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Comparing Gray's and Cox models in 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.


Twenty-eight day Cox univariate analysis demonstrated 9 of 26 factors had non-proportional hazards. A multivariate Cox model identified 7 significant predictors, 4 predictors with non-proportional hazards (presence of comorbidity, hypotension, acute renal failure, and chronic liver disease) and 3 predictors with proportional hazards (Pseudomonas etiology, no identified etiology and pulmonary site of infection). Gray's model also identified seven risk factors. Age was a significant predictor, while a urinary site of infection portended a significantly better prognosis. Three of the common risk factors between the two models had non-proportional hazards (presence of comorbidity, hypotension, and acute renal failure [ARF]). The figure demonstrates that the Gray's model captured the large variation (ie non-proportionality) of the hazard ratio for ARF over time.




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.

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Kasal, J., Jovanovic, Z., Clermont, G. et al. Comparing Gray's and Cox models in sepsis survival. Crit Care 5, P248 (2001).

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  • Acute Renal Failure
  • Clinical Risk Factor
  • Proportional Hazard Assumption
  • Schoenfeld Residual
  • Sepsis Survival