Individuals diagnosed with cancer progress through disease stages with rates that are often unobserved but potentially estimable. We use deconvolution as a method to partition population survival data into two components: time from diagnosis to an intermediate endpoint, and time from the intermediate endpoint to death. Using overall survival data from diagnosis and 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 frailty to influence the correlation between time to the intermediate endpoint and time to death.
We apply the deconvolution method to SEER data. First, we estimate time to progress to a later stage of cancer after diagnosis to simulate the benefit that could be induced by early detection for several cancers. Second, we estimate time to metastatic recurrence of breast cancer and melanoma. Finally, we validate the deconvolution method for individuals with prostate cancer using clinical trial data on both time from diagnosis to prostate cancer death and time from diagnosis to the intermediate endpoint of metastasis.