Abstract

The classical setting of survival analysis requires data collected on incident cases—subjects who experience the initiating event (e.g. onset of disease) after the start of the study. However, a prevalent cohort study design is often more feasible which cross-sectionally recruit subjects who have already experienced the initiating event. These subjects are then followed up for the remainder of their lives until they experience the terminating event (e.g. death). While more efficient, this design introduces structural selection bias, as the sampled population does not match the target population. Additionally, the censoring mechanism in such sampling design is informative.

 

For many diseases, such as dementia, where it is reasonable to assume the incidence follows a regular point process, a more efficient approach–known as the unconditional approach– can be adopted. We propose a method for obtaining uniform confidence bands for the mean residual life function based on its unconditional nonparametric maximum likelihood estimator (NPMLE). To achieve this, we first establish results on the uniform strong consistency, weak convergence, and asymptotic efficiency of the NPMLE. Given the intractable form of the limiting processes, we numerically approximate the functionals of the asymptotic processes of the normalized NPMLEs. Additionally, we introduce the first two-sample method for constructing uniform confidence bands to compare life expectancy differences between two patient groups, allowing us to scrutinise the effects of various covariates. Our methodology is robust, based on most efficient estimator, and avoids restrictive constraints. The proposed procedures are applied to analyse a set of real data on patients with dementia from the Canadian Study of Health and Aging. Our analysis provides novel information on the progression of the disease in Canada.

 

Speaker

Ali Shariati

Research Area

Statistics seminar

Affiliation

UNSW, Sydney

Date

Friday, 4 Oct 2024, 4:00 pm

Venue

Rm 4082, Anita B. Lawrence Center