The large sample coverage probability of confidence intervals in general regression models after a preliminary hypothesis test
本文推导了一个计算方便的公式，用于计算一般回归模型中经过初步假设检验后置信区间的大样本覆盖概率，避免了模拟估计，并通过逻辑回归中比值比的实例进行了验证。
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 a triple integral, irrespective of the dimension of this specified vector parameter. We illustrate the application of this formula to a confidence interval for the odds ratio of myocardial infarction when the exposure is recent oral contraceptive use, following a preliminary test where 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.