Maximum Average-Power (MAP) Tests

Chen, Lin An; Hung, Hui-Nien; Chen, Chih-Rung

doi:10.1080/03610920701215480

Cited by 16 publications

(7 citation statements)

References 8 publications

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“…With this metric, two tests are always comparable. Additionally, α‐level tests maximizing the average power always exist, although these may be randomized (Chen et al ., 2007).…”

Section: Bayesian Expected Power (Bep)mentioning

confidence: 99%

Optimality of testing procedures for survival data in the nonproportional hazards setting

2020

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Most statistical tests for treatment effects used in randomized clinical trials with survival outcomes are based on the proportional hazards assumption, which often fails in practice. Data from early exploratory studies may provide evidence of nonproportional hazards, which can guide the choice of alternative tests in the design of practice‐changing confirmatory trials. We developed a test to detect treatment effects in a late‐stage trial, which accounts for the deviations from proportional hazards suggested by early‐stage data. Conditional on early‐stage data, among all tests that control the frequentist Type I error rate at a fixed α level, our testing procedure maximizes the Bayesian predictive probability that the study will demonstrate the efficacy of the experimental treatment. Hence, the proposed test provides a useful benchmark for other tests commonly used in the presence of nonproportional hazards, for example, weighted log‐rank tests. We illustrate this approach in simulations based on data from a published cancer immunotherapy phase III trial.

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“…With this metric, two tests are always comparable. Additionally, α‐level tests maximizing the average power always exist, although these may be randomized (Chen et al ., 2007).…”

Section: Bayesian Expected Power (Bep)mentioning

confidence: 99%

Optimality of testing procedures for survival data in the nonproportional hazards setting

2020

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“…'s of θ and σ 2 . This test will be called the maximum average power (MAP) test, a term borrowed from Chen et al (2007). This is also a Bayes test statistic.…”

Section: Deriving a Test More Powerful Than F Smentioning

confidence: 99%

“…To do so, we modify the prior distribution and derive the most powerful test, M AP test. Here MAP stands for Maximum Average Powerful, a term first coined in Chen et al (2007). This test is computationally extensive.…”

Section: Introductionmentioning

confidence: 99%

Optimal Tests Shrinking Both Means and Variances Applicable to Microarray Data Analysis

Hwang¹,

Liu²

2010

Statistical Applications in Genetics and Molecular Biology

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As a consequence of the "large p small n" characteristic for microarray data, hypothesis tests based on individual genes often result in low average power. There are several proposed tests that attempt to improve power. Among these, the FS test that was developed using the concept of James-Stein shrinkage to estimate the variances showed a striking average power improvement. In this paper, we establish a framework in which we model the key parameters with a distribution to find an optimal Bayes test which we call the MAP test (where MAP stands for Maximum Average Power). Under this framework, the FS test can be derived as an empirical Bayes test approximating the MAP test corresponding to modeling the variances. By modeling both the means and the variances with a distribution, a MAP statistic is derived which is optimal in terms of average power but is computationally intensive. An empirical Bayes test called the FSS test is derived as an approximation to the MAP tests and can be computed instantaneously. The FSS statistic shrinks both the means and the variances and has numerically identical average power to the MAP tests. Much numerical evidence is presented in this paper that shows that the proposed test performs uniformly better in average power than the other tests in the literature, including the classical F test, the FS test, the test of Wright and Simon, the moderated t-test, SAM, Efron's t test, the B-statistic and Storey's optimal discovery procedure. A theory is established which indicates that the proposed test is optimal in power when controlling the false discovery rate (FDR).

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“…In this article, we develop an optimal test for RNA-seq data analysis while controlling the FDR, where the optimality is defined as achieving the maximum of the power averaged across all genes for which null hypotheses are false. This test, which we call the test with maximum average power (MAP), is introduced in Chen, Hung, and Chen (2007) and further studied in Hwang and Liu (2010) for microarray data analysis. The statistics of the proposed test provide a natural way of controlling the FDR.…”

Section: Introductionmentioning

confidence: 99%

An Optimal Test with Maximum Average Power While Controlling FDR with Application to RNA‐Seq Data

Liu

2013

Biometrics

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The recent RNA-seq technology is an attractive method to study gene expression. One of the most important goals in RNA-seq data analysis is to detect genes differentially expressed across treatments. Although several statistical methods have been published, there are no theoretical justifications for whether these methods are optimal or how to search for the optimal test. Furthermore, most proposed tests are designed for testing whether the mean expression levels are exactly the same or not across treatments, whereas sometimes, biologists are interested in detecting genes with expression changes larger than a certain threshold. Another issue with current methods is that the false discovery rate (FDR) control is not well studied. In this manuscript, we propose a test to address all the above issues. Under model assumptions, we derive an optimal test that achieves the maximum of average power among those that control FDR at the same level. We also provide an approximated version, the approximated most average powerful (AMAP) test, for practical implementation. The proposed method allows for testing null hypotheses that are much more general than the ones most previous studies have considered, and it leads to a natural way of controlling the FDR. Through simulation studies, we show that our test has a higher power than other methods, including the widely-used edgeR, DESeq, and baySeq methods, as well as better FDR control than two other FDR control procedures commonly used in practice. For demonstration, we also apply the proposed method to a real RNA-seq dataset obtained from maize.

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Maximum Average-Power (MAP) Tests

Cited by 16 publications

References 8 publications

Optimality of testing procedures for survival data in the nonproportional hazards setting

Optimality of testing procedures for survival data in the nonproportional hazards setting

Optimal Tests Shrinking Both Means and Variances Applicable to Microarray Data Analysis

An Optimal Test with Maximum Average Power While Controlling FDR with Application to RNA‐Seq Data

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