Small sample behaviour of hypothesis tests related to indirect standardized rates: a Monte Carlo study

Area of Science:

• Biostatistics
• Statistical modeling
• Epidemiology

Background:

• Comparing event frequencies across populations is challenging due to confounding variables.
• Statistical models for rate data offer a solution for comparative analyses.
• The multiplicative model is a recently developed statistical approach for rate data.

Purpose of the Study:

• To evaluate the performance of the multiplicative model using a Monte Carlo simulation.
• To assess the behavior of different statistical test statistics within the multiplicative model framework.
• To compare the likelihood ratio test statistic with the weighted least squares and Pearson statistics for a 4x3 table of rates.

Main Methods:

• A Monte Carlo simulation was employed to study a 4x3 table of rates.
• The performance of the likelihood ratio test statistic was examined under varying expected cell counts.
• The weighted least squares test statistic was compared against the likelihood ratio and Pearson statistics.

Main Results:

• The likelihood ratio test statistic was conservative for small expected cell counts but performed well for large counts.
• The likelihood ratio test statistic showed liberal behavior for moderate expected cell counts.
• The weighted least squares test statistic was consistently more conservative and less powerful than both the likelihood ratio and Pearson statistics.

Conclusions:

• The multiplicative model is a viable statistical tool for analyzing rate data.
• The likelihood ratio test statistic demonstrates reliable performance in the multiplicative model, especially with larger sample sizes.
• Weighted least squares methods may be less suitable for this type of analysis due to lower power and conservatism.