Frequency of Visiting a Doctor: A right Truncated Count Regression Model with Excess Zeros

Count response variables are frequently encountered in medical data, which calls for the use of count regression models. In this study, we introduce the hurdle Conway-Maxwell Poisson (HCMP) regression model where the outcome variable is the number of doctor visits, complicated by excess zeros and over-dispersion from troublesome extreme values. A truncation approach is proposed to handle extreme values, leading to the definition of a truncated HCMP (THCMP) model. Parameter estimates are derived using maximum likelihood. Results of a case study on a RWM dataset investigated effects of response truncation at 6.65, 3.08 and 1.75% for the THCMP and truncated hurdle Poisson (THP) models. In a simulation study, responses were generated from a mixture of HCMP (50%) and HP (50%) probability models. THCMP and THP model performance was compared with respect to parameter estimation bias, goodness-of-fit and outcome estimates for truncation levels of 5 and 10%. As measured by AIC, the THCMP model exhibited better goodness-of-fit at all truncation levels compared to the THP model. Estimation bias increased with higher truncation levels for both models, but to a lesser degree for the THCMP model.