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Control sample size when cases are given in constant ratio stratum-matched case-control studies.

J M Nam1, T R Fears

  • 1Biostatistics Branch, National Cancer Institute, Rockville, Maryland 20892.

Statistics in Medicine
|September 30, 1992
PubMed
Summary
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This study provides a condition for solving the number of controls (k) in case-control studies. It details the maximum power of the Cochran test and the minimum cases needed for desired statistical power.

Area of Science:

  • Biostatistics
  • Epidemiological Research Methods

Background:

  • Strata-matched case-control studies are frequently used in epidemiological research.
  • Determining the optimal number of controls (k) relative to cases is crucial for study power.

Purpose of the Study:

  • To establish conditions for the existence of a numerical solution for k in strata-matched case-control studies.
  • To derive the maximum statistical power of the Cochran test for a fixed number of cases.
  • To provide a formula for the minimum number of cases required to achieve a specified power.

Main Methods:

  • Derivation of a necessary and sufficient condition for the existence of a solution for k.
  • Calculation of the maximum power of the Cochran test.
  • Development of an approximate formula for the minimum required number of cases.

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Main Results:

  • A condition is established for the numerical solvability of k.
  • The maximum power of the Cochran test is determined, which may be less than one.
  • An approximate formula for the minimum number of cases for a given power is provided.
  • The convergence of iterative methods for finding k is dependent on the number of cases exceeding this minimum.

Conclusions:

  • The study clarifies the relationship between the number of cases, controls, and statistical power in strata-matched case-control studies.
  • It provides practical guidance for sample size calculations and the interpretation of study power.
  • The diminishing incremental gain in efficiency with increasing k is highlighted.