Selection of Appropriate Model for Quality of Life Data of Strabismus Patients Despite Censorship

Abstract

Introduction: Previous studies on the quality of life of strabismus patients have not examined the existence of censoring to express the relation between the response variable and its predictors.  
Methods & Materials: The information used in this study is a conducted cross-sectional study in 2012. The sample size is 90 children in the age range (4-18) years and with congenital strabismus. We used the RAND Health Insurance Study questionnaire with ten subscales to evaluate the quality of life, which was increased to 11 dimensions by adding some items related to eye alignment concerns introduced by Archer et al. The demographic profile is also recorded by 13 other questions. We have expressed the relationship between the independent and response variables in each of the 11 dimensions of the questionnaire and the overall quality of life score by fitting the multiple linear regression model. Then we fitted the two models of classic Tobit and CLAD, which are for censoring, to all dimensions of the questionnaire.
Results: We showed that in fitting the models to the overall quality of life scale variable, the best model is the multiple linear regression. Because the response variable was normal, and there was no censoring (ceiling and floor effect). However, in the depression subscale, due to the high censoring (28.89% of the ceiling effect) and the almost normal distribution of the response variable (p-value of skewness< 0.05), the appropriate model according to the criteria is the classic Tobit (AIC = 546.33). That is, the classic Tobit model is the best alternative to the multiple linear regression model in the presence of censoring. But these conditions did not exist in all variables. In the subscale, there was a severe censoring performance constraint (67.78% of the ceiling effect). When censoring is high, the distribution of the response variable becomes very skewed, and the distribution of response variables deviates drastically from normal. The distribution of the performance constraint variable was very skewed (p-value <0.001). Here the RMSE standard scale for the classic Tobit model was 28.74, which is much higher than the standard scale for the multiple linear regression model (14.23). The best model for the high censoring was CLAD.
Conclusion: To use the appropriate statistical method in the analysis, one must look at how the response variable is distributed. The multiple linear regression model is very widely used, but in the presence of censoring, the use of this model gives skewed results. In this case, the classic Tobit model and its derived model, CLAD, are replaced. The nonparametric CLAD model calculates accurate estimates with minimum defaults and censoring.