Sample size determination for 2-step studies with dichotomous response

Man Lai TANG*, Nian Sheng Tang, Vincent J. Carey

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

8 Citations (Scopus)


In this article, we consider problems with correlated data that can be summarized in a 2 × 2 table with structural zero in one of the off-diagonal cells. Data of this kind sometimes appear in infectious disease studies and two-step procedure studies. We propose two kinds of approximate sample size formulas, based on rate ratio, for comparison of the marginal and conditional probabilities in a correlated 2 × 2 table with structural zero. The first type of formula is derived to guarantee a pre-specified power of a hypothesis test at certain significance level while the second type of formula is developed to bound the width of a confidence interval with specified confidence level. Our empirical studies confirm that sample size formulas based on the log-transformation and score tests outperform that based on the Wald's test. We illustrate our methodologies with a real example from a two-phase treatment study.

Original languageEnglish
Pages (from-to)1166-1180
Number of pages15
JournalJournal of Statistical Planning and Inference
Issue number3
Publication statusPublished - 1 Mar 2006

Scopus Subject Areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

User-Defined Keywords

  • Asymptotic inference
  • Correlated binary data
  • Rate ratio
  • Score test
  • Structural zero


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