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The proportional hazards model of Cox (1972, Journal of the Royal Statistical Society, Series B 34, 187--220), with a time-dependent covariate, is used to analyze serial cancer marker data. A particular advantage of this method is the case with which missing marker data are handled. Analysis of a real data set shows that high levels of the cancer marker carcinoembryonic antigen (CEA) are associated with increased risk of death in patients with resected colorectal cancer. Several aspects of CEA marker history are analyzed, including CEA level at death time t, CEA level 200 days prior to time t, and whether or not CEA exceeded 5 ng/ml prior to t. Methods to test the hypothesis of no marker effect and to give estimates and confidence intervals for model parameters are outlined both for continuous and for grouped time-to-response data. For grouped data a likelihood ratio test of the proportional hazards assumption is suggested.
Mitchell H. Gail (1981) studied this question.