permutation tests

Özet Parametrik testler evren dağılımına ilişkin bir takım varsyaımların karşılanmasını gerektirir. Bu varsayımların karşılanmadığı durumlarda araştırmacılar parametrik olmayan istatistiksel yöntemler kullanılır. Geleneksel para-metrik olmayan yöntemlerde sıra puanları ve sıra ortalamalarına dayalı işlemler gerçekleştirirken yeniden örnek-leme yöntemleri bu sürece farklı bir bakış açısı getirmiştir. En yaygın kullanılan yeniden örnekleme yöntemlerinin başında randomizasyon testleri gelir. Randomizasyon testlerinin temel mantığı orijinal örneklemden hesaplanan test istatistiğinin rastgele olarak oluşturulan örneklemlerdeki test istatistiği ile karşılaştırılmasına dayalıdır. Bu an-lamda kullanımı dünyada gitgide yaygınlaşan randomizasyon testlerine ilişkin yeterli sayıda kaynak olmaması, özel-likle Türkiye'de kullanımının çok sınırlı olması bu makalenin yazımına temel oluşturmuştur. Ayrıca randomizasyon testlerinin son yıllarda gündemde önemli bir yer tutan R progrlamla dili üzerinden örneklendirilerek açıklanması çalışmanın diğer bir önemli unsuru olarak düşünülmektedir. Bu çalışmada randomizasyon testlerinin R proglam-la dili ile örneklendirilerek açıklanması amaçlanmıştır. Bu bağlamda randomizasyon testlerinin temel kavramları açıklanmış akabinde sosyal bilimler alanında yaygun kullanıldığı düşünülen bağımsız ve tekrarlı örneklemler için t testi, bağınmsız gruplar için tek yönlü varyans analizi ve korelasyon analizi özelinde R kodlarından faydalanılarak örneklendirmelere gidilmiştir. Bu çalışma ile özellikle Türkiye'de randomizasyon testlerinin ve R progrlamlama dili-nin kullanımının yaygınlaştırılması beklenmektedir. Anahtar Kelimeler: yeniden örnekleme yöntemleri, randomizasyon restleri, permütasyon testleri, r proglamla-ma dili, parametrik olmayan testler, bootsrap Abstract Parametric tests such as t-test, ANOVA, etc. requires some assumptions about the distribution of the scores in the universe. If those assumptions are not met it is a good idea to compute non-parametric tests instead of para-metric tests. Traditional non-parametric tests such as Wilcoxon Sum of Ranks and Kruskal Wallis tests etc. focus on the sum of ranks and mean ranks to compare the group scores. On the other hand, resampling methods present a different point of view on this process. One of the mostly used resampling methods is the randomization test. The basic principles of randomization tests are comparing the original test statistic (t values, F values, r coefficient, etc.) to the test statistics derived from randomly generated samples. Although usage of randomization tests in the world is pervading day by day in Turkey it is very rarely used. This may be because of insufficient written source published in Turkey. Moreover, the R programming language has become very popular recently. So in this study, it is aimed to explain the computation process of randomization tests using R codes. In this study, at first, some basic concepts about randomization tests were presented. Then randomization tests were exemplified for independent samples t-test, repeated sample t-test, one-way analysis of variance (one way ANOVA) using R codes. It is hoped that this study guide and motivate researchers to use randomizations tests and r programming language in their research.

We propose statistical methods for comparing phenomics data generated by the Biolog Phenotype Microarray (PM) platform for high-throughput phenotyping. Instead of the routinely used visual inspection of data, with no sound inferential basis, we develop two approaches. The first approach is based on quantifying the distance between mean or median curves from two treatments, and then applying a permutation test; we also consider a permutation test applied to areas under mean curves. The second approach employs functional principal component analysis. Properties of the proposed methods are investigated on both simulated data and data sets from the PM platform.

A new approach for multiplicity control (Optimal Subset) is presented. It is based on the selection of the best subset of partial (univariate) hypotheses which, when combined, produce the minimal p-value. The second step consists in multiplicity adjustment. In this work we show how to perform this new procedure in the permutation framework, choosing adequate combining functions and permutation strategies. The optimal subset approach can be very useful in exploratory studies because it performs a weak control for multiplicity which can be a valid alternative to the classic False Discovery Rate (FDR). A comparative simulation study and application to neuroimaging real data shows it is particularly useful in exploratory studies and when there is a high number of hypotheses. We also show how stepwise regression may be a special case of Optimal Subset procedures and how to adjust the p-value of the selected model taking into account the multiplicity arising from the various possible mode...

Nonlinear mixed effects models allow investigating individual differences in drug concentration profiles (pharmacokinetics) and responses. Pharmacogenetics focusses on the genetic component of this variability. Two tests often used to detect a gene effect on a pharmacokinetic parameter are i) the Wald test, assessing whether estimates for the gene effect are significantly different from 0 and ii) the likelihood ratio test comparing models with and without the genetic effect. Because those asymptotic tests show inflated type I error on small sample size and/or with unevenly distributed genotypes, we develop two alternatives and evaluate them by means of a simulation study. First, we assess the performance of the permutation test using the Wald and the likelihood ratio statistics. Second, for the Wald test we propose the use of the F-distribution with four different values for the denominator degrees of freedom. We also explore the influence of the estimation algorithm using both the First-Order Conditional Estimation with interaction linearisation-based algorithm and the Stochastic Approximation Expectation Maximization algorithm. We apply these methods to the analysis of the pharmacogenetics of indinavir in HIV patients recruited in the COPHAR2-ANRS 111 trial. Results of the simulation study show that the permutation test seems appropriate but at the cost of an additional computational burden. One of the four F-distribution based approaches provides a correct type I error estimate for the Wald test and should be further investigated.