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Confidence intervals for weighted proportions

J L Waller1, C L Addy, K L Jackson

  • 1Department of Epidemiology and Biostatistics, University of South Carolina, Columbia 29208.

Statistics in Medicine
|May 30, 1994
PubMed
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This study introduces a superior method for calculating confidence intervals in stratified two-stage sampling, especially with rare events. The F-distribution method with rescaling offers better accuracy for proportion estimation in complex survey designs.

Area of Science:

  • Statistics
  • Survey Methodology
  • Biostatistics

Background:

  • Calculating confidence intervals for proportions in stratified two-stage sampling is challenging, particularly with few events and unequal strata sizes.
  • Traditional binomial-based methods may fail when normal approximations are invalid due to small event counts.

Purpose of the Study:

  • To evaluate and compare five distinct methods for constructing a single, overall confidence interval for a proportion in stratified two-stage sampling.
  • To identify the most reliable method for proportion estimation considering weighting schemes and small event numbers.

Main Methods:

  • Computer simulations were employed to assess coverage probability and bias of five confidence interval construction methods.
  • Methods compared included binomial variance, F-distribution approximations, exact confidence limits for zero prevalence, and variations with rescaling factors.

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Main Results:

  • The F-distribution method combined with stratum-specific intervals and a rescaling factor demonstrated the best coverage probability.
  • Binomial variance methods exhibited negative bias, while F-distribution methods showed positive bias.

Conclusions:

  • The F-distribution method with rescaling is recommended for constructing confidence intervals in stratified two-stage sampling with few events.
  • Accurate proportion estimation in complex surveys requires careful consideration of the chosen confidence interval method and potential biases.