Control of Type I Error Rates in Bayesian Sequential Designs

Sequential Multiple Hypothesis Testing with Type I Error Control

This work studies multiple hypothesis testing in the setting when we obtain data sequentially and may choose when to stop sampling. We summarize the notion of a sequential pvalue (one that can be continually updated and still maintain a type I error guarantee) and provide several examples from the literature. This tool allows us to convert fixedhorizon step-up or step-down multiple hypothesis t...

Sequential Tests of Multiple Hypotheses Controlling Type I and II Familywise Error Rates.

This paper addresses the following general scenario: A scientist wishes to perform a battery of experiments, each generating a sequential stream of data, to investigate some phenomenon. The scientist would like to control the overall error rate in order to draw statistically-valid conclusions from each experiment, while being as efficient as possible. The between-stream data may differ in distr...

Multiple testing. Part I. Single-step procedures for control of general type I error rates.

The present article proposes general single-step multiple testing procedures for controlling Type I error rates defined as arbitrary parameters of the distribution of the number of Type I errors, such as the generalized family-wise error rate. A key feature of our approach is the test statistics null distribution (rather than data generating null distribution) used to derive cut-offs (i.e., rej...

Optimal sequential designs in phase I studies

Phase I clinical trials are conducted in order to find the maximum tolerated dose of a given drug out of a set of doses, usually finite. In general, once a formal target function and a suitable probability structure are defined, optimization of sequential studies can theoretically be achieved using backward induction. This is a computationally heavy task and most of the proposed methods can be ...

A Randomization Method to Control the Type I Error Rates in Best Subset Regression