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

TL;DR

This paper presents a new formula for calculating the large sample coverage probability of confidence intervals after a preliminary hypothesis test in general regression models, simplifying computations compared to simulation methods.

Contribution

The authors derive a computationally efficient formula for coverage probability that only requires numerical integration, applicable regardless of the dimension of the parameter vector.

Findings

The formula accurately estimates coverage probability in practical examples.

Application to logistic regression demonstrates the method's utility.

Comparison with simulation confirms the formula's effectiveness.

Abstract

We derive a computationally convenient formula for the large sample coverage probability of a confidence interval for a scalar parameter of interest following a preliminary hypothesis test that a specified vector parameter takes a given value in a general regression model. Previously, this large sample coverage probability could only be estimated by simulation. Our formula only requires the evaluation, by numerical integration, of either a double or triple integral, irrespective of the dimension of this specified vector parameter. We illustrate the application of this formula to a confidence interval for the log odds ratio of myocardial infarction when the exposure is recent oral contraceptive use, following a preliminary test that two specified interactions in a logistic regression model are zero. For this real-life data, we compare this large sample coverage probability with the actual coverage probability of this confidence interval, obtained by simulation.