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This problem concerns the evaluation of predictors which could potentially be used to decide on which patients to perform colonoscopy.

Study design: Analysis of administrative data - patients referred to gastroenterology. For each patient, it is known which symptoms they had at time of referral. The objective of the study is to fit a model of the form glm(cancer ~ symptom1 + symptom2 +...., family=binomial()) where cancer is defined as "a colonoscopy would have given positive result if performed shortly after the referral". For some patients, cancer was diagnosed several years after the referral, and we assume that a cancer is diagnosible at time of referral if it was actually diagnosed within three years of the referral (and no negative test results were obtained in the meantime).

Problem: Some patients had less than three years of follow up so they are only partially known not to have cancer at time of referral, and weights need to be assigned to them.

Proposed solution: Let CI(t) be the Kaplan-Meier estimate of the probably of being diagnosed with cancer within time t after referral (cummulative incidence), conditional on the patient not having had a colonoscopy immediately after the referral. For a patient with follow up time = 3 years, the weight will be 1. More generally, the weight will be CI(t)/CI(3).

Does anyone know if someone described this method already? Any help greatly appreciated!

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