1) To modify existing recurrence-time models for screening to simulate the biasing effects of realistic cancer screening patterns in an observational study of cancer mortality nested within the PLCO trial cohort. 2) To incorporate length-bias and self-selection into the bias model developed in aim 1. 3) To further enhance the bias model to include other confounders of the main effect that may also be associated with screening and to simulate regressions to adjust for these confounders. 4) To adapt the back-calculation method of Brookmeyer and Gail (1988) to the estimation of preclinical incidence and duration using observed screening and clinical incidence rates. 5) To design a variety of nested case-control studies of smoking and lung cancer to investigate how the smoking-lung cancer estimates change based on the frequency of screening among the risk-factor strata. 6) The mathematical model we propose is based on a progressive disease model overlaid with a simple screening model (a recurrence time model). Using this model we are able to quantify the people who would be left out of or included in the study as a result of the presence of screening which sequentially allows us to quantify the amount of screening bias. Modifying this computer simulation for mortality studies, we will be able to simulate the amount of possible bias from screening and simulate an analysis of the relationship between smoking and the incidence and mortality in an age-specific cohort of men at risk in the PLCO study-lung cancer arm. For this project, in addition to lead-time bias, we will include self-selection bias in the model and incorporate length-biased selection adjustment through differential survival for mortality studies in an effort to increase the validity of our final calculated relative risk. We will also include overdiagnosis bias both by extending the tail of the preclinical phase distribution and by using bimodal distributions. We will explore incorporating a second risk factor into our model to allow us to see interactive effects between the risk factors if they exist and to examine the effect of adjusting for other potential confounders on the estimated effect of the risk factor of interest. We will also explore the feasibility of modifying the back-calculation methods presented elsewhere, to allow us to obtain the study specific preclinical duration distribution and preclinical incidence rate from clinical incidence and screen detection timing. Modification will focus on accommodating overdiagnosis and imperfect test sensitivity. In parallel with the first four aims as stated above, we will design a variety of nested case-control studies of the effect of smoking on lung cancer to investigate how the estimates change based on the design. For example, lagging the ascertainment period by zero, one, or two years following randomization, more ascertainment bias should be progressively introduced into the design. Because smoking has a large, known effect on lung cancer, changes in the estimated effect due to various degrees of screening bias should be evident if they exist.