Interpretation of exposure effect in competing risks setting under accelerated failure time models

  • alireza abadi Department of Community Medicine, Faculty of Medicine, Shahid Beheshti University of Medical Sciences, Tehran, Iran
  • bagher pahlavanzade Department of Biostatistics, School of Allied Medical Sciences, Shahid Beheshti University of Medical Sciences, Tehran, Iran
  • farid zayeri Associate Professor of Biostatistics, Departments of Biostatistics, Faculty of Paramedical Sciences, Shahid Beheshti University of Medical Sciences, Tehran, Iran
  • taban Baghfalaki Department of Statistics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran.
Keywords: competing risk, cause-specific hazard, cause-specific survival, Weibull, accelerated failure time model


Background & Aim: In survival studies, incidence of competing risks causes that the time of event of interest to be unknown. Analysis of competing risk data, often implemented using hazard-based method under proportional hazard assumption. In this study, we interpreted covariate effect under accelerated failure time model and cause-specific survival function. Methods & Materials: We considered weibull hazard and survival function as cause-specific hazard and survival function and explored the relation between these function. Estimation of parameters performed using Bayesian methods with non-informative priors that implemented in R2WinBUGS package of R software. Results: Simulation study showed that, the relation between hazard and survival parameters for weibull distribution is also established between parameters of cause-specific hazard and cause-specific survival function. This relation also verified in PBC data set for logarithm of serum bilirubin and D-penicillamine effect. Conclusion: Although in competing risk studies, most of the analysis performed under PH assumption, analysis based on AFT models will also be applicable for these data. In these setting, coefficients can be interpreted as effects of covariate on time to each event.



Haller B, Schmidt G, Ulm K. Applying competing risks regression models: an overview. Lifetime data analysis. 2013:1-26.

Haller B. The analysis of competing risks data with a focus on estimation of cause-specific and subdistribution hazard ratios from a mixture model: lmu; 2014.

Kalbfleisch JD, Prentice RL. The statistical analysis of failure time data: John Wiley & Sons; 2011.

Beyersmann J, Allignol A, Schumacher M. Competing risks and multistate models with R: Springer Science & Business Media; 2011.

Klein JP, Van Houwelingen HC, Ibrahim JG, Scheike TH. Handbook of survival analysis: CRC Press; 2016.

Prentice RL, Kalbfleisch JD, Peterson Jr AV, Flournoy N, Farewell VT, Breslow NE. The analysis of failure times in the presence of competing risks. Biometrics. 1978:541-54.

Jeong JH, Fine J. Direct parametric inference for the cumulative incidence function. Journal of the Royal Statistical Society: Series C (Applied Statistics). 2006;55(2):187-200.

Fine JP, Gray RJ. A proportional hazards model for the subdistribution of a competing risk. Journal of the American statistical association. 1999;94(446):496-509.

Jeong JH. A new parametric family for modelling cumulative incidence functions: application to breast cancer data. Journal of the Royal Statistical Society: Series A (Statistics in Society). 2006;169(2):289-303.

Cheng Y. Modeling cumulative incidences of dementia and dementia-free death using a novel three-parameter logistic function. The International Journal of Biostatistics. 2009;5(1).

Shayan Z, Ayatollahi S, Zare N. A parametric method for cumulative incidence modeling with a new four-parameter log-logistic distribution. Theoretical Biology and Medical Modelling. 2011;8(1):43.

Lau B, Cole SR, Gange SJ. Parametric mixture models to evaluate and summarize hazard ratios in the presence of competing risks with time‚Äźdependent hazards and delayed entry. Statistics in medicine. 2011;30(6):654-65.

Lau B, Cole SR, Moore RD, Gange SJ. Evaluating competing adverse and beneficial outcomes using a mixture model. Statistics in medicine. 2008;27(21):4313-27.

Dang UJ, McNicholas PD. Accelerated Failure Time Models for Competing Risks in a Cluster Weighted Modelling Framework. arXiv preprint arXiv:13120859. 2013.

Klein JP, Basu AP. Weibull accelerated life tests when there are competing causes of failure. Communications in Statistics-Theory and Methods. 1981;10(20):2073-100.

Klein JP, Basu AP. Accelerated Life Testing Under Competing Exponential Failure Distributions. MISSOURI UNIV-COLUMBIA DEPT OF STATISTICS, 1981.

Klein JP, Basu AP. Accelerated life tests under competing Weibull causes of failure. Communications in statistics-Theory and methods. 1982;11(20):2271-86.

DeGroot MH, Goel PK. Bayesian estimation and optimal designs in partially accelerated life testing. Naval Research Logistics (NRL). 1979;26(2):223-35.

Tan Y, Zhang C, Chen X, editors. Bayesian analysis of incomplete data from accelerated life testing with competing failure modes. Reliability, Maintainability and Safety, 2009 ICRMS 2009 8th International Conference on; 2009: IEEE.

Bunea C, Mazzuchi T. Competing failure modes in accelerated life testing. Journal of Statistical Planning and Inference. 2006;136(5):1608-20.

Xu A, Tang Y. Objective Bayesian analysis of accelerated competing failure models under Type-I censoring. Computational Statistics & Data Analysis. 2011;55(10):2830-9.

Luo S. A Bayesian approach to joint analysis of multivariate longitudinal data and parametric accelerated failure time. Statistics in medicine. 2014;33(4):580-94.

Kleinbaum D, Klein M. Statistics for Biology and Health (survival analysis, ). New York: Springer-Verlag; 2005.

Rizopoulos D. Joint models for longitudinal and time-to-event data: With applications in R: CRC Press; 2012.

Benichou J, Gail MH. Estimates of absolute cause-specific risk in cohort studies. Biometrics. 1990:813-26.

Jiang R, editor Analysis of accelerated life test data involving two failure modes. Advanced Materials Research; 2011: Trans Tech Publ.

Tai BC, Machin D, White I, Gebski V. Competing risks analysis of patients with osteosarcoma: a comparison of four different approaches. Statistics in medicine. 2001;20(5):661-84.

Hyun S, Lee J, Sun Y. Proportional hazards model for competing risks data with missing cause of failure. Journal of statistical planning and inference. 2012;142(7):1767-79.

Klein JP, Moeschberger ML. Survival analysis: techniques for censored and truncated data: Springer Science & Business Media; 2005.

How to Cite
abadi alireza, pahlavanzade bagher, zayeri farid, Baghfalaki taban. Interpretation of exposure effect in competing risks setting under accelerated failure time models. jbe. 4(2):45-2.
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