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Revisiting proportion estimators.

Dankmar Böhning1, Chukiat Viwatwongkasem

  • 1Free University Berlin/Humboldt University at Berlin, Berlin, Germany. boehning@zedat.fu-berlin.de

Statistical Methods in Medical Research
|April 6, 2005
PubMed
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This study introduces a new parametric method for proportion estimation, particularly useful for sparse data in clinical trials and epidemiology. An optimal parameter value of c=1 is recommended for improved accuracy and reliable confidence intervals.

Area of Science:

  • Biostatistics
  • Statistical Modeling

Background:

  • Conventional proportion estimators face challenges with sparse data and small sample sizes.
  • Accurate variance estimation for proportions is critical in applications like multicenter trials and epidemiological studies.

Purpose of the Study:

  • To investigate a parametric family of proportion estimators, p(c) = (X + c)/(n + 2c), for improved accuracy with sparse data.
  • To determine the optimal value of parameter 'c' by minimizing average mean squared error and bias.

Main Methods:

  • Exploration of the parametric family p(c) and its application to estimating p(c)(1-p(c)).
  • Analysis of estimation strategies for choosing 'c' based on minimizing average mean squared error and bias.
  • Evaluation of the impact of 'c' on confidence interval construction.

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Main Results:

  • The optimal 'c' for minimizing the average mean squared error of p(c) is independent of sample size (n) and equals 1.
  • The optimal 'c' for minimizing the average mean squared error of p(c)(1-p(c)) depends on 'n', with a limiting value of 0.833.
  • A near-optimal value of c=1 is beneficial for constructing confidence intervals.

Conclusions:

  • The proposed parametric method offers a robust alternative to conventional proportion estimators, especially in data-sparse scenarios.
  • A practical recommendation of c=1 simplifies implementation while maintaining statistical benefits for proportion estimation and confidence intervals.