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

我建议开发统计方法来(1)评估诊断测试的性能和预后评分；(2)估计风险（累积发病率）函数，并从中得出个性化的“如果”，如果选择特定的医疗或生活方式干预的获益概率。在目标(1)中，主要焦点将放在从多元逻辑回归中得出的“c”统计量上。c在生物统计学上的最初用途是作为roc曲线下的面积（auc），用于测量成像测试（用评定量表解释）和实验室测试（用间隔量表测量）的判别能力。然而，该指数也是SAS（多重）LOGISTIC程序的标准输出，并且越来越多地用于评估来自预测因子向量的诊断和预后评分系统的能力。如果从与模型拟合的数据相同的数据中计算，则统计量高估了系统的真实性能。实际上，通过构造，从PROC LOGISTIC计算出的c统计量不能小于null 0.5。几位作者（从几十年前的Cornfield和Lachenbruch，到最近的Copas、Rockette和pinsky）研究了决定这种偏见程度的因素。我建议开发一个简单的“调整后的c”统计，类似于调整后的r平方统计。我预计所需的衰减/收缩将是案例和非案例数量的函数，以及有用和无用的候选预测变量的数量。第二个重点将是在简单的成像或实验室测试情况下，当观察到的auc为统一时，真实auc的简化下置信界限。Obuchowshi为这种情况提供了限制，但不幸的是，它们过于特定于发行版而不能普遍使用。我的计划是利用基于重叠指数分布的简单和封闭形式的公式，以及我们1997年在《学术放射学》上发表的论文中对var（auc）结构的见解。Aim(2)有两部分。首先是为一种新方法（与我的同事emiettinen一起开发）制定指导方针，以将平滑时间风险函数拟合到生存型数据中，其中事件E=1表示不希望的结果。目的是估计累积发病率作为患者特征和生活方式/医疗管理选择向量的函数。该方法基于对人-时刻的采样；主要的未知因素是抽样方法的选择，该方法能给出最稳定的个体化累积发生率估计。第二个目标是为具有个人概况向量x的个体在时间范围T内获得收益的概率推导区间估计，并且考虑医疗/行为行动（a =1）或不（a =0），即Prob[E=1 | x， T, a =0] - Prob[E=1 | x， T, a =1]的差异。希望个性化的间隔是基于测试的，这样就可以从研究报告中通常包含的信息中计算出来。我们关注个体化风险差异，作为对过分强调“普通”患者和风险比而不是对个人重要的事情的回应：对于像我这样的个人，具有概况x，如果我选择一种行动而不是另一种行动，在时间范围T上E的概率有什么不同？举个例子，2005年NEJM关于一项随机对照试验的报告，该报告记录了根治性前列腺切除术在多大程度上降低了前列腺癌的死亡风险：10年内前列腺癌的“平均”死亡率，随机分配到观察等待组的为15%，随机分配到手术组的为10%；风险比为0.55。该报告没有包含对患者/肿瘤概况（诊断年龄，Gleason评分，治疗前PSA水平）的男性有用的信息，这些信息比总结结果可能适用的“平均”概况更有利/更不利。通过针对个性化风险的方法，并且不依赖于从Cox比例风险模型中获得的非平滑估计，我们计划改变统计报告的当代文化，使其对个人“客户”更加敏感。

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'.