Multiple imputation score tests and an application to Cochran-Mantel-Haenszel statistics.

Area of Science:

• Statistics
• Biostatistics
• Statistical Methods

Background:

• Standard multiple imputation primarily targets parameter estimation.
• Score tests are crucial for hypothesis testing in statistical models.
• Existing methods for score tests with missing data may have limitations.

Purpose of the Study:

• To propose and evaluate a novel method for conducting score tests following multiple imputation.
• To compare the performance of the proposed method against a Wilson-Hilferty transformation-based approach for the Cochran-Mantel-Haenszel (CMH) test.
• To assess the impact of missing data on the Type I error rates of different methods.

Main Methods:

• Development of a multiple imputation technique specifically for score tests.
• Application of the proposed method using the Cochran-Mantel-Haenszel (CMH) test.
• Comparison with a method utilizing the Wilson-Hilferty transformation of the CMH statistic.

Main Results:

• The proposed multiple imputation method successfully preserves the nominal significance level across three alternative hypotheses.
• The Wilson-Hilferty transformation method inflates Type I error for "row means differ" and "general association" alternatives.
• Type I error inflation in the Wilson-Hilferty method exacerbates with higher proportions of missing data.

Conclusions:

• The proposed multiple imputation method offers a more reliable approach for score tests with missing data compared to the Wilson-Hilferty transformation.
• Accurate significance level control is critical, particularly in the presence of substantial missingness.
• This method enhances the validity of statistical inference in analyses with incomplete datasets.