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Approximate confidence interval construction for risk difference under inverse sampling

机译：反采样下风险差异的近似置信区间构造

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摘要

For studies with dichotomous outcomes, inverse sampling (also known as negative binomial sampling) is often used when the subjects arrive sequentially, when the underlying response of interest is acute, and/or when the maximum likelihood estimators of some epidemiologic indices are undefined. Although exact unconditional inference has been shown to be appealing, its applicability and popularity is severely hindered by the notorious conservativeness due to the adoption of the maximization principle and by the tedious computing time due to the involvement of infinite summation. In this article, we demonstrate how these obstacles can be overcome by the application of the constrained maximum likelihood estimation and truncated approximation. The present work is motivated by confidence interval construction for the risk difference under inverse sampling. Wald-type and score-type confidence intervals based on inverting two one-sided and one two-sided tests are considered. Monte Carlo simulations are conducted to evaluate the performance of these confidence intervals with respect to empirical coverage probability, empirical confidence width, and empirical left and right non-coverage probabilities. Two examples from a maternal congenital heart disease study and a drug comparison study are used to demonstrate the proposed methodologies.
机译：对于具有二分结果的研究，当受试者先后到达，感兴趣的潜在反应为急性和/或未定义某些流行病学指标的最大似然估计量时，通常使用逆采样（也称为负二项式采样）。尽管已经证明精确无条件推论很有吸引力，但是由于采用了最大化原理而臭名昭著的保守性以及由于涉及无穷求和的繁琐的计算时间而严重阻碍了其适用性和普及性。在本文中，我们演示了如何通过应用约束最大似然估计和截断近似来克服这些障碍。本研究的工作是通过置信区间构建逆采样下的风险差异。考虑基于反转两个单边和一个单边检验的Wald型和得分型置信区间。进行蒙特卡洛模拟以评估这些置信区间相对于经验覆盖率，经验置信度宽度以及经验左和右非覆盖概率的性能。来自孕妇先天性心脏病研究和药物比较研究的两个例子被用来证明所提出的方法。

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