The regression model for censored survival data proposed by D. R. Cox (1972) stimulated research in survival analysis and statistical theory more generally. The particular semiparametric relative risk model which Cox developed has been generalized, extended, and pushed in a number of important directions. It is now widely understood that the proportional hazards model special case, although perhaps the most often applied, suffers from potential difficulties of interpretation in situations in which the model is miss-specified. On the other hand, the assumption of proportional hazards can often be overly restrictive from the perspective of prediction. This has prompted a variety of efforts to develop nonparametric relaxations of the proportional hazards model which retain interpretability and yet which perform well in current settings including those involving high-dimensional covariates.

In this talk, I will give a selective (and somewhat personal) review of some of the history of the Cox model, including current efforts to accommodate estimation of the nonparametric parts of the model via neural networks. At the same time, it remains desirable to incorporate parametric components (or descriptive statistics with desirable properties) to obtain interpretability and stability under censoring and miss-specification.

Along the way, I will connect these developments with some of the key contributions of Norman Breslow.


About Norman E. Breslow and Endowed Lecture:

Norman E. Breslow was a Professor and former Chair of the Department of Biostatistics in School of Public Health, of the University of Washington.

Dr. Breslow has made pioneering contributions to methodological developments in survival and categorical data analysis, generalized linear mixed models, and outcome dependent sampling. A founding member of the National Wilms Tumor Study Group, he has made important contributions in cancer epidemiology. His two research monographs with Dr. N.E. Day, published by the International Agency for Research on Cancer, have had major impact on the design and analysis of case-control and cohort studies in epidemiology. He is recognized as a Highly Cited Researcher by the Institute for Scientific Information.

Dr. Breslow has received numerous awards for his research work. He is a Fellow of the American Statistical Association, Fellow of the American Association for the Advancement of Science, Member of the Institute of Medicine of the National Academy of Sciences, Honorary Fellow of the Royal Statistical Society and Honorary Life Member of the International Biometric Society. He holds honorary doctorates from the University of Bordeaux II and (jointly) from the University of Hasselt and the Catholic University of Leuven.

Dr. Norman Breslow passed away on December 9, 2015, following a battle with prostate cancer.

The Breslow Endowed Lectureship in Biostatistics was established in 2006 in honor and recognition of Dr. Norman E. Breslow’s contributions to the field of Biostatistics. It is awarded to a biostatistical scholar who has significantly contributed to methodology and applications in the health sciences.