Goodness-of-Fit for Length-Biased Survival Data with Right-Censoring

Abstract

Cross-sectional surveys are often used in epidemiological studies to identify subjects with a disease. When estimating the survival function from onset of disease, this sampling mechanism introduces bias, which must be accounted for. If the onset times of the disease are assumed to be coming from a stationary Poisson process, this bias, which is caused by the sampling of prevalent rather than incident cases, is termed length-bias. A one-sample Kolomogorov-Smirnov type of goodness-of-fit test for right-censored length-biased data is proposed and investigated with Weibull, log-normal and log-logistic models. Algorithms detailing how to efficiently generate right-censored length-biased survival data of these parametric forms are given. Simulation is employed to assess the effects of sample size and censoring on the power of the test. Finally, the test is used to evaluate the goodness-of-fit using length-biased survival data of patients with dementia from the Canadian Study of Health and Aging.