Robustness of zero truncated negative binomial models over traditional models with application to analysing factor association to length of ICU stay in a middle-income country

Traditional linear and logistic regression models are unsuitable for count outcomes, leading to biased or inefficient estimates. For truncated count data, appropriate models that account for truncation are essential. This study aimed to compare poisson, negative binomial (NB), zero-truncated poisson, and zero-truncated negative binomial (ZTNB) models using simulated and real intensive care unit (ICU) data to identify factors association with length of ICU stay. Data were simulated under varying sample sizes to assess model performance. Real data were obtained from a prospective study conducted in the Surgical ICU at CMC Vellore between January and June 2019, including 489 adult patients with an ICU stay of more than 48 hours who received enteral or total parenteral nutrition within one week of admission. Both simulated and real ICU data demonstrated that the ZTNB model provided a good fit for zero-truncated length of stay outcomes. Although the ZTNB and NB models showed similar performance, model selection criteria, particularly the Akaike Information Criterion (AIC), favoured the ZTNB model, indicating its suitability for zero-truncated and overdispersed count data.