A likelihood ratio test for nested proportions.

Area of Science:

• Biostatistics
• Health Services Research
• Epidemiology

Background:

• Assessing changes in event proportions after interventions is crucial for policy and medical decisions.
• Nested proportions, where later data is a subset of earlier data, pose challenges for standard statistical methods.
• Existing methods like two-sample proportion tests, longitudinal analysis, and recurrent event approaches are not directly applicable to nested proportions.

Purpose of the Study:

• To propose a novel statistical test for comparing two nested proportions.
• To address the conditionality and subject dependencies inherent in nested proportion data.
• To provide a practical method for analyzing nested proportions in applied research settings.

Main Methods:

• Development of a likelihood ratio test utilizing the product of conditional probabilities.
• The proposed test accommodates conditionality, subject dependencies, and cluster effects.
• Implementation in SAS PROC NLMIXED for practical application.

Main Results:

• Simulation studies demonstrated that the proposed approach yields unbiased estimates and adequate statistical power.
• The new method generally outperforms the two-sample proportion z-test and the Cochran-Mantel-Haenszel test, especially with heterogeneity.
• The test effectively handles the complexities of nested data structures.

Conclusions:

• The proposed likelihood ratio test provides a statistically sound and practical solution for comparing nested proportions.
• This method enables more accurate analysis of event rate changes in scenarios like emergency department return visits.
• The approach offers advantages over existing methods for nested proportion analysis in medical and policy research.