Predicting longitudinal trajectories of health probabilities with random-effects multinomial logit regression

Area of Science:

• Biostatistics
• Longitudinal Data Analysis
• Health Outcomes Research

Background:

• Longitudinal health data often involves multiple ordinal or nominal categories.
• Random-effects multinomial logit models are standard for clustered longitudinal data.
• Parameter estimates require retransformation of random effects for accurate probability predictions.

Purpose of the Study:

• To develop a novel retransformation method for unbiased longitudinal health probability predictions.
• To derive accurate longitudinal growth trajectories from health outcome data.
• To transform regression coefficients into meaningful conditional effects on predicted probabilities.

Main Methods:

• Developed and applied a retransformation method for random-effects multinomial logit models.
• Utilized the delta method to estimate variances of predicted probabilities.
• Transformed regression coefficients to conditional effects on predicted probabilities.
• Empirically illustrated the method using the Asset and Health Dynamics among the Oldest Old dataset.

Main Results:

• The retransformation method yields unbiased longitudinal health probability trajectories.
• Failure to retransform random effects results in severely biased health trajectories.
• Covariate effects on health probabilities are overestimated when retransformation is neglected.

Conclusions:

• Accurate longitudinal health probability modeling necessitates retransforming random effects.
• The proposed retransformation method provides unbiased estimates and interpretable covariate effects.
• Ignoring retransformation in random-effects multinomial logit models can lead to significant analytical errors.