Sojourn time and lead time projection in lung cancer screening

We investigate screening sensitivity, transition probability and sojourn time in lung cancer screening for male heavy smokers using the Mayo Lung Project data. We also estimate the lead time distribution, its property, and the projected effect of taking regular chest X-rays for lung cancer detection.We apply the statistical method developed by Wu et al. [1] using the Mayo Lung Project (MLP) data, to make Bayesian inference for the screening test sensitivity, the age-dependent transition probability from disease-free to preclinical state, and the sojourn time distribution, for male heavy smokers in a periodic screening program. We then apply the statistical method developed by Wu et al. [2] using the Bayesian posterior samples from the MLP data to make inference for the lead time, the time of diagnosis advanced by screening for male heavy smokers. The lead time is distributed as a mixture of a point mass at zero and a piecewise continuous distribution, which corresponds to the probability of no-early-detection, and the probability distribution of the early diagnosis time. We present estimates of these two measures for male heavy smokers by simulations.The posterior sensitivity is almost symmetric, with posterior mean 0.89, and posterior median 0.91; the 95% highest posterior density (HPD) interval is (0.72, 0.98). The posterior mean sojourn time is 2.24 years, with a posterior median of 2.20 years for male heavy smokers. The 95% HPD interval for the mean sojourn time is (1.57, 3.35) years. The age-dependent transition probability is not a monotone function of age; it has a single maximum at age 68. The mean lead time increases as the screening time interval decreases. The standard error of the lead time also increases as the screening time interval decreases.Although the mean sojourn time for male heavy smokers is longer than expected, the predictive estimation of the lead time is much shorter. This may provide policy makers important information on the effectiveness of the chest X-rays and sputum cytology in lung cancer early detection.