Estimating time to intermediate endpoints using population-level survival data and deconvolution methods, with application to cancer progression and recurrence

Abstract

Individuals diagnosed with cancer progress through disease stages with transition rates that are often unobserved but potentially estimable. We focus on deconvolution as a method to partition population-level survival data into two distinct components: (1) time from diagnosis to an intermediate endpoint and (2) time from the intermediate endpoint to death. Using data on overall survival from diagnosis and survival from the intermediate endpoint to death we propose a novel deconvolution method to estimate the distribution of the time from diagnosis to the intermediate endpoint. The method allows for an individual-level frailty to influence the correlation between time to the intermediate endpoint and time to death. We focus on two main applications to cancer. In our first application, we validate the deconvolution method using data on individuals with prostate cancer. We estimate the time to metastasis from diagnosis and compare this with the observed time to metastasis from the SPCG-4 clinical trial. In our second application, we use deconvolution methods to estimate the time to distant metastatic recurrence of melanoma using data from the Surveillance, Epidemiology, and End Results program.