In studies of serial cancer markers or disease states and their relation to survival, data on the marker or state are usually obtained at infrequent time points during follow-up. A Markov model is developed to assess the dependence of risk of death on marker level or disease state and inferences within this model are based directly on data collected in this haphazard way. An application relating changing levels of serum alpha-fetoprotein to death in hepatocellular carcinoma is discussed in detail.

Summary Regression models of the proportional hazards type are applied to the analysis of censored survival data. Methods of inference associated with the models and techniques for checking model assumptions are presented and applied to the analysis of some data arising from a clinical trial in medicine.

In many survival time studies or studies on the progression of a disease, information is often incomplete in the sense that it is known only that a patient has been in certain disease states at several time points. In this paper, conditions concerning the interrelationship between the disease process and the examination scheme (i.e., the pattern of examination times) are derived under which a valid statistical inference is possible. These conditions are confronted with examination schemes that are of practical importance in clinical research. A cancer marker study is used as an example to estimate the magnitude of the potential bias when the conditions derived are violated.

Summary. The modal DNA values of 1465 tumours, together with other factors of possible prognostic importance, were related to the survival of the patients, using regression models (Kay, 1977). For most tumour sites except the testis, the distributions of modal DNA values were bimodal, with peaks at the diploid level and in the triploid-tetraploid range. For all tumour sites except the cervix uteri, patients in the low (near-diploid) range showed better survival; the reverse was true for squamouscell carcinoma of the cervix uteri. Other variables showed the following effects: for all sites except the testis, younger patients showed a better survival; for the cervix and corpus uteri, breast and ovary, increasing clinical stage was associated with poorer survival. Where evaluated, histological grade appeared to be associated with survival rate, the less well differentiated tumours having a worse prognosis, except for the breast, where the reverse correlation was noted. For carcinoma of the bladder, females had a poorer survival rate than males.

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