Random Intercept Models for Both Outcome and Predictor Categories (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 (see the above Chap. 28), if as predictors, they can be assessed with automatic nonparametric tests (see the above Chap. 29). 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-linear equations (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 published in “Machine learning in medicine-cookbook 2” as Chap. 6, 2014.