Cox Regression in Survival Analysis: Practical Insights for Clinicians

António Gomes; Bruna Costa; Vitor Nunes; Constança Coelho

doi:10.20344/amp.23078

Authors

António Gomes Surgery Department. Hospital Fernando Fonseca. Amadora. https://orcid.org/0000-0003-3976-238X
Bruna Costa Champalimaud Centre for the Unknown. Lisbon. https://orcid.org/0000-0002-6697-7258
Vitor Nunes Surgery Department. Hospital Fernando Fonseca. Amadora. https://orcid.org/0000-0002-8762-2472
Constança Coelho Genetics Laboratory. Faculdade de Medicina. Universidade de Lisboa. Lisbon. https://orcid.org/0000-0002-5331-2257

DOI:

https://doi.org/10.20344/amp.23078

Keywords:

Investigative Techniques, Models, Statistical, Proportional Hazards Models, Regression Analysis, Survival Analysis

Abstract

Survival analysis is a fundamental tool in clinical research for evaluating time-to-event outcomes. While the Kaplan-Meier method remains a widely used univariable approach for estimating survival probabilities and comparing groups, it does not account for multiple risk factors simultaneously. To address this limitation, multivariable regression models are employed, with the Cox proportional hazards model (Cox regression) being the most commonly used. This paper provides a practical guide to Cox regression for clinicians, emphasizing its application in survival analysis rather than focusing on mathematical derivations. We discuss key concepts, including hazard ratios, model assumptions, variable selection, and interpretation of results. Additionally, we explore essential methodological considerations, such as assessing proportional hazards assumptions, handling missing data, and avoiding overfitting. By offering a step-by-step approach to implementing Cox regression in clinical research, this article aims to enhance understanding and improve the quality of survival analysis in medical studies. Practical examples illustrate how to interpret Cox regression results and their relevance in clinical decision-making.

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References

Gomes AP, Costa B, Marques R, Nunes V, Coelho C. Kaplan-Meier survival analysis: practical insights for clinicians. Acta Med Port. 2024;37:280-5.

Bugnard F, Ducrot C, Calavas D. Advantages and inconveniences of the Cox model compared with the logistic model: application to a study of risk factors of nursing cow infertility. Vet Res. 1994;25: 134-9.

Haushona N, Esterhuizen TM, Thabane L, Machekano R. An empirical comparison of time-to-event models to analyse a composite outcome in the presence of death as a competing risk. Contemp Clin Trials Commun. 2020;19:100639.

Swindell WR. Accelerated failure time models provide a useful statistical framework for aging research. Exp Gerontol. 2009;44:190-200.

Shen Y, Yu S, Zhang Y, Wang S, Chen J, Xu Y, et al. The exploration of surgery and survival prediction in patients with peritoneal metastasis from gastric adenocarcinoma based on the SEER database. J Gastrointest Oncol. 2024;15:597-611.

Cox DR. Regression models and life-tables. J R Stat Soc B. 1972;34:187-202.

Kleinbaum DG, Klein M. Survival analysis: a self-learning text. Berlin: Springer Nature; 2012.

Akinyemi JO, Afolabi RF, Awolude OA. Semi-parametric model for timing of first childbirth after HIV diagnosis among women of childbearing age in Ibadan, Nigeria. PLoS One. 2020;15:e0240247.

Chen J, Cheng Z, Yao Y, Wang S. Variation of all-cause mortality with fat-free mass index (FFMI) and fat mass index (FMI) in individuals with asthma: results from the NHANES retrospective cohort study. J Epidemiol Glob Health. 2024;14:1555-68.

Park SH, David J. Reassessing Schoenfeld residual tests of proportional hazards in political science event history analyses. Am J Polit Sci. 2015;59:1072-87.

Grambsch PM, Therneau TM. Proportional hazards tests and diagnostics based on weighted residuals. Biometrika. 1994;81:515-26.

Beyersmann J, Schumacher M. Time-dependent covariates in the proportional hazards model: background, structure, and interpretation. Lifetime Data Anal. 2007;13:401-18.

Fisher LD, Lin DY. Time-dependent covariates in the Cox proportional-hazards regression model. Annu Rev Public Health. 1999;20:145-57.

Therneau TM, Grambsch PM. Modeling survival data: extending the Cox model. Berlin: Springer Nature; 2000.

Suissa S. Immortal time bias in observational studies of drug effects. Pharmacoepidemiol Drug Saf. 2007;16:241-7.

Andersen PK, Gill RD. Cox’s regression model for counting processes: a large-sample study. Ann Stat. 1982;10:1100-20.

Arslan J, Benke KK. Application of machine learning to ranking predictors of anti-VEGF response. Life. 2022;12:1176060.

Jin M. Imputation methods for informative censoring in survival analysis with time-dependent covariates. Contemp Clin Trials. 2024;136:107401.

Ogundimu EO, Altman DG, Collins GS. Adequate sample size for developing prediction models is not simply related to events per variable. J Clin Epidemiol. 2016;76:175-82.

Peduzzi P, Concato J, Feinstein AR, Holford TR. Importance of events per independent variable in proportional hazards regression analysis: II. Accuracy and precision of regression estimates. J Clin Epidemiol. 1995;48:1503-10.

Vittinghoff E, McCulloch CE. Relaxing the rule of ten events per variable in logistic and Cox regression. Am J Epidemiol. 2007;165:710-8.

Hsieh FY, Lavori PW. Sample-size calculations for the Cox proportional hazards regression model with nonbinary covariates. Control Clin Trials. 2000;21:552-60.

Riley RD, Snell KI, Ensor J, Burke DL, Harrell FE Jr, Moons KG, et al. Minimum sample size for developing a multivariable prediction model: part II – binary and time-to-event outcomes. Stat Med. 2019;38:1276-96.

Schoenfeld DA. Sample-size formula for the proportional-hazards regression model. Biometrics. 1983;39:499-503.

Postuma RB, Iranzo A, Hu M, Högl B, Boeve BF, Manni R, et al. Risk and predictors of dementia and parkinsonism in idiopathic REM sleep behaviour disorder: a multicentre study. Brain. 2019;142:744-59.

Spreafico M, Hazewinkel AD, van de Sande MA, Gelderblom H, Fiocco M. Machine learning versus Cox models for predicting overall survival in osteosarcoma: analysis of the EURAMOS-1 trial. Cancers. 2024;16:2880.

Kantidakis G, Hazewinkel AD, Fiocco M. Neural networks for survival prediction in medicine: a review and critical appraisal. Comput Math Methods Med. 2022;2022:1176060.

Wiegrebe S, Kopper P, Sonabend R, Bischl B, Bender A. Deep learning for survival analysis: a review. Artif Intell Rev. 2024;57:65.

Hazewinkel AD, Gelderblom H, Fiocco M. Prediction models with survival data: a comparison between machine learning and the Cox model. medRxiv. 2022:2022.03.29.22273112.

Moncada-Torres A, van Maaren MC, Hendriks MP, Siesling S, Geleijnse G. Explainable machine learning can outperform Cox regression and provide insights in breast cancer survival. Sci Rep. 2021;11:6968.

Wu Z, Cheng C, Sun X, Wang J, Guo D, Chen S, et al. The synergistic effect of the triglyceride-glucose index and serum uric acid on major adverse cardiovascular events after CABG: a multicentre cohort study. Cardiovasc Diabetol. 2023;22:103.