Simultaneous confidence intervals of risk differences in stratified paired designs

Nian Sheng Tang*, Shi Fang Qiu, Man Lai TANG, Guang Yong Zou, Dan Yu

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

5 Citations (Scopus)


In stratified matched-pair studies, risk difference between two proportions is one of the most frequently used indices in comparing efficiency between two treatments or diagnostic tests. This article presents five simultaneous confidence intervals and two bootstrap simultaneous confidence intervals for risk differences in stratified matched-pair designs. The proposed confidence intervals are evaluated with respect to their coverage probabilities, expected widths, and ratios of the mesial noncoverage to noncoverage probability. Empirical results show that (1) hybrid simultaneous confidence intervals outperform nonhybrid simultaneous confidence intervals; (2) hybrid simultaneous confidence intervals based on median estimator outperform those based on maximum likelihood estimator; and (3) hybrid simultaneous confidence intervals incorporated with Wilson score and Agresti coull intervals and the bootstrap t-percentile simultaneous interval based on median unbiased estimators behave satisfactorily for small to large sample sizes in the sense that their empirical coverage probabilities are close to the prespecified nominal confidence level, and their ratios of the mesial noncoverage to noncoverage probabilities lie in [0.4,0.6] and are hence recommended. Real examples from clinical studies are used to illustrate the proposed methodologies.

Original languageEnglish
Pages (from-to)361-377
Number of pages17
JournalJournal of Biopharmaceutical Statistics
Issue number2
Publication statusPublished - 11 Mar 2013

Scopus Subject Areas

  • Statistics and Probability
  • Pharmacology
  • Pharmacology (medical)

User-Defined Keywords

  • Bootstrap simultaneous confidence interval
  • Median unbiased estimate
  • Risk difference
  • Simultaneous confidence interval
  • Stratified matched-pair design


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