Applying Additive Hazards Models for Analyzing Survival in Patients with Colorectal Cancer in Fars Province, Southern Iran

Document Type : Research Articles


1 Noncommunicable Diseases Research Center, Fasa University of Medical Sciences, Fasa,Iran.

2 Department of Epidemiology and Biostatistics, Faculty of Health,Tehran University of Medical Sciences,Tehran, Iran.

3 Social Determinants in Health Promotion Research Center, Department of Public Health, Hormozgan University of Medical Sciences, Bandar Abbas, Iran

4 Department of Epidemiology and Biostatistics, Faculty of Public Health. Kerman University of Medical Sciences, Kerman, Iran.

5 Colorectal Research Center, Shiraz University of Medical Sciences, Shiraz, Iran


Introduction: Colorectal cancer (CRC) is a commonly fatal cancer that ranks as third worldwide and third and the fifth in Iranian women and men, respectively. There are several methods for analyzing time to event data. Additive hazards regression models take priority over the popular Cox proportional hazards model if the absolute hazard (risk) change instead of hazard ratio is of primary concern, or a proportionality assumption is not made. Methods: This study used data gathered from medical records of 561 colorectal cancer patients who were admitted to Namazi Hospital, Shiraz, Iran, during 2005 to 2010 and followed until December 2015. The nonparametric Aalen’s additive hazards model, semiparametric Lin and Ying’s additive hazards model and Cox proportional hazards model were applied for data analysis. The proportionality assumption for the Cox model was evaluated with a test based on the Schoenfeld residuals and for test goodness of fit in additive models, Cox-Snell residual plots were used. Analyses were performed with SAS 9.2 and R3.2 software. Results: The median follow-up time was 49 months. The five-year survival rate and the mean survival time after cancer diagnosis were 59.6% and 68.1±1.4 months, respectively. Multivariate analyses using Lin and Ying’s additive model and the Cox proportional model indicated that the age of diagnosis, site of tumor, stage, and proportion of positive lymph nodes, lymphovascular invasion and type of treatment were factors affecting survival of the CRC patients. Conclusion: Additive models are suitable alternatives to the Cox proportionality model if there is interest in evaluation of absolute hazard change, or no proportionality assumption is made.


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