Study of depression influencing factors with zero-inflated regression models in a large-scale population survey

Objectives The number of depression symptoms can be considered as count data in order to get complete and accurate analyses findings in studies of depression. This study aims to compare the goodness of fit of four count outcomes models by a large survey sample to identify the optimum model for a risk factor study of the number of depression symptoms. Methods 15 820 subjects, aged 10 to 80 years old, who were not suffering from serious chronic diseases and had not run a high fever in the past 15 days, agreed to take part in this survey; 15 462 subjects completed all the survey scales. The number of depression symptoms was the sum of the 'positive' responses of seven depression questions. Four count outcomes models and a logistic model were constructed to identify the optimum model of the number of depression symptoms. Results The mean number of depression symptoms was 1.37 +/- 1.55. The over-dispersion test statistic O was 308.011. The alpha dispersion parameter was 0.475 (95% CI 0.443 to 0.508), which was significantly larger than 0. The Vuong test statistic Z was 6.782 and the P value was <0.001, which showed that there were too many zero counts to be accounted for with traditional negative binomial distribution. The zero-inflated negative binomial (ZINB) model had the largest log likelihood and smallest AIC and BIC, suggesting best goodness of fit. In addition, predictive probabilities for many counts in the ZINB model fitted the observed counts best. Conclusions All fitting test statistics and the predictive probability curve produced the same findings that the ZINB model was the best model for fitting the number of depression symptoms, assessing both the presence or absence of depression and its severity.