Testing the non-unity of rate ratio under inverse sampling

Area of Science:

• Epidemiology
• Biostatistics

Background:

• Inverse sampling is a suitable alternative to binomial sampling for specific study designs.
• Challenges exist in estimating epidemiologic indices with maximum likelihood estimators under certain conditions.

Purpose of the Study:

• To evaluate statistical tests for rate ratios in case-control studies using inverse sampling.
• To compare the performance of different test statistics and P-value calculation methods.

Main Methods:

• Investigated Wald, unconditional score, likelihood ratio, and conditional score statistics.
• Employed asymptotic, conditional exact, and Mid-P methods for P-value calculation.
• Utilized Monte Carlo simulation to assess empirical sizes and powers.

Main Results:

• Asymptotic and conditional score tests demonstrated well-controlled type I error rates and superior power.
• The exact Wald test is recommended for strict type I error control.
• The Mid-P Wald test offers higher power with acceptable size fluctuations.

Conclusions:

• Score tests are generally preferred for their balance of accuracy and power in inverse sampling case-control studies.
• Specific Wald test versions are suitable depending on the priority of error control versus power.
• Methodologies were demonstrated using a real-world heart disease study example.