Developments in the two-event modeling of cohort data with time-dependent exposure patterns: Analytical methods for fitting and ROC analysis for model assessment

The analytical form of the exact solution of the survival function of the two-event model incorporating time-dependent exposure patterns is derived and implemented in a computer program. This exact solution is applied to the Allegheny County nonwhite coke and noncoke oven workers' lung cancer mortality and coke oven emission exposure data. The exposure, measured by the coal tar pitch volatiles (CTPV), is shown to have a significant effect on the net proliferation rate of the intermediate cells. In biological terms, this means that the CTPV plays the role of a promoter in the carcinogenesis of lung cancer among the coke oven workers. The likelihood ratio test and the bootstrap method are used for inference.; Based on the fitted two-event model, a six-fold increase in the lifetime risk of dying from lung cancer is observed for the workers exposed heavily to coke oven emissions for at least 40 years compared to a comparable group of workers not working in the coke ovens. The associated uncertainty is assessed by the bootstrap method.; Two test procedures are proposed and developed based on the theory of ROC analysis. The first test, ROC1, is for assessing goodness of fit in modeling complicated data with time-dependent exposure patterns. Results from using this test indicate that the two-event model fits the data adequately. The second test, ROC2, is for selecting the parameters. The results from using ROC2 test are in agreement with those from the likelihood ratio test suggesting that CTPV acts as a promoter. The possibility of CTPV being also an initiator and/or a completer is suggested by the ROC2 test. However, this observation may be due to type I error and should be investigated further.