Statistical analysis of disease onset during lifespan with left truncation

We consider a new nonparametric method for analyzing the onset of a chronic condition, e.g., dementia, when death occurs frequently in the study population. In contrast to the commonly used semi-competing risks or illness-death model, we study the distribution of the disease onset time conditional on the death time, which consists of two components that provide straightforward interpretations of the disease onset during the lifespan. Without imposing any model assumption, we propose a kernel-weighted product-limit estimator that properly handles the left-truncation, a common issue in aging studies. The estimator is asymptotically normal and its variance can be estimated by a Greenwood-type variance estimator. We use the integrated Brier score for the bandwidth selection and illustrate the proposed method with simulation studies, an analysis of The 90+ Study, and an analysis of the UC Health Data Warehouse.