arXiv subjects

Anh-Tuan Hoang

Publications and source records attributed to Anh-Tuan Hoang.

5 recordsLinked to original sources

arXiv2024

A procedure for multiple testing of partial conjunction hypotheses based on a hazard rate inequality

The partial conjunction null hypothesis is tested in order to discover a signal that is present in multiple studies. The standard approach of carrying out a multiple test procedure on the partial conjunction (PC) $p$-values can be extremely conservative. We suggest alleviating this conservativeness, by eliminating many of the conservative PC $p$-values prior to the application of a multiple test procedure. This leads to the following two step procedure: first, select the set with PC $p$-values below a selection threshold; second, within the selected set only, apply a family-wise error rate or false discovery rate controlling procedure on the conditional PC $p$-values. The conditional PC $p$-values are valid if the null p-values are uniform and the combining method is Fisher. The proof of their validity is based on a novel inequality in hazard rate order of partial sums of order statistics which may be of independent interest. We also provide the conditions for which the false discovery rate controlling procedures considered will be below the nominal level. We demonstrate the potential usefulness of our novel method, CoFilter (conditional testing after filtering), for analyzing multiple genome wide association studies of Crohn's disease.

stat.ME↗

arXiv2023

Multiple testing of composite null hypotheses for discrete data using randomized $p$-values

$P$-values that are derived from continuously distributed test statistics are typically uniformly distributed on $(0,1)$ under least favorable parameter configurations (LFCs) in the null hypothesis. Conservativeness of a $p$-value $P$ (meaning that $P$ is under the null hypothesis stochastically larger than a random variable which is uniformly distributed on $(0,1)$) can occur if the test statistic from which $P$ is derived is discrete, or if the true parameter value under the null is not an LFC. To deal with both of these sources of conservativeness, we present two approaches utilizing randomized $p$-values, namely single-stage and two-stage randomization. We illustrate their effectiveness for testing a composite null hypothesis under a binomial model. We also give an example of how the proposed $p$-values can be used to test a composite null in group testing designs. Similar to previous findings, we find that the proposed randomized $p$-values are less conservative compared to non-randomized $p$-values under the null hypothesis, but that they are stochastically not smaller under the alternative. The problem of establishing the validity of randomized $p$-values is not trivial and has received attention in previous literature. We show that our proposed randomized $p$-values are valid under various discrete statistical models which are such that the distribution of the corresponding test statistic belongs to an exponential family. The behaviour of the power function for the tests based on the proposed randomized $p$-values as a function of the sample size is also investigated. Simulations and a real data analysis are used to compare the different considered $p$-values.

stat.ME↗

arXiv2021

Combining independent p-values in replicability analysis: A comparative study

Given a family of null hypotheses $H_{1},\ldots,H_{s}$, we are interested in the hypothesis $H_{s}^γ$ that at most $γ-1$ of these null hypotheses are false. Assuming that the corresponding $p$-values are independent, we are investigating combined $p$-values that are valid for testing $H_{s}^γ$. In various settings in which $H_{s}^γ$ is false, we determine which combined $p$-value works well in which setting. Via simulations, we find that the Stouffer method works well if the null $p$-values are uniformly distributed and the signal strength is low, and the Fisher method works better if the null $p$-values are conservative, i.e. stochastically larger than the uniform distribution. The minimum method works well if the evidence for the rejection of $H_{s}^γ$ is focused on only a few non-null $p$-values, especially if the null $p$-values are conservative. Methods that incorporate the combination of $e$-values work well if the null hypotheses $H_{1},\ldots,H_{s}$ are simple.

stat.AP↗

arXiv2020

On the usage of randomized p-values in the Schweder-Spjotvoll estimator

We are concerned with multiple test problems with composite null hypotheses and the estimation of the proportion $π_{0}$ of true null hypotheses. The Schweder-Spjøtvoll estimator $\hatπ_0$ utilizes marginal $p$-values and only works properly if the $p$-values that correspond to the true null hypotheses are uniformly distributed on $[0,1]$ ($\mathrm{Uni}[0,1]$-distributed). In the case of composite null hypotheses, marginal $p$-values are usually computed under least favorable parameter configurations (LFCs). Thus, they are stochastically larger than $\mathrm{Uni}[0,1]$ under non-LFCs in the null hypotheses. When using these LFC-based $p$-values, $\hatπ_0$ tends to overestimate $π_{0}$. We introduce a new way of randomizing $p$-values that depends on a tuning parameter $c\in[0,1]$, such that $c=0$ and $c=1$ lead to $\mathrm{Uni}[0,1]$-distributed $p$-values, which are independent of the data, and to the original LFC-based $p$-values, respectively. For a certain value $c=c^{\star}$ the bias of $\hatπ_0$ is minimized when using our randomized $p$-values. This often also entails a smaller mean squared error of the estimator as compared to the usage of the LFC-based $p$-values. We analyze these points theoretically, and we demonstrate them numerically in computer simulations under various standard statistical models.

stat.ME↗

arXiv2020

Randomized p-values for multiple testing and their application in replicability analysis

We are concerned with testing replicability hypotheses for many endpoints simultaneously. This constitutes a multiple test problem with composite null hypotheses. Traditional $p$-values, which are computed under least favourable parameter configurations, are over-conservative in the case of composite null hypotheses. As demonstrated in prior work, this poses severe challenges in the multiple testing context, especially when one goal of the statistical analysis is to estimate the proportion $π_0$ of true null hypotheses. Randomized $p$-values have been proposed to remedy this issue. In the present work, we discuss the application of randomized $p$-values in replicability analysis. In particular, we introduce a general class of statistical models for which valid, randomized $p$-values can be calculated easily. By means of computer simulations, we demonstrate that their usage typically leads to a much more accurate estimation of $π_0$. Finally, we apply our proposed methodology to a real data example from genomics.

stat.ME↗