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Combining one‐sample confidence procedures for inference in the two‐sample case
Author(s) -
Fay Michael P.,
Proschan Michael A.,
Brittain Erica
Publication year - 2015
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.12231
Subject(s) - confidence interval , confidence distribution , cdf based nonparametric confidence interval , robust confidence intervals , coverage probability , statistics , censoring (clinical trials) , nominal level , mathematics , sample size determination , exact statistics , inference , poisson distribution , binomial proportion confidence interval , credible interval , confidence region , confidence and prediction bands , computer science , negative binomial distribution , artificial intelligence
Summary We present a simple general method for combining two one‐sample confidence procedures to obtain inferences in the two‐sample problem. Some applications give striking connections to established methods; for example, combining exact binomial confidence procedures gives new confidence intervals on the difference or ratio of proportions that match inferences using Fisher's exact test, and numeric studies show the associated confidence intervals bound the type I error rate. Combining exact one‐sample Poisson confidence procedures recreates standard confidence intervals on the ratio, and introduces new ones for the difference. Combining confidence procedures associated with one‐sample t ‐tests recreates the Behrens–Fisher intervals. Other applications provide new confidence intervals with fewer assumptions than previously needed. For example, the method creates new confidence intervals on the difference in medians that do not require shift and continuity assumptions. We create a new confidence interval for the difference between two survival distributions at a fixed time point when there is independent censoring by combining the recently developed beta product confidence procedure for each single sample. The resulting interval is designed to guarantee coverage regardless of sample size or censoring distribution, and produces equivalent inferences to Fisher's exact test when there is no censoring. We show theoretically that when combining intervals asymptotically equivalent to normal intervals, our method has asymptotically accurate coverage. Importantly, all situations studied suggest guaranteed nominal coverage for our new interval whenever the original confidence procedures themselves guarantee coverage.

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