By Ding-Geng Chen, Jiahua Chen, Xuewen Lu, Grace Y. Yi, Hao Yu
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In addition, the hurdle Poisson and hurdle NB models fit better than their corresponding ZIP and ZINB models, which suggests that the zero counts were best modeled as being only structural zeroes. Furthermore, we included the random effect terms in the model to compare the goodness of fit of ZIP, ZINB, hurdle Poisson and hurdle NB models with various configuration of random effect terms, ranging from the model without any random effect terms, models with random effect term in one of the two model components and models with random effect terms in both model components.
24 %/ had same-day surgery, which constitutes the zero counts in LOS. Among those inpatients who stayed in hospital overnight, the number of days ranged from 1 to 156, with 75 % having fewer than a week of stay. Suppose that the data were generated under an independent and identically distributed Poisson regression with mean parameter as the mean 4:5 days, which is the mean of the LOS in our data. Under such model, we would expect about 1 % of zeros, which is far fewer 0s than observed. The proportion of zeros and the right-skewed non-zero counts suggest the potential zero inflation relative to the conventional Poisson distribution and overdispersion.
When ij D 1, no patients received day surgery and the data follows a truncated count distribution, whereas, when ij D 0, no patients stayed in hospital overnight. ij ranges between 0 and 1. The parameter ij measures the expected mean counts of LOS (in days) for those patients who stayed in hospital overnight, so as ij increases, the average LOS increases. Both logit. ij / and log. ij / are assumed to depend on a function of covariates. In addition, the random effects at the health district level are introduced in the model to account for possible correlation between the two components.