arXiv subjects

Daniel Ochieng

Publications and source records attributed to Daniel Ochieng.

3 recordsLinked to original sources

arXiv2025

A Comparison of the Bayesian Posterior Probability and the Frequentist $p$-Value in Testing Equivalence Hypotheses

Equivalence tests, otherwise known as parity or similarity tests, are frequently used in ``bioequivalence studies" to establish practical equivalence rather than the usual statistical significant difference. In this article, we propose an equivalence test using both the $p$-value and a Bayesian procedure by computing the posterior probability that the null hypothesis is true. Since these posterior probabilities follow the uniform $[0,1]$ distribution under the null hypothesis, we use them in a Two One-Sided Test (TOST) procedure to perform equivalence tests. For certain specifications of the prior parameters, test based on these posterior probabilities are more powerful and less conservative than those based on the $p$-value. We compare the parameter values that maximize the power functions of tests based on these two measures of evidence when using different equivalence margins. We also derive the correlation coefficient between these two measures of evidence. Furthermore, we also consider the effect of the prior variance on the conservativity and power function of the test based on the posterior probabilities. Finally, we provide examples and a small-scale simulation study to compare their performance in terms of type I error rate control and power in a single test, as well as in multiple testing, considering the power of the false discovery rate procedure.

stat.ME↗

arXiv2024

Multiple testing of interval composite null hypotheses using randomized p-values

One class of statistical hypothesis testing procedures is the indisputable equivalence tests, whose main objective is to establish practical equivalence rather than the usual statistical significant difference. These hypothesis tests are prone in bioequivalence studies, where one would wish to show that, for example, an existing drug and a new one under development have the same therapeutic effect. In this article, we consider a two-stage randomized (RAND2) p-value utilizing the uniformly most powerful (UMP) p-value in the first stage when multiple two-one-sided hypotheses are of interest. We investigate the behavior of the distribution functions of the two p-values when there are changes in the boundaries of the null or alternative hypothesis or when the chosen parameters are too close to these boundaries. We also consider the behavior of the power functions to an increase in sample size. Specifically, we investigate the level of conservativity to the sample sizes to see if we control the type I error rate when using either of the two p-values for any sample size. In multiple tests, we evaluate the performance of the two p-values in estimating the proportion of true null hypotheses. We conduct a family-wise error rate control using an adaptive Bonferroni procedure with a plug-in estimator to account for the multiplicity that arises from the multiple hypotheses under consideration. We verify the various claims in this research using simulation study and real-world data analysis.

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arXiv2022

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.

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