Abstract
In healthcare research, medical expenditure data for the elderly are typically semicontinuous and right-skewed, which involve a point mass at zero and may exhibit heteroscedasticity. The problem of a substantial proportion of zero values prevents traditional regression techniques based on the Gaussian, gamma, or inverse Gaussian distribution, which may lead to understanding the standard errors of the parameters and overestimating their significance. A common way to counter the problem is using zero-adjusted models. However, due to the right-skewness in the nonzeros' response, conventional zero-adjusted models such as zero-adjusted gamma, zero-adjusted Inverse Gaussian, and classic Tobit may not perform well. Here, we firstly generalize those three types of the conventional zero-adjusted model to solve the problem of right-skewness in health care. The generalized zero-adjusted models are very flexible and include the zero-adjusted Weibull, zero-adjusted gamma, zero-adjusted inverse Gaussian, and classic Tobit models as their special cases. Using the Chinese Longitudinal Healthy Longevity Survey, we find that, according to the AIC, SBC, and deviance criteria, the zero-adjusted generalized gamma model is the best one of these generalized models to predict the odds of zero cost accurately. In order to depict the predictors affecting the amount expenditure, we further discuss the situations where the mean, dispersion of a nonzero amount expenditure and model the probability of a zero amount of ZAGG in terms of predictor variables using suitable link functions, respectively. Our analysis shows that age, health, chronic diseases, household income, and residence are the main factors influencing the medical expenditure for the elderly, but the insurance is not significant. To the best of our knowledge, little study focused on these situations, and this is the first time.
Highlights
In healthcare research, medical expenditure data for the elderly are typically semicontinuous and right-skewed, which involve a point mass at zero and may exhibit heteroscedasticity. e problem of a substantial proportion of zero values prevents traditional regression techniques based on the Gaussian, gamma, or inverse Gaussian distribution, which may lead to understanding the standard errors of the parameters and overestimating their significance
We selected ten predictors according to the demand for health and health care of the Grossman model. e estimates of the Tobit model were quite different from others in the value range and sign, which had the largest values of Akaike’s information criterion (AIC), Schwarz Bayesian criterion (SBC), and global deviance. is suggested that the Tobit model fitted the data very badly. e new generalized Tobit model and other zero-adjusted models were more similar
The AIC, SBC, and global deviance (GD) of the zero-adjusted generalized gamma model and zero-adjusted generalized inverse Gaussian model were obviously smaller than those other models
Summary
Medical expenditure data for the elderly are typically semicontinuous and right-skewed, which involve a point mass at zero and may exhibit heteroscedasticity. e problem of a substantial proportion of zero values prevents traditional regression techniques based on the Gaussian, gamma, or inverse Gaussian distribution, which may lead to understanding the standard errors of the parameters and overestimating their significance. Ese phenomena will lead to a large number of zero consumption expenditures in the medical expenditure data of the elderly [6, 7], which will result in right-skewed problems in the distribution of medical consumption data. Because of the point mass at zero and skewness, these problems can hardly be taken into account by traditional regression models such as Poisson, OLS, and gamma models Ignoring these phenomena would lead to misspecified regression-based estimators and overestimated/underestimated effects. E aim of this paper is to propose a type of generalized zero-adjusted model to better fit the semicontinuous data, explore the influencing factors of elderly’s medical expense, use this type of model to predict the amount of medical consumption of the elderly, and compare the results with conventional models In order to predict more accurately, the medical expenses of the elderly new models need to be proposed. e aim of this paper is to propose a type of generalized zero-adjusted model to better fit the semicontinuous data, explore the influencing factors of elderly’s medical expense, use this type of model to predict the amount of medical consumption of the elderly, and compare the results with conventional models
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