The large sample coverage probability of confidence intervals in general regression models after a preliminary hypothesis test

摘要

We derive a computationally convenient formula for the large sample coverageprobability of a confidence interval for a scalar parameter of interestfollowing a preliminary hypothesis test that a specified vector parameter takesa given value in a general regression model. Previously, this large samplecoverage probability could only be estimated by simulation. Our formula onlyrequires the evaluation, by numerical integration, of either a double or tripleintegral, irrespective of the dimension of this specified vector parameter. Weillustrate the application of this formula to a confidence interval for the logodds ratio of myocardial infarction when the exposure is recent oralcontraceptive use, following a preliminary test that two specified interactionsin a logistic regression model are zero. For this real-life data, we comparethis large sample coverage probability with the actual coverage probability ofthis confidence interval, obtained by simulation.