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Comparison of Cox and Gray’s survival models in severe sepsis*

Kasal, Jan MD; Jovanovic, Zorana MSc; Clermont, Gilles MD, CM, MSc; Weissfeld, Lisa A. PhD; Kaplan, Vladimir MD; Watson, R. Scott MD, MPH; Angus, Derek C. MB, ChB, MPH, FCCM

doi: 10.1097/01.CCM.0000114819.37569.4B

Background Although survival is traditionally modeled using Cox proportional hazards modeling, this approach may be inappropriate in sepsis, in which the proportional hazards assumption does not hold. Newer, more flexible models, such as Gray’s model, may be more appropriate.

Objectives To construct and compare Gray’s model and two different Cox models in a large sepsis cohort. To determine whether hazards for death after sepsis were nonproportional. To explore how well the different survival modeling approaches describe these data.

Design Analysis of combined data from the treatment and placebo arms of a large, negative, sepsis trial.

Setting Intensive care units at 136 U.S. medical centers.

Subjects A total of 1090 adults aged 18 yrs or older with signs and symptoms of severe sepsis and documented or probable Gram-negative infection.

Measurements We considered 27 potential baseline risk factors and modeled survival over the 28 days after the onset of sepsis. We tested proportionality in single-variable Cox analysis using Schoenfeld residuals and log–log plots. We constructed a traditional multivariable Cox model, a multivariable Cox model with time-varying covariates, and a multivariable Gray’s model.

Results In single-variable analyses, 20 of the 27 potential factors were significantly associated with mortality, and 10 of 20 had nonproportional hazards. In multivariate analysis, all three models retained a very similar set of significant covariates (two models retained the identical set of nine variables, and the third differed only in that it retained the same nine plus a tenth variable). Four of the nine common covariates had nonproportional hazards. Of the three models, Gray’s model best captured these changing hazard ratios over time.

Conclusion We confirm that many of the important predictors of mortality in severe sepsis are nonproportional and find that Gray’s model seems best suited for modeling survival in this condition.

From the CRISMA Laboratory (Clinical Research, Investigation, and Systems Modeling of Acute Illness), Department of Critical Care Medicine (JK, GC, VK, RSW, DCA), and the Departments of Biostatistics (LAW) and Health Policy and Management (DCA), Graduate School of Public Health, University of Pittsburgh, Pittsburgh, PA; the Department of Critical Care Medicine/Internal Medicine, Cumberland Medical Center, Crossville, TN (JK); the Institute of Public Health, University of Copenhagen, Copenhagen, Denmark (ZJ); and the Department of Internal Medicine, University Hospital, Zurich, Switzerland (VK).

Funded, in part, by grant AHRQ/NHLBI R01 HS/HL11620-1.

Presented, in part, as an abstract at the 21st International Symposium of Emergency and Intensive Care Medicine, Brussels, Belgium, 2001.

Modeling approaches that ignore time-dependent effects of risk factors on mortality can lead to incorrect inferences; thus, in settings such as sepsis, in which the proportionality assumption fails to hold, we suggest conducting survival analysis using Gray’s model.

© 2004 by the Society of Critical Care Medicine and Lippincott Williams & Wilkins