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R.L. Prentice 36532.5 Clinical trial data analysis methodsAs noted in the Introduction, statistical methods are rather well developed forthe comparison of failure times between randomized groups in clinical trials.However, methods for understanding the key biological pathways leading toan observed treatment effect are less well developed. Efforts to explain treatmentdifferences in terms of post-randomization biomarker changes may belimited by biomarker sample timing issues and temporal aspects of treatmenteffects. Furthermore, such efforts may be thwarted by measurement error issuesin biomarker assessment. Biomarker change from baseline may be highlycorrelated with treatment assignment, implying likely sensitivity of mediationanalysis to even moderate error in intermediate variable assessment.Another area in need of statistical methodology development is that ofmultivariate failure time data analysis. While Kaplan–Meier curves, censoreddata rank tests, and Cox regression provide well-developed tools for the analysisof univariate failure time data, corresponding established tools have notstabilized for characterizing dependencies among failure times, and for examiningtreatment effects jointly with a set of failure time outcomes. For example,in the context of the postmenopausal hormone therapy trials mentioned earlier(Anderson et al., 2004; Writing Group for the Women’s Health InitiativeInvestigators, 2002), one could ask whether data on stroke occurrence canbe used to strengthen the estimation of treatment effects on coronary heartdisease, and vice versa, in a nonparametric manner. The lack of standardizedapproaches to addressing this type of question can be traced to the lack ofa suitable nonparametric maximum likelihood estimation of the multivariatesurvivor function, which could point the way to nonparametric and semiparametriclikelihood approaches to the analysis of more complex multivariatefailure time data structures.32.6 Summary and conclusionStatistical thinking and innovation have come to play a major role throughoutbiomedical research during the 50 years of COPSS’ existence. Public healthaspects of these developments have lagged somewhat due to the need to relysubstantially on purely observational data for most purposes, for practicalreasons. Such observational data are valuable and adequate for many purposes,but they may require innovative biomarker supplementation for exposuresthat are difficult to assess, as in nutritional and physical activityepidemiology. This could include supplementation by intermediate outcome,or full-scale, randomized prevention trials for topics of great public healthimportance, such as postmenopausal hormone therapy; and supplementation