Manski Charles F, Tetenov Aleksey
Department of Economics and Institute for Policy Research, Northwestern University, Evanston, IL 60208;
Department of Economics, University of Bristol, Bristol BS8 1TU, United Kingdom; Collegio Carlo Alberto, Moncalieri (TO) 10024, Italy.
Proc Natl Acad Sci U S A. 2016 Sep 20;113(38):10518-23. doi: 10.1073/pnas.1612174113. Epub 2016 Sep 6.
Medical research has evolved conventions for choosing sample size in randomized clinical trials that rest on the theory of hypothesis testing. Bayesian statisticians have argued that trials should be designed to maximize subjective expected utility in settings of clinical interest. This perspective is compelling given a credible prior distribution on treatment response, but there is rarely consensus on what the subjective prior beliefs should be. We use Wald's frequentist statistical decision theory to study design of trials under ambiguity. We show that ε-optimal rules exist when trials have large enough sample size. An ε-optimal rule has expected welfare within ε of the welfare of the best treatment in every state of nature. Equivalently, it has maximum regret no larger than ε We consider trials that draw predetermined numbers of subjects at random within groups stratified by covariates and treatments. We report exact results for the special case of two treatments and binary outcomes. We give simple sufficient conditions on sample sizes that ensure existence of ε-optimal treatment rules when there are multiple treatments and outcomes are bounded. These conditions are obtained by application of Hoeffding large deviations inequalities to evaluate the performance of empirical success rules.
医学研究已经形成了在基于假设检验理论的随机临床试验中选择样本量的惯例。贝叶斯统计学家认为，在临床相关的情况下，试验设计应旨在最大化主观预期效用。鉴于治疗反应有可信的先验分布，这种观点很有说服力，但对于主观先验信念应该是什么，很少能达成共识。我们使用沃尔德的频率主义统计决策理论来研究在模糊性下的试验设计。我们表明，当试验有足够大的样本量时，存在ε - 最优规则。一个ε - 最优规则在每种自然状态下的预期福利与最佳治疗的福利相差不超过ε。等价地，它的最大遗憾不超过ε。我们考虑在按协变量和治疗分层的组内随机抽取预定数量受试者的试验。我们报告了两种治疗和二元结果这一特殊情况的精确结果。当有多种治疗且结果有界时，我们给出了样本量的简单充分条件，以确保存在ε - 最优治疗规则。这些条件是通过应用霍夫丁大偏差不等式来评估经验成功规则的性能而得到的。
