Bayesian lead time estimation for the Johns Hopkins Lung Project data

Problem statement: Lung cancer screening using X-rays has been controversial for many years. A major concern is whether lung cancer screening really brings any survival benefits, which depends on effective treatment after early detection. The problem was analyzed from a different point of view and estimates were presented of the projected lead time for participants in a lung cancer screening program using the Johns Hopkins Lung Project (JHLP) data. Method: The newly developed method of lead time estimation was applied where the lifetime T was treated as a random variable rather than a fixed value, resulting in the number of future screenings for a given individual is a random variable. Using the actuarial life table available from the United States Social Security Administration, the lifetime distribution was first obtained, then the lead time distribution was projected using the JHLP data. Results: The data analysis with the JHLP data shows that, for a male heavy smoker with initial screening ages at 50, 60, and 70, the probability of no-early-detection with semiannual screens will be 32.16%, 32.45%, and 33.17%, respectively; while the mean lead time is 1.36, 1.33 and 1.23 years. The probability of no-early-detection increases monotonically when the screening interval increases, and it increases slightly as the initial age increases for the same screening interval. The mean lead time and its standard error decrease when the screening interval increases for all age groups, and both decrease when initial age increases with the same screening interval. Conclusion: The overall mean lead time estimated with a random lifetime T is slightly less than that with a fixed value of T. This result is hoped to be of benefit to improve current screening programs.