease, incident studies provide the best quality estimates; in contrast, prevalent studies introduce a sampling bias, which, if the onset time of the disease follows a stationary Poisson process, is called length bias. When both types of data are available, combining the samples under the assumption that failure times in incident and prevalent cohorts come from the same distribution function, could improve the estimation process from a revalent sample. We verify this assumption using a Smirnov type of test and construct a likelihood function from a combined sample to parametrically estimate the survival through maximum likelihood approach. Finally, we use Accelerated Failure Time models to compare the effect of covariates on survival in incident, prevalent, and combined populations. Properties of the proposed test and the combined estimator are assessed using simulations, and illustrated with data from the Canadian Study of Health and Aging.