Estimation of Sojourn Time and Transition Probability of Lung Cancer forSmokers using the PLCO Data

Objectives: The goal of this study is to investigate time durations in the disease-free state and the preclinical state of lung cancer for male and female smokers, using lung cancer data from the Prostate, Lung, Colorectal and Ovarian Cancer Screening Trial. Methods: We applied a modified likelihood function to the lung cancer data, to obtain maximum likelihood estimate and make Bayesian inference of the transition probability from the disease-free to the preclinical state, and the sojourn time distribution. The data was stratified by age and gender for smokers in the periodic screening program. A scaled Beta distribution was used for the transition probability density function, and a Weibull distribution was used to model the sojourn time in the preclinical state. Results: The epidemiological estimate of screening sensitivity is 0.649 for males and 0.68 for females. The transition probabilities are not the same for males and females: it is increasing monotonically to 80 years old for males; while it has a single maximum at age 72.5 for females. For male, the maximum likelihood estimate of mean sojourn time is 1.82 years, the Bayesian posterior mean and median sojourn time is 1.50 and 1.48 years, respectively. For female, the corresponding maximum likelihood estimate, posterior mean and median sojourn time are 1.84, 1.74 and 1.79 years respectively. The Bayesian mean lifetime risks for male and female smokers developing lung cancer are 12.0%, and 6.8%, respectively. Conclusion: Our estimation showed that male smokers are more susceptible to lung cancer, because they have a higher lifetime risk and higher transition probability density than the same aged female smokers. Once they enter into the preclinical state, the male smokers have a shorter mean sojourn time than the female, meaning that they are quicker to develop clinical symptom of lung cancer.