A comparison of different methods of zero-inflated data analysis and its application in health surveys

Count data with excessive zeros and/or over-dispersion are prevalent in a wide variety of disciplines, such as public health, psychology, and environmental science. Different regression models have been proposed to deal with data with a preponderance of zero observations. These approaches include: a. transform the data to make it normal and use ordinary least-squares regression (LST); b. Poisson regression (Poisson); c. negative binomial regression (NB); d. zero-inflated Poisson regression (ZIP); e. zero-inflated negative binomial regression (ZINB); f. zero-altered Poisson regression (ZAP); and g. zero-altered negative binomial regression (ZANB). There is no clear guideline as to which one to use and it is possible that one approach is more preferable than the others under different degrees of zero-inflation and over-dispersion. This study aimed to evaluate the performance of the above seven models under different conditions of zero-inflation and over-dispersion and to examine the amount of bias and poor fit resulting from fitting various models. Simulated datasets were generated with a mixture of different proportions of zeros (20%, 40%, 60%, and 80%) and a negative binomial distribution with different dispersion parameters (10, 50, and 100). Health survey data from the Behavioral Risk Factor Surveillance System (BRFSS) study were then analyzed to further assess zero-inflated procedures and explore the relationship between physical activity and health related quality of life. Akaike Information Criterion (AIC) values and Vuong tests were used to evaluate relative quality of the regression models. Results from the simulation study showed that the ZINB and the ZANB models had smaller AIC values in all conditions of zero-inflation and over-dispersion which indicate better performance than for the other models. The LST model had the worst fit to the data under every condition. As for the empirical study, the ZANB model was chosen as the final model and results showed that compared with highly active people, inactive people were likely to experience 1.39 more unhealthy days. Females and older people were more likely to report unhealthy days. Results also showed that estimated regression coefficients and standard errors differed across different models. There was a tendency for the worse models to have smaller standard errors and to make Type I errors. Overall, this study suggests using special zero-inflated models like ZINB or ZANB when the data have both excessive zeros and skewness in the non-zero part.