Abstract

In March 1972, David Cox presented his paper “Regression Models and Life Tables” to a meeting of the Royal Statistical Society. The paper and the ensuing lively discussion were published in the Journal of the Royal Statistical Society, Series B (Methodological), Vol. 34, No. 2 (1972), pp. 187-220 . According to the Web of Science, this paper has had over 23300 citations, which is almost certainly a gross underestimate. Most of those citations are from the medical literature, since what Cox did was to provide a simple yet extremely flexible solution, based on his formulation of a “proportional hazards model”, to the problem of comparing survival across different individuals while taking full account of differing treatments, baseline and time-varying personal characteristics, withdrawal from follow-up, etc. In 1990, Cox won the prestigious Kettering Prize and Gold Medal for Cancer Research for “the development of the Proportional Hazard Regression Model.” The importance of the paper as a contribution to Science is thus clear. But its contributions to statistical methodology were of equal originality and importance, and it is those I propose to discuss.

Cox’s model was perhaps one of the earliest examples of a “semiparametric model”, and his method of eliminating the nonparametric part through the formation of a “partial likelihood” was certainly imaginative. But his argument for the validity of the method was heuristic in the extreme, and it was not until much later that it was set on a firm mathematical basis through the application of martingale theory. It could be argued that its philosophical basis, which has much in common with the prequential approach to statistical inference, is less secure. I hope others will join me in a thorough-going discussion of the contents and ramifications of this pathbreaking paper.