Comparison of the results of Cox proportional hazards model and parametric models in the study of length of stay in a tertiary teaching hospital in Tehran, Iran

Survival analysis is a set of methods used for analysis of the data which exist until the occurrence of an event. This study aimed to compare the results of the use of the semi-parametric Cox model with parametric models to determine the factors influencing the length of stay of patients in the inpatient units of Women Hospital in Tehran, Iran. In this historical cohort study all 3421 charts of the patients admitted to Obstetrics, Surgery and Oncology units in 2008 were reviewed and the required patient data such as medical insurance coverage types, admission months, days and times, inpatient units, final diagnoses, the number of diagnostic tests, admission types were collected. The patient length of stay in hospital 'leading to recovery' was considered as a survival variable. To compare the semi-parametric Cox model and parametric (including exponential, Weibull, Gompertz, log-normal, log-logistic and gamma) models and find the best model fitted to studied data, Akaike's Information Criterion (AIC) and Cox-Snell residual were used. P<0.05 was considered as statistically significant. AIC and Cox-Snell residual graph showed that the gamma model had the lowest AIC (4288.598) and the closest graph to the bisector. The results of the gamma model showed that factors affecting the patient length of stay were admission day, inpatient unit, related physician specialty, emergent admission, final diagnosis and the number of laboratory tests, radiographies and sonographies (P<0.05). The results showed that the gamma model provided a better fit to the studied data than the Cox proportional hazards model. Therefore, it is better for researchers of healthcare field to consider this model in their researches about the patient length of stay (LOS) if the assumption of proportional hazards is not fulfilled.