Statistical methods for assessing diagnostic tests & estimating individualized probabilities of therapeutic benefit

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I propose to develop statistical methods to (1) assess the performance of diagnostic tests and prognostic scoresand (2) estimate risk (cumulative incidence) functions and, from them, individualized 'what if' probabilities ofbenefit if a specific medical or lifestyle intervention is selected.In aim (1) the primary focus will be on the 'c' statistic derived from multiple logistic regression. The initialbiostatistical use of c was as the area under the roc curve (auc), to measure the discriminant ability of imagingtests (interpreted on a rating scale) and laboratory tests (measured on an interval scale). However, the index isalso standard output from the SAS (multiple) LOGISTIC procedure and is increasingly used to assess theability of diagnostic and prognostic scoring systems derived from a vector of predictors. If calculated from thesame data from which the model is fitted, the statistic overestimates the true performance of the system.Indeed, by construction, the c statistic calculated from PROC LOGISTIC cannot be less than the null 0.5.Several authors (from Cornfield and Lachenbruch several decades ago, to Copas, Rockette, and Pinskyrecently) have studied the factors that determine the magnitude of this bias. I propose to develop a simple'adjusted-c' statistic, similar to the adjusted-r-squared statistic. I expect that the needed attenuation/shrinkagewill be a function of the numbers of cases and non-cases, and the numbers of useful -- and useless -- candidatepredictor variables.A secondary focus will be on simplified lower confidence bound for the true auc when - in the simple imagingor laboratory test situations -- the observed auc is unity. Obuchowshi has provided limits for this situation, butunfortunately they are too distribution-specific to be of general use. My plan is to draw on the simplicity andclosed-form formulae based on overlapping exponential distributions, and on the insights on the var(auc)structure in our paper in Academic Radiology in 1997.Aim (2) has two parts. The first is to develop guidelines for a novel way (developed with my colleagueMiettinen) to fit smooth-in-time hazard functions to survival-type data, where the event E=1 represents anundesirable outcome. The purpose is to estimate cumulative incidence as a function of a vector of patientcharacteristics and lifestyle/medical management options. The approach is based on sampling theperson-moments; the main unknown is the choice of the sampling approach that gives the most stable estimateof the individualized cumulative incidence. The second aim is to derive an interval estimate for the probabilityof benefit within a time horizon T, for an individual with a personal profile vector x, and contemplatedmedical/behavioral Action (A=1) or not (A=0), i.e. the difference Prob[E=1 | x, T, A=0] - Prob[E=1 | x, T,A=1]. The hope is to have the individualized interval be test-based, so that it can be calculated from theinformation usually contained in study reports.We focus on individualized risk differences as a response to the inordinate emphasis on the 'average' patientand on hazard ratios rather than what matters to an individual: for individuals such as I, with profile x, what isthe difference in the probability of E over a time-horizon T if I choose one action over another? As an example,consider the 2005 NEJM report on an RCT which documented the extent to which radical prostatectomyreduces the risk of death from prostate cancer: the 'average' prostate cancer case-fatality rate within 10 yearswas 15% for those randomized to watchful waiting and 10% for those randomized to surgery; the hazard ratiowas 0.55. The report contained no useful information for men with a patient / tumour profile (age at diagnosis,Gleason score, pre-treatment PSA level) that was more/less favourable than the 'average' profile to which thesummary results presumably apply. With methods that are aimed at individualized risk, and that do not rely onthe non-smooth estimates obtained from Cox's proportional hazards model, we plan to change thecontemporary culture of statistical reporting to be more responsive to individual 'clients'.