Estudi de l'estat de Salut autopercebut: Modelització de l'índex d'utilitat EQ-5D mitjançant un model tobit

Abstract

Objective: Health status measures usually have an asymmetric distribution and present a high percentage of respondents with the best possible score (ceiling effect), specially when they are assessed in the overall population. Different methods to model this type of variables have been proposed that take into account the ceiling effect: the tobit models, the Censored Least Absolute Deviations (CLAD) models or the two-part models, among others. The objective of this work was to describe the tobit model, and compare it with the Ordinary Least Squares (OLS) model, that ignores the ceiling effect. Methods: Two different data sets have been used in order to compare both models: a) real data comming from the European Study of Mental Disorders (ESEMeD), in order to model the EQ5D index, one of the measures of utilities most commonly used for the evaluation of health status; and b) data obtained from simulation. Cross-validation was used to compare the predicted values of the tobit model and the OLS models. The following estimators were compared: the percentage of absolute error (R1), the percentage of squared error (R2), the Mean Squared Error (MSE) and the Mean Absolute Prediction Error (MAPE). Different datasets were created for different values of the error variance and different percentages of individuals with ceiling effect. The estimations of the coefficients, the percentage of explained variance and the plots of residuals versus predicted values obtained under each model were compared. Results: With regard to the results of the ESEMeD study, the predicted values obtained with the OLS model and those obtained with the tobit models were very similar. The regression coefficients of the linear model were consistently smaller than those from the tobit model. In the simulation study, we observed that when the error variance was small (s=1), the tobit model presented unbiased estimations of the coefficients and accurate predicted values, specially when the percentage of individuals wiht the highest possible score was small. However, when the errror variance was greater (s=10 or s=20), the percentage of explained variance for the tobit model and the predicted values were more similar to those obtained with an OLS model. Conclusions: The proportion of variability accounted for the models and the percentage of individuals with the highest possible score have an important effect in the performance of the tobit model in comparison with the linear model.