Joint Distribution Of Test Statistics Research Articles

Group sequential testing for cluster randomized trials with time-to-event endpoint.

We propose group sequential methods for cluster randomized trials (CRTs) with time-to-event endpoint. The alpha spending function approach is used for sequential data monitoring. The key to this approach is determining the joint distribution of test statistics and the information fraction at the time of interim analysis. We prove that the sequentially computed log-rank statistics in CRTs do not have independent increment property. We also propose an information fraction for group sequential trials with clustered survival data and a corresponding sample size determination approach. Extensive simulation studies are conducted to evaluate the performance of our proposed testing procedure using some existing alpha spending functions in terms of expected sample size and maximal sample size. Real study examples are taken to demonstrate our method.

Evaluation of multiple prediction models: A novel view on model selection and performance assessment.

Model selection and performance assessment for prediction models are important tasks in machine learning, e.g. for the development of medical diagnosis or prognosis rules based on complex data. A common approach is to select the best model via cross-validation and to evaluate this final model on an independent dataset. In this work, we propose to instead evaluate several models simultaneously. These may result from varied hyperparameters or completely different learning algorithms. Our main goal is to increase the probability to correctly identify a model that performs sufficiently well. In this case, adjusting for multiplicity is necessary in the evaluation stage to avoid an inflation of the family wise error rate. We apply the so-called maxT-approach which is based on the joint distribution of test statistics and suitable to (approximately) control the family-wise error rate for a wide variety of performance measures. We conclude that evaluating only a single final model is suboptimal. Instead, several promising models should be evaluated simultaneously, e.g. all models within one standard error of the best validation model. This strategy has proven to increase the probability to correctly identify a good model as well as the final model performance in extensive simulation studies.

A correction for sample overlap in genome-wide association studies in a polygenic pleiotropy-informed framework

BackgroundThere is considerable evidence that many complex traits have a partially shared genetic basis, termed pleiotropy. It is therefore useful to consider integrating genome-wide association study (GWAS) data across several traits, usually at the summary statistic level. A major practical challenge arises when these GWAS have overlapping subjects. This is particularly an issue when estimating pleiotropy using methods that condition the significance of one trait on the signficance of a second, such as the covariate-modulated false discovery rate (cmfdr).ResultsWe propose a method for correcting for sample overlap at the summary statistic level. We quantify the expected amount of spurious correlation between the summary statistics from two GWAS due to sample overlap, and use this estimated correlation in a simple linear correction that adjusts the joint distribution of test statistics from the two GWAS. The correction is appropriate for GWAS with case-control or quantitative outcomes. Our simulations and data example show that without correcting for sample overlap, the cmfdr is not properly controlled, leading to an excessive number of false discoveries and an excessive false discovery proportion. Our correction for sample overlap is effective in that it restores proper control of the false discovery rate, at very little loss in power.ConclusionsWith our proposed correction, it is possible to integrate GWAS summary statistics with overlapping samples in a statistical framework that is dependent on the joint distribution of the two GWAS.

A powerful approach to the study of moderate effect modification in observational studies.

Effect modification means the magnitude or stability of a treatment effect varies as a function of an observed covariate. Generally, larger and more stable treatment effects are insensitive to larger biases from unmeasured covariates, so a causal conclusion may be considerably firmer if this pattern is noted if it occurs. We propose a new strategy, called the submax-method, that combines exploratory, and confirmatory efforts to determine whether there is stronger evidence of causality-that is, greater insensitivity to unmeasured confounding-in some subgroups of individuals. It uses the joint distribution of test statistics that split the data in various ways based on certain observed covariates. For L binary covariates, the method splits the population L times into two subpopulations, perhaps first men and women, perhaps then smokers and nonsmokers, computing a test statistic from each subpopulation, and appends the test statistic for the whole population, making test statistics in total. Although L binary covariates define interaction groups, only tests are performed, and at least of these tests use at least half of the data. The submax-method achieves the highest design sensitivity and the highest Bahadur efficiency of its component tests. Moreover, the form of the test is sufficiently tractable that its large sample power may be studied analytically. The simulation suggests that the submax method exhibits superior performance, in comparison with an approach using CART, when there is effect modification of moderate size. Using data from the NHANES I epidemiologic follow-up survey, an observational study of the effects of physical activity on survival is used to illustrate the method. The method is implemented in the package which contains the NHANES example. An online Appendix provides simulation results and further analysis of the example.

Sample Size Calculations for Combination Drugs of 2 Monotherapies With a Single Approved Dose Level: Binary Endpoint Cases.

In this article, we study the sample size calculations for the combination drugs of 2 monotherapies with a single approved dose level when the primary endpoints are binary. Two study cases are examined: In the first, each monotherapy has the same indication, while in the second, each monotherapy has a different indication. The sample sizes are calculated by using an asymptotic joint distribution of test statistics and employing unequal allocation for 3 popular measures of 2 proportions: the risk difference, the log relative risk, and the log odds ratio. Results show that our proposed method produces smaller total sample sizes compared with the heuristic method. The total sample sizes can be reduced by incorporating unequal allocation and dependency between 2 test statistics.

Sample Size Calculations for Combination Drugs of Two Monotherapies With One Approved Dose Level

In this article, we consider sample size calculations for combination drugs of two monotherapies that each has only one approved dose level. We modify the method of Laska and Meiner by employing the asymptotic joint distribution of test statistics to derive the power function and using unequal allocation to minimize the total sample sizes. Two cases are investigated. In the first case, each monotherapy has the same indication. A heuristic method, the method of Laska and Meiner, and the proposed method are compared in terms of the total sample sizes. We show that the proposed method produces the smallest total sample sizes. In the second case, each monotherapy has a different indication. While the method of Laska and Meiner cannot be applied in this case, we show that the proposed method can be employed and that it produces smaller total sample sizes than a heuristic method.

Nieklasyczne procedury testowań wielokrotnych

The range of applications of classical multiple testing procedures is limited due to model assumptions, and in many cases classic solutions are non-existent. In such situations non-classical multiple testing procedures allow to control the effect of multiple testing. Although they are popular for computational simplicity and a wide range of applications, marginal multiple testing procedures do not take into account joint distribution of test statistics, which make them more conservative than joint multiple testing procedures. The range of applications of joint procedures introduced by Westfall and Young (1993) is limited due to the subset pivotality requirement. Thus, joint multiple testing procedures suggested by Dudoit and van der Laan (2008) seem very promising. A wide range of applications, the possibility of choosing the Type I error rate and easily accessible software (MTP procedure is implemented in R multtest package) are their obvious advantages. Unfortunately, the results of the analysis of MPT procedure obtained by Werft and Benner (2009) revealed that it does not control FDR in case of numerous sets of hypotheses and small samples. Furthermore, the simulation experiment presented in the article showed that MTP procedure does not control FWER, either.

Applying the Generalized Partitioning Principle to Control the Generalized Familywise Error Rate

In multiple testing, strong control of the familywise error rate (FWER) may be unnecessarily stringent in some situations such as bioinformatic studies. An alternative approach, discussed by Hommel and Hoffmann (1988) and Lehmann and Romano (2005), is to control the generalized familywise error rate (gFWER), the probability of incorrectly rejecting more than m hypotheses. This article presents the generalized Partitioning Principle as a systematic technique of constructing gFWER-controlling tests that can take the joint distribution of test statistics into account. The paper is structured as follows. We first review classical partitioning principle, indicating its conditioning nature. Then the generalized partitioning principle is introduced, with a set of sufficient conditions that allows it to be executed as a computationally more feasible step-down test. Finally, we show the importance of having some knowledge of the distribution of the observations in multiple testing. In particular, we show that step-down permutation tests require an assumption on the joint distribution of the observations in order to control the familywise error rate.

A modified Benjamini–Hochberg multiple comparisons procedure for controlling the false discovery rate

When performing simultaneous statistical tests, the Type I error concept most commonly controlled by analysts is the familywise error rate, i.e., the probability of committing at least one Type I error. However, this criterion is unduly stringent for some practical situations and therefore may not be appropriate. An alternative concept of error control was provided by Benjamini and Hochberg (J. Roy. Statist. Soc. B 57 (1995) 289) who advocate control of the expected proportion of falsely rejected hypotheses which they term the false discovery rate or FDR. These authors devised a step-up procedure for controlling the FDR. In this article, when the joint distribution of test statistics is known, continuous, and positive regression dependent on each one from a subset of true null hypotheses, we derive and discuss a modification of their procedure which affords increased power. An example is provided to illustrate our proposed method.