Comparing Gray's and Cox models in sepsis survival
KeywordsAcute Renal Failure Clinical Risk Factor Proportional Hazard Assumption Schoenfeld Residual Sepsis Survival
A difficulty in modeling survival after sepsis is that hazards may not be proportional, thus violating a key assumption of traditional Cox survival models. We modeled survival after sepsis using Gray's approach, a new spline-based technique that does not rely on the proportional hazards assumption. We then compared hazard ratios over time between Gray's and Cox models.
Gray's model will yield different estimates of hazards over time in sepsis when compared to Cox.
We analyzed 1090 patients recently enrolled in a US multicenter sepsis trial. We considered 26 potential baseline demographic and clinical risk factors and modeled survival over the first 28 days from the onset of sepsis. We tested proportionality in univariate Cox analysis using Schoenfeld residuals and log-log plots. We then constructed a standard multivariate Cox model and a Gray's model. We evaluated the validity of the proportional hazards assumption in the predictors selected by the Cox model. We compared the selection of predictors by both models.
Accurate survival models must take into account the observation that mortality risk factors have non-proportional hazards. Of several alternatives to a standard Cox model, Gray's model appears particularly promising.