Categorizing a continuous predictor subject to measurement error

Abstract

Epidemiologists often categorize a continuous risk predictor, even when the true risk model is not a categorical one. Nonetheless, such categorization is thought to be more robust and interpretable, and thus their goal is to fit the categorical model and interpret the categorical parameters. We address the question: with measurement error and categorization, how can we do what epidemiologists want, namely to estimate the parameters of the categorical model that would have been estimated if the true predictor was observed? We develop a general methodology for such an analysis, and illustrate it in linear and logistic regression. Simulation studies are presented and the methodology is applied to a nutrition data set. Discussion of alternative approaches is also included.

Keywords: Categorization; differential misclassification; epidemiology practice; inverse problems; measurement error.

Fig 1.

EATS data of Section 5. Top panel: Normal qq-plot of the mean Fat Density over 4 recalls. This indicates that the mean Fat Density is approximately normally distributed and qualifies for the assumptions in our numerical example. Middle panel: Normal qq-plot of differences of observed Fat density, as a diagnosis that U is approximately normally distributed. Bottom panel: Mean and standard deviation plot to diagnose heteroscedasticity, showing that there is little heteroscedasticity in the measurement errors.