Sufficient Sample Size and Power in Multilevel Ordinal Logistic Regression Models

Area of Science:

• Biostatistics
• Epidemiology
• Health Services Research

Background:

• Multilevel models are frequently used in biomedical research with nested data, such as patients within doctor groups.
• Ordinal outcome variables, representing categories like disease severity (mild, severe, extremely severe), are common in these models.

Purpose of the Study:

• To compare the performance of Maximum Likelihood (ML) and Penalized Quasilikelihood (PQL) estimation methods for multilevel cumulative logit models with ordinal outcomes.
• To determine the sample size requirements for achieving adequate statistical power with these methods.

Main Methods:

• Simulation study comparing ML and PQL estimation in multilevel cumulative logit models.
• Analysis focused on three-category and five-category ordinal outcome variables.
• Power analysis to determine group sample size requirements.

Main Results:

• For three-category ordinal outcomes, ML estimation outperformed PQL.
• For five-category ordinal outcomes, PQL performed comparably to ML, with slightly higher power observed for PQL.
• A minimum of 50 groups is necessary for both ML and PQL methods to achieve a power exceeding 0.80.

Conclusions:

• The choice between ML and PQL methods for multilevel ordinal logistic models depends on the number of outcome categories.
• Sample size is a critical factor for achieving sufficient power in these models, with at least 50 groups recommended.
• Both methods are viable, but PQL may offer a slight advantage in power for models with more outcome categories.