Inference of Sojourn Time and Transition Density using the NLST X-ray Screening Data in Lung Cancer

Aims: The aim of this study is to provide statistical inference of the sojourn time and the transition probability from the disease free to the preclinical state of lung cancer for male and female smokers using lung cancer data from the National Lung Screening Trial (NLST). Materials and Methods: We applied a likelihood function to the lung cancer data, to obtain Bayesian inference of the transition probability and the sojourn time distribution. A log-normal distribution was used for the transition probability density function multiplied by 30%, and a Weibull distribution was used to model the sojourn time in the preclinical state. Results: The estimate of screening sensitivity is 0.61 for males and 0.62 for females. Early transition happened before age 50 and lasted until after age 90. The transition probability from the disease free to the preclinical state has a single maximum at around age 73 for males and 72 for females. For male, the Bayesian posterior mean, and median sojourn time are 1.33 and 1.27 years, respectively. For female, the corresponding posterior mean, and median sojourn time are 1.23 and 1.21 years, respectively. Conclusion: Our estimation showed that male smokers are more vulnerable to lung cancer, because they have a higher transition probability density than the same aged female smokers. The female smokers have a slightly shorter mean sojourn time than the male, meaning that they are quicker to develop clinical symptom of lung cancer.