A Multi-state Piecewise Exponential Model of Hospital Outcomes after Injury

To allow more accurate prediction of hospital length of stay (LOS) after serious injury or illness, a multi-state model is proposed, in which transitions from the hospitalized state to three possible outcome states (home, long-term care, or death) are assumed to follow constant rates for each of a limited number of time periods. This results in a piecewise exponential (PWE) model for each outcome. Transition rates may be affected by time-varying covariates, which can be estimated from a reference database using standard statistical software and Poisson regression. A PWE model combining the three outcomes allows prediction of LOS. Records of 259,941 injured patients from the US Nationwide Inpatient Sample were used to create such a multi-state PWE model with four time periods. Hospital mortality and LOS for patient subgroups were calculated from this model, and time-varying covariate effects were estimated. Early mortality was increased by anatomic injury severity or penetrating mechanism, but these effects diminished with time; age and male sex remained strong predictors of mortality in all time periods. Rates of discharge home decreased steadily with time, while rates of transfer to long-term care peaked at five days. Predicted and observed LOS and mortality were similar for multiple subgroups. Conceptual background and methods of calculation are discussed and demonstrated. Multi-state PWE models may be useful to describe hospital outcomes, especially when many patients are not discharged home.