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Approximating the distribution of maximally selected McNemar's statistics
1Department of Statistics, Columbia University, New York, New York 10032, USA. dan@stat.columbia.edu
Biometrics
|September 14, 2000
Summary
Researchers developed a new statistical method for analyzing dichotomous outcomes in paired data. This approach correctly adjusts p-values when thresholds are optimized, improving the accuracy of epidemiologic analyses.
Area of Science:
- Epidemiology
- Biostatistics
- Statistical modeling
Background:
- Summarizing continuous outcomes by thresholds is common in epidemiology.
- McNemar's test is used for dichotomous paired data to test marginal distribution equality.
- Standard McNemar's test is inaccurate when the threshold maximizes the test statistic due to multiple comparisons.
Purpose of the Study:
- To derive the distribution of a maximally selected McNemar's statistic.
- To provide a method for accurate p-value adjustment in such cases.
- To illustrate the methodology with a real-world application.
Main Methods:
- Derivation of the distribution for a maximally selected McNemar's statistic.
- Application of Durbin's approximation (1985) for estimating p-values.
- Simulation experiments to assess approximation accuracy at moderate sample sizes.
Main Results:
- The distribution of the maximally selected McNemar's statistic was derived.
- Durbin's approximation was shown to be a viable method for estimating p-values.
- The methodology was successfully applied to matched prostate cancer case-control data.
Conclusions:
- The derived method and Durbin's approximation provide accurate p-values for maximally selected McNemar's statistics.
- This improves statistical rigor in epidemiologic studies using optimized thresholds.
- The findings are applicable to various fields involving paired dichotomous data analysis.