Random Intercept for Categorical Outcome and Predictor Variables (55 Patients)

Abstract

Categories are very common in medical research. Examples include age classes, income classes, education levels, drug dosages, diagnosis groups, disease severities, etc. Statistics has generally difficulty to assess categories, and traditional models require either binary or continuous variables. If in the outcome, categories can be assessed with multinomial regression (Chap. 44). If as predictors, they can be assessed with linear regression for categorical predictors (Chap. 8). However, with multiple categories or with categories both in the outcome and as predictors, random intercept models may provide better sensitivity of testing. The latter models assume that for each predictor category or combination of categories x₁, x₂,…slightly different a-values can be computed with a better fit for the outcome category y than a single a-value.

$$ \mathrm{y}=\mathrm{a}+{\mathrm{b}}_1{\mathrm{x}}_1+{\mathrm{b}}_2{\mathrm{x}}_2+\dots . $$

We should add that, instead of the above linear equation, even better results were obtained with log-transformed outcome variables (log = natural logarithm).

$$ \log\ \mathrm{y}=\mathrm{a}+{\mathrm{b}}_1{\mathrm{x}}_1+{\mathrm{b}}_2{\mathrm{x}}_2+\dots . $$

This chapter was previously partly published in “Machine learning in medicine-cookbook 2” as Chap. 6, 2014.