Exact and approximate unconditional confidence intervals for proportion difference in the presence of incomplete data

Man-Lai TANG, Man Ho Alpha LING, Guo-Liang TIAN

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17 Citations (Scopus)

Abstract

Confidence interval (CI) construction with respect to proportion/rate difference for paired binary data has become a standard procedure in many clinical trials and medical studies. When the sample size is small and incomplete data are present, asymptotic CIs may be dubious and exact CIs are not yet available. In this article, we propose exact and approximate unconditional test‐based methods for constructing CI for proportion/rate difference in the presence of incomplete paired binary data. Approaches based on one‐ and two‐sided Wald's tests will be considered. Unlike asymptotic CI estimators, exact unconditional CI estimators always guarantee their coverage probabilities at or above the pre‐specified confidence level. Our empirical studies further show that (i) approximate unconditional CI estimators usually yield shorter expected confidence width (ECW) with their coverage probabilities being well controlled around the pre‐specified confidence level; and (ii) the ECWs of the unconditional two‐sided‐test‐based CI estimators are generally narrower than those of the unconditional one‐sided‐test‐based CI estimators. Moreover, ECWs of asymptotic CIs may not necessarily be narrower than those of two‐sided‐based exact unconditional CIs. Two real examples will be used to illustrate our methodologies. Copyright © 2008 John Wiley & Sons, Ltd.
Original languageEnglish
Pages (from-to)625-641
JournalStatistics in Medicine
Volume28
Issue number4
DOIs
Publication statusPublished - Feb 2009

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Incomplete Data
Confidence interval
Proportion
Confidence Intervals
Estimator
Paired Data
Binary Data
Coverage Probability
Confidence Level
Wald Test
Clinical Trials
Sample Size
Empirical Study
Confidence
Methodology

Citation

Tang, M.-L., Ling, M.-H., & Tian, G.-L. (2009). Exact and approximate unconditional confidence intervals for proportion difference in the presence of incomplete data. Statistics in Medicine, 28(4), 625-641. doi: 10.1002/sim.3490

Keywords

  • Asymptotic inference
  • Incomplete data
  • Paired binary data
  • Test‐based confidence interval
  • Unconditional exact inference