Logistic regression with missing responses and predictors: a review of existing approaches and a case study

TL;DR

This paper reviews methods for logistic regression with missing data, compares their performance through simulations, and applies the best methods to a real case study on childhood obesity, providing practical guidance.

Contribution

It offers a comprehensive review of existing approaches for logistic regression with missing data and evaluates their performance, highlighting maximum likelihood as the most effective method.

Findings

Maximum likelihood yields the least bias and variance.

Multiple imputation with five datasets performs nearly as well.

All methods agree on the importance of past obesity and physical scores.

Abstract

In this work logistic regression when both the response and the predictor variables may be missing is considered. Several existing approaches are reviewed, including complete case analysis, inverse probability weighting, multiple imputation and maximum likelihood. The methods are compared in a simulation study, which serves to evaluate the bias, the variance and the mean squared error of the estimators for the regression coefficients. In the simulations, the maximum likelihood methodology is the one that presents the best results, followed by multiple imputation with five imputations, which is the second best. The methods are applied to a case study on the obesity for schoolchildren in the municipality of Viana do Castelo, North Portugal, where a logistic regression model is used to predict the International Obesity Task Force (IOTF) indicator from physical examinations and the past values of the obesity status. All the variables in the case study are potentially missing, with gender as the only exception. The results provided by the several methods are in well agreement, indicating the relevance of the past values of IOTF and physical scores for the prediction of obesity. Practical recommendations are given.