To model and estimate a PSA threshold for prostate cancer diagnosis: Dissemination of PSA testing has the following two time-to-event elements: (1) the timing of the initial test, if any, and (2) the gaps between subsequent tests. To illustrate, Mariotto et al (2007) looks at the gap time distribution for intervals between a baseline PSA test and the follow-up test, if any. Predictive factors of interest include age and racial disparity, among others. The gap time might be a function of age and disparity, certainly, but also may depend on the perceived risk of prostate cancer at the baseline medical examination/test. This risk might be a function of the baseline PSA level and/or the PSA trend, represented by the change in reading between the last two tests. Other relevant risk factors might include the outcome of any digital rectal examination, family history of prostate cancer, and so on. Of course, public education and information dissemination are also influential factors for PSA testing and re-testing. The gap time is a natural first hitting time in the language of threshold regression. A patient may schedule a PSA test when uncertainty or worry about the health of his prostate has risen to some threshold or critical worry point. Another important element is the issue of a biopsy. The research program should not only look at the relation of PSA to diagnosis of prostate cancer but also to the biopsy decision, in an effort to answer the following questions: What is the relation of PSA level to the decision to biopsy? To the likelihood of cancer if there is a biopsy? And, finally, to the severity stage of the cancer if it's detected? We propose to use threshold regression to conduct statistical inferences to these questions.

Angela Mariotto, NIH/NCI; Surveillance Research Program, Email: mariotta@mail.nih.gov

Ruth Etzioni, Fred Hutchinson Cancer Research Center; Email: retzioni@fredhutch.org