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

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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.