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360 Statistics and public health researchodds ratio estimator standing out as a key statistical and epidemiological contribution.Also nonparametric methods, and hazard rate estimators, enteredthrough the Kaplan and Meier (1958) survivor function estimator.These modeling approaches came together in the Cox (1972) regressionmodel, one of the most influential and highly cited statistical papers of alltime. The semiparametric Cox model extended the ratio modeling into a fullhazard ratio regression approach, while also incorporating a nonparametricbaseline hazard rate that valuably relaxed parametric models, such as theWeibull model, that had previously been used. Furthermore, the parametrichazard ratio component of this semiparametric model could be relaxed inimportant ways by including, for example, stratification on key confoundingfactors, treatment by time interactions to relax proportionality assumptions,and stochastic time-dependent covariates to examine associations for covariatescollected during study follow-up. For relatively rare outcomes, the Coxmodel proportional hazards special case is well approximated by a correspondingodds ratio regression model, and logistic regression soon became the mainstayapproach to the analysis of case-control epidemiological data (Prenticeand Pyke, 1979).Over the past 30 years, valuable statistical methods have been developedfor data structures that are more complex than a simple cohort follow-up witha univariate failure time outcome. Many such developments were motivatedby substantive challenges in biomedicine. These include nested case-controland case-cohort sampling procedures to enhance estimation efficiency withrare disease outcomes; methods for the joint analysis of longitudinal and failuretime data; sequential data analysis methods; missing and mismeasureddata methods; multivariate failure time methods, including recurrent eventand correlated/clustered failure time methods; and event history models andmethods more generally. Many of these developments along with correspondingstatistical theory have been summarized in book form where pertinentreferences may be found; see, e.g., Andersen et al. (1993) and Kalbfleisch andPrentice (2002).In the last decade, foci for the development of statistical methods inbiomedical applications have included the incorporation of high-dimensionalgenomic data, with regularization approaches to deal with dimensionality anddata sparsity as in, e.g., Tibshirani (1994); methods for the development,evaluation and utilization of biomarkers for many purposes, including earlydisease detection, disease recurrence detection, and objective exposure assessment;and methods for disease risk prediction that integrate with conceptsfrom the diagnostic testing literature. Relative disease rate modeling, and theCox model in particular, provided a foundation for many of these developments.