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

在许多生物和医学试验中，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剂量水平的治疗时。因此，小样本量经常出现，例如在临床前试验中。因此，即使在样本量较小的情况下也能控制预先指定的第一类误差水平的统计方法具有特别重要的实际意义。此外，当数据按两个以上的因素(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，这种设计(例如多中心试验)通常使用(I)析因或一般线性模型来评估。如果研究单位也随着时间的推移而被观察到，则通过(Ii)重复测量设计来模拟数据。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察结果不一定是独立的。然而，阶乘模型和重复测量的大多数统计过程都是基于特定的模型假设(例如，所有组中的正态分布误差项和同方差)。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的布局中。因此，经典的估计方法和检验过程可能会由于检验过程的第一类错误水平而导致错误的结论。本项目的目的是(A)为一般模型开发非参数检验和可信区间，以(B)在小样本的情况下控制第一类误差。在(A)中，区分了对具有度量数据的参数线性模型的推断和更一般的非参数秩基程序，包括独立设计和独立设计。在这里，没有对观测值做出具体的分布假设(除了参数模型，其中数据被假设为度量)。为了解决(B)部分的自举问题，研究了置换和一般的重采样方法，由此得到了基于重采样的程序，该程序可用于研究析因设计和重复测量设计中的特定研究问题，用于检验全局假设。程序的开发不仅将基于模拟，还将证明测试程序的类型1误差水平的渐近控制。此外，所有程序将在广泛的模拟研究中与当前技术水平进行比较。此外，为了对程序的非用户友好应用，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.