Estimating life expectancy in the Canadian elderly population with dementia using prevalent cohort survival data

Dementia is globally one of the leading causes of death and the primary cause of dependency and disability in senior citizens. Life expectancy with dementia, defined as the average remaining lifespan for cases with dementia, is a key epidemiological concept in geriatrics. In spite of its significance for medical research and policy-making, this measure has not been studied for people with dementia in the Canadian population. We employ data from the Canadian Study of Health and Aging, a nationwide cross-sectional study on geriatrics with follow-up for survival, to study life expectancy among elderly Canadians with dementia. Even though practically more feasible, the collected survival data using such sampling mechanism suffer from two forms of bias: selection bias due to left truncation, also known as survivor bias, and bias owing to loss to follow-up. While the latter is often inevitable in longitudinal studies when the subjects under study may drop out before the terminating event occurs, the former is a structural cross-sectional sampling bias occurring because long-term survivors are favoured by such a sampling mechanism. To the best of our knowledge, life expectancy and margins of error under these two types of bias have not hitherto been studied in the literature. Taking these complexities into account, we study the nonparametric maximum likelihood estimator of age-specific life expectancy and its uniform margins of error. Based on this estimator, we devise the first two-sample method for constructing uniform margins of error for the difference in life expectancy between two groups of patients, which is then applied to scrutinise the effects of various covariates. Our methodology enjoys robustness and high efficiency while avoiding restrictive constraints. Simulation studies are conducted to validate the performance of the proposed procedures. Our analysis provides novel information on the progression of the disease in Canada, revealing the pronounced effects of sex and type of dementia on life expectancy. A comprehensive body of theoretical results, essential for paving the way for methodological development and beyond, is documented in the Supplementary Material.