Robust Cox Regression as an Alternative Method to Estimate Adjusted Relative Risk in Prospective Studies with Common Outcomes

Authors

  • Wuxiang Xie Department of Epidemiology and Biostatistics, Imperial College London, UK
  • Fanfan Zheng Brainnetome Center, Institute of Automation, Chinese Academy of Sciences, Beijing, China

DOI:

https://doi.org/10.6000/1929-6029.2016.05.04.1

Keywords:

Robust Cox regression, Modified Poisson regression, Logistic regression, Relative risk, Odds ratio.

Abstract

Objective: To demonstrate the use of robust Cox regression in estimating adjusted relative risks (and confidence intervals) when all participants with an identical follow-up time and when a common outcome is investigated.

Methods: In this paper, we propose an alternative statistical method, robust Cox regression, to estimate adjusted relative risks in prospective studies. We use simulated cohort data to examine the suitability of robust Cox regression.

Results: Robust Cox regression provides estimates that are equivalent to those of modified Poisson regression: regression coefficients, relative risks, 95% confidence intervals, P values. It also yields reasonable probabilities (bounded by 0 and 1). Unlike modified Poisson regression, robust Cox regression allows for four automatic variable selection methods, it directly computes adjusted relative risks for continuous variables, and is able to incorporate time-dependent covariates.

Conclusion: Given the popularity of Cox regression in the medical and epidemiological literature, we believe that robust Cox regression may gain wider acceptance and application in the future. We recommend robust Cox regression as an alternative analytical tool to modified Poisson regression. In this study we demonstrated its utility to estimate adjusted relative risks for common outcomes in prospective studies with two or three waves of data collection (spaced similarly).

References

Johnsen SH, Fosse E, Joakimsen O, Mathiesen EB, Stensland-Bugge E, Njølstad I, Arnesen E. Monocyte count is a predictor of novel plaque formation: a 7-year follow-up study of 2610 persons without carotid plaque at baseline the Tromso Study. Stroke 2005; 36: 715-9.https://doi.org/10.1161/01.STR.0000158909.07634.83 DOI: https://doi.org/10.1161/01.STR.0000158909.07634.83

Zhang J, Yu KF. What's the relative risk? A method of correcting the odds ratio in cohort studies of common outcomes. JAMA 1998; 280: 1690-1.https://doi.org/10.1001/jama.280.19.1690 DOI: https://doi.org/10.1001/jama.280.19.1690

Zou G. A modified poisson regression approach to prospective studies with binary data. Am J Epidemiol 2004; 159: 702-6.https://doi.org/10.1093/aje/kwh090 DOI: https://doi.org/10.1093/aje/kwh090

Lee J. Odds ratio or relative risk for cross-sectional data? Int J Epidemiol 1994; 23: 201-3.https://doi.org/10.1093/ije/23.1.201 DOI: https://doi.org/10.1093/ije/23.1.201

Breslow N. Covariance analysis of censored survival data. Biometrics 1974; 30: 89-99.https://doi.org/10.2307/2529620 DOI: https://doi.org/10.2307/2529620

Barros AJ, Hirakata VN. Alternatives for logistic regression in cross-sectional studies: an empirical comparison of models that directly estimate the prevalence ratio. BMC Med Res Methodol 2003; 3: 21.https://doi.org/10.1186/1471-2288-3-21 DOI: https://doi.org/10.1186/1471-2288-3-21

Lin DY, Wei LJ. The Robust Inference for the Cox Proportional Hazards Model. Journal of the American Statistical Association 1989; 84: 1074-8.https://doi.org/10.1080/01621459.1989.10478874 DOI: https://doi.org/10.1080/01621459.1989.10478874

Cox DR. Regression Models and Life-Tables. Journal of the Royal Statistical Society 1972; 34: 187-220. DOI: https://doi.org/10.1111/j.2517-6161.1972.tb00899.x

SAS Institute I: SAS/STAT sofeware, version 9.2. Cary, NC: SAS Institute, Inc 2008.

McNutt LA, Wu C, Xue X, et al. Estimating the relative risk in cohort studies and clinical trials of common outcomes. Am J Epidemiol 2003; 57: 940-3.https://doi.org/10.1093/aje/kwg074 DOI: https://doi.org/10.1093/aje/kwg074

Deddens JA, Petersen MR. Approaches for estimating prevalence ratios. Occup Environ Med 2008; 65: 481-6.https://doi.org/10.1136/oem.2007.034777 DOI: https://doi.org/10.1136/oem.2007.034777

Yu B, Wang Z. Estimating relative risks for common outcome using PROC NLP. Comput Methods Programs Biomed 2008; 90: 179-86.https://doi.org/10.1016/j.cmpb.2007.12.010 DOI: https://doi.org/10.1016/j.cmpb.2007.12.010

Chu H, Cole SR. Estimation of risk ratios in cohort studies with common outcomes: a Bayesian approach. Epidemiology 2010; 21: 855-62.https://doi.org/10.1097/EDE.0b013e3181f2012b DOI: https://doi.org/10.1097/EDE.0b013e3181f2012b

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Published

2016-12-09

How to Cite

Xie, W., & Zheng, F. (2016). Robust Cox Regression as an Alternative Method to Estimate Adjusted Relative Risk in Prospective Studies with Common Outcomes. International Journal of Statistics in Medical Research, 5(4), 231–239. https://doi.org/10.6000/1929-6029.2016.05.04.1

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General Articles