Resampling-based statistical inference methods for the evaluation of complex models in biometrics - Part II

在许多生物学和医学试验中，涉及两个以上的治疗组，例如， 当研究单位被随机分配到不同的治疗剂量水平时。因此，小样本量经常发生，例如在临床前试验中。因此，统计方法，控制预先分配的类型-1错误的水平，即使小样本量是特别实际的重要性。此外，当数据按两个以上因素（年龄，性别等）分层时，数据分析变得具有挑战性。在统计实践中，此类设计（例如多中心试验）通常使用（i）析因或一般线性模型进行评估。如果研究单位也随时间观察，则通过（ii）重复测量设计对数据进行建模。析因模型和重复测量设计之间的主要区别是，在同一单元上观察到的观测值可能不一定是独立的。然而，大多数析因模型和重复测量的统计过程都是基于特定的模型假设（例如，所有组的正态分布误差项和方差齐性）。但是，这些假设在许多实际应用中并不满足，特别是在双向和更高方向的布局中。因此，经典的估计方法和测试程序可能会导致错误的结论，这是由于测试程序的高度膨胀或收缩的1型错误水平，本项目的目的是（a）为一般模型开发非参数检验和置信区间，（B）即使在小样本量下也能控制I类错误。它区别于具有度量数据的参数线性模型的推断和更一般的非参数基于秩的程序，无论是对于依赖设计还是独立设计。在这里，没有对观测值进行特定的分布假设（参数模型除外，其中数据被假设为度量）。为了解决（B）部分的问题，本文研究了Bootstrap、置换和一般再抽样方法，并由此导出了基于再抽样的方法，可用于研究析因设计和重复测量设计中关于检验总体假设的具体研究问题。程序的开发不仅是基于模拟，还将提供试验程序的1型误差水平的渐近控制的证明。此外，所有程序将在广泛的模拟研究中与当前最先进的技术进行比较。此外，为了程序的unser友好应用，将开发免费提供的软件包（用于R）。

In many biological and medical trials, more than two treatment groups are involved, e.g., when study units are randomized to different dose levels of a treatment. Hereby, small sample sizes occur frequently, e.g. in pre-clinical trials. Thus, statistical methods which control the pre-assigned type-1 error level even with small sample sizes are of particular practical importance. Furthermore, data analysis gets challenging, when data is stratified by more than two factors (age, gender, etc).In statistical practice, such designs (e.g. multi-center trials) are usually evaluated using (i) factorial or general linear models. If the study units are also observed over time, data is modeled by a (ii) repeated measures design. The main difference between factorial models and repeated measures designs is, that the observations being observed on the same unit may not be necessarily independent. Thus, the dependency structure needs to be taken care of by the inference methods.Most of the statistical procedures for factorial models and repeated measures, however, are based on specific model assumptions (e.g. normal distributed error terms and homoscedastic variances across all groups). But, these assumptions are not met in many practical applications, particularly in two-and higher way layouts. Hereby, classical estimation methods and testing procedures may result in wrong conclusions, due to highly inflated, or deflated, type-1 error levels of the test procedures, respectively.It is the aim of the present project(a) to develop nonparametric tests and confidence intervals for general models which(b) control the type I error even with small sample sizes.In (a) it is distinguished between inference for parametric linear models with metric data and more general nonparametric rank-based procedures, both for dependent and independent designs. Here, no specific distributional assumptions of the observations are made (except for the parametric model, where the data is assumed to be metric). To solve part (b) bootstrap, permutation and general resampling methods are investigated.Hereby resampling based procedures, which can be used to study specific study questions in factorial- and repeated measures designs with regard to testing global hypotheses will be derived. The development of the procedures will not only be simulation based, also proofs of the asymptotic control of type-1 error level of the test procedures will be presented.In addition, all procedures will be compared in extensive simulation studies with the current state of the art. Moreover, for an unser friendly application of the procedures, freely available software packages (for R) will be developed.