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Flexible alternatives to the Cox model, and more

Author

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  • Patrick Royston

    (UK Medical Research Council)

Abstract

Since its introduction to a wondering public in 1972, the Cox proportional hazards regression model has become an overwhelmingly popular tool in the analysis of censored survival data. However, some features of the Cox model may cause problems for the analyst or an interpreter of the data. They include the restrictive assumption of proportional hazards for covariate effects, and "loss" (non-estimation) of the baseline hazard function induced by conditioning on event times. In medicine, the hazard function is often of fundamental interest since it represents an important aspect of the time course of the disease in question. In the present article, the Stata implementation of a class of exible parametric survival models recently proposed by Royston and Parmar (2001) will be described. The models start by assuming either proportional hazards or proportional odds (user- selected option). The baseline distribution function is modeled by restricted cubic regression spline in log time, and parameter estimation is by maximum likelihood. Model selection and choice of knots for the spline function are discussed. Interval- censored data and models in which one or more covariates have non-proportional effects are also supported by the software. Examples based on a study of prognostic factors in breast cancer are given. Copyright 2001 by Stata Corporation.

Suggested Citation

  • Patrick Royston, 2001. "Flexible alternatives to the Cox model, and more," Stata Journal, StataCorp LP, vol. 1(1), pages 1-28, November.
    • Handle: RePEc:tsj:stataj:v:1:y:2001:i:1:p:1-28
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    Citations

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    Cited by:

    1. Eddie Gibson & Ian Koblbauer & Najida Begum & George Dranitsaris & Danny Liew & Phil McEwan & Amir Abbas Tahami Monfared & Yong Yuan & Ariadna Juarez-Garcia & David Tyas & Michael Lees, 2017. "Modelling the Survival Outcomes of Immuno-Oncology Drugs in Economic Evaluations: A Systematic Approach to Data Analysis and Extrapolation," PharmacoEconomics, Springer, vol. 35(12), pages 1257-1270, December.
    2. Paul C. Lambert & Patrick Royston, 2009. "Further development of flexible parametric models for survival analysis," Stata Journal, StataCorp LP, vol. 9(2), pages 265-290, June.
    3. Patrick Royston, 2006. "Explained variation for survival models," Stata Journal, StataCorp LP, vol. 6(1), pages 83-96, March.
    4. Martin Gaksch & Rolf Jorde & Guri Grimnes & Ragnar Joakimsen & Henrik Schirmer & Tom Wilsgaard & Ellisiv B Mathiesen & Inger Njølstad & Maja-Lisa Løchen & Winfried März & Marcus E Kleber & Andreas Tom, 2017. "Vitamin D and mortality: Individual participant data meta-analysis of standardized 25-hydroxyvitamin D in 26916 individuals from a European consortium," PLOS ONE, Public Library of Science, vol. 12(2), pages 1-15, February.
    5. Therese M.-L. Andersson & Paul C. Lambert, 2012. "Fitting and modeling cure in population-based cancer studies within the framework of flexible parametric survival models," Stata Journal, StataCorp LP, vol. 12(4), pages 623-638, December.
    6. Sébastien Mary, 2022. "A replication note on humanitarian aid and violence," Empirical Economics, Springer, vol. 62(3), pages 1465-1494, March.
    7. Patrick Royston, 2007. "Profile likelihood for estimation and confidence intervals," Stata Journal, StataCorp LP, vol. 7(3), pages 376-387, September.
    8. Nan Liu, 2021. "Market buoyancy, information transparency and pricing strategy in the Scottish housing market," Urban Studies, Urban Studies Journal Limited, vol. 58(16), pages 3388-3406, December.
    9. Caudill, Jonathan W. & Trulson, Chad R., 2016. "The hazards of premature release: Recidivism outcomes of blended-sentenced juvenile homicide offenders," Journal of Criminal Justice, Elsevier, vol. 46(C), pages 219-227.
    10. Rolock, Nancy & White, Kevin R., 2016. "Post-permanency discontinuity: A longitudinal examination of outcomes for foster youth after adoption or guardianship," Children and Youth Services Review, Elsevier, vol. 70(C), pages 419-427.
    11. Houghton, Lauren C. & Troisi, Rebecca & Sommer, Marni & Katki, Hormuzd A. & Booth, Mark & Choudhury, Osul A. & Hampshire, Kate R., 2020. "“I'm not a freshi”: Culture shock, puberty and growing up as British-Bangladeshi girls," Social Science & Medicine, Elsevier, vol. 258(C).
    12. Amin Moniri-Morad & Mohammad Pourgol-Mohammad & Hamid Aghababaei & Javad Sattarvand, 2019. "Reliability-based covariate analysis for complex systems in heterogeneous environment: Case study of mining equipment," Journal of Risk and Reliability, , vol. 233(4), pages 593-604, August.
    13. Enzo Coviello, 2009. "Covariate-adjusted cumulative incidence in the presence of competing risks," Italian Stata Users' Group Meetings 2009 02, Stata Users Group.
    14. M. Kathleen Thomas & Priyanka Singh & Kristin Klopfenstein, 2015. "Arts education and the high school dropout problem," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 39(4), pages 327-339, November.
    15. Jonathan Karnon & Orla Caffrey & Clarabelle Pham & Richard Grieve & David Ben‐Tovim & Paul Hakendorf & Maria Crotty, 2013. "Applying Risk Adjusted Cost‐Effectiveness (Rac‐E) Analysis To Hospitals: Estimating The Costs And Consequences Of Variation In Clinical Practice," Health Economics, John Wiley & Sons, Ltd., vol. 22(6), pages 631-642, June.

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