Approximate confidence interval construction for risk difference under inverse sampling

Man Lai TANG*, Maozai Tian

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)87-98
Number of pages12
JournalStatistics and Computing
Issue number1
Publication statusPublished - Jan 2010

Scopus Subject Areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Theory and Mathematics

User-Defined Keywords

  • Asymptotic confidence interval
  • Exact confidence interval
  • Inverse sampling
  • Risk difference
  • Score test
  • Truncated approximations


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