In the context of the OP, the same result should occur if this predictive "frequentist-matching property" occurs when the observation of interest is the test statistic. In group sequential clinical trials, the patients enrollment is partitioned into multiple stages. Here the observation of interest is a sample standard deviation, and the Bayesian predictive distribution of this standard deviation enjoys the "frequentist-matching property": Bayesian $100p\%$-prediction intervals coincidentally are frequentist $100p\%$-prediction intervals. The conclusion is that indeed the Bayesian prediction approach (with an appropriate noninformative prior) controls the frequentist probability of success. Patient heterogeneity has become pivotal to the. Baskets trials are used in oncology to study interventions that are developed to target a specific feature (often genetic alteration or immune phenotype) that is observed across multiple tissue types and/or tumor histologies. It is not really related to the power of a hypothesis test but the approach is of the same spirit as the question of the OP: the goal is to guarantee a given probability of success for a certain event, similarly to the question of the OP in the context of hypothesis testing. This article discusses and compares statistical designs of basket trial, from both frequentist and Bayesian perspectives. adaptive designs from a frequentist perspective in great generality. Here is an example of using the Bayesian predictive distribution for planning a new experience: Sample size determination for a Gaussian mean Stopping an A/B test early because the results are statistically significant is usually a bad idea. stopping times based on sequential testing or other adaptive stopping rules.
It would be easy to explore such questions using simulations, but does there exist some theoretical results about such questions ? Combines the benefits of sequential and fixed sample testing: early stopping and. Then collect the new sample and perform the test.Īdopting this methodology, what about the probability to reject $H_0$ in function of $\theta$ ? Sequential frequentist (default), Just start running your experiment.Otherwise use the predictive distribution to evaluate the required new sample size to get $80\%$ predictive power to reject $H_0$.Here is a table with the results of these analyses. Our contributions can also be viewed as providing frequentist guarantees to the Bayesian sequential test. Suppose we perform a hypothesis test from a random sample $(x_i)_^n$ with $n=10$ The Pocock approach to group sequential testing requires a significance level of 0.0158 at each analysis. More specifically, our test statistic can be interpreted as a Bayes factor, which can be readily used in a traditional Bayesian analysis.
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