Applicability of multiplicative and additive hazards regression models in survival analysis

Abstract

Background: Survival analysis is sometimes called “time-to-event analysis”. The Cox model is used widely in survival analysis, where the covariates act multiplicatively on unknown baseline hazards. However, the Cox model requires the proportionality assumption, which limits its applications. The additive hazards model has been used as an alternative to the Cox model, where the covariates act additively on unknown baseline hazards. Objectives and methods: In this thesis, performance of the Cox multiplicative hazards model and the additive hazards model have been demonstrated and applied to the transfer, lifting and repositioning (TLR) injury prevention study. The TLR injury prevention study was a retrospective, pre-post intervention study that utilized a non-randomized control group. There were 1,467 healthcare workers from six hospitals in Saskatchewan, Canada who were injured from January 1, 1999 to December 1, 2006. De-identified data sets were received from the Saskatoon Health Region and Regina Qu’appelle Health Region. Time to repeated TLR injury was considered as the outcome variable. The models’ goodness of fit was also assessed. Results: Of a total of 1,467 individuals, 149 (56.7%) in the control group and 114 (43.3%) in the intervention group had repeated injuries during the study period. Nurses and nursing aides had the highest repeated TLR injuries (84.8%) among occupations. Back, neck and shoulders were the most common body parts injured (74.9%). These covariates were significant in both Cox multiplicative and additive hazards models. The intervention group had 27% fewer repeated injuries than the control group in the multiplicative hazards model (HR= 0.63; 95% CI=0.48-0.82; p-value=0.0002). In the additive model, the hazard difference between the intervention and the control groups was 0.002. Conclusion: Both multiplicative and additive hazards models showed similar results, indicating that the TLR injury prevention intervention was effective in reducing repeated injuries. The additive hazards model is not widely used, but the coefficient of the covariates is easy to interpret in an additive manner. The additive hazards model should be considered when the proportionality assumption of the Cox model is doubtful.