Correction when using Estimates in Logistic Regression for Longitudinal Data: An example of sepsis and C-reactive protein

Rosa C. S. Oliveira¹

1. Matemática, Faculdade de Ciências, Porto, Portugal.

Correspondence should be addressed to: rosita21@gmail.com.

Section:Research Paper, Product Type: Journal-Paper
Vol.7 , Issue.2 , pp.55-64, Apr-2020

Online published on Apr 30, 2020

Copyright © Rosa C. S. Oliveira . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
A usual aim in longitudinal studies is to characterize the relationship between a dichotomous outcome and both time-independent and time-dependent covariates. In this paper, we study nonlinear generalized mixed-effects regression models for analysis of longitudinal data. We use a two-stage approach that first fits a linear model to the longitudinal data estimating the random effect that describes the trend for each method and then uses the estimated intercept and slope as predictors for the covariates used in a probit model. We show how to adapt a regression calibration and the best linear unbiased obtained from a linear mixed model approaches to this context and compare these approaches with a naive analysis where the estimation error is ignored. The methods are applied to health data collected during a study designed to evaluate the epidemiology of community-acquired sepsis in a larger cohort of infected intensive care unit patients. We show that the straight use of the estimates in the probit model produces biased estimates of their outcome. Nonetheless, regression calibration and linear mixed effect offer little or no advantage when sample sizes are small, they perform best when samples are reasonably large and especially when the error of prediction (measurement error) or the effects are not small. Our study indicates that the naive approach produces weak results and that regression calibration and linear mixed effect method provides a way to obtain unbiased estimators, especially when is correction advocated, practically indistinguishable.

Key-Words / Index Term :
error of prediction, general nonlinear model, longitudinal data

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