# Survival analysis and regression models

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## Summary

Time-to-event outcomes are common in medical research as they offer more information than simply whether or not an event occurred. To handle these outcomes, as well as censored observations where the event was not observed during follow-up, survival analysis methods should be used. Kaplan-Meier estimation can be used to create graphs of the observed survival curves, while the log-rank test can be used to compare curves from different groups. If it is desired to test continuous predictors or to test multiple covariates at once, survival regression models such as the Cox model or the accelerated failure time model (AFT) should be used. The choice of model should depend on whether or not the assumption of the model (proportional hazards for the Cox model, a parametric distribution of the event times for the AFT model) is met. The goal of this paper is to review basic concepts of survival analysis. Discussions relating the Cox model and the AFT model will be provided. The use and interpretation of the survival methods model are illustrated using an artificially simulated dataset.

## Keywords

Survival analysis Cox proportional hazards model accelerated failure time model## Notes

### Acknowledgments

We would like to thank Dr Edsel Pena and Dr Fadi Hage for their valuable comments and suggestions.

## References

- 1.Kaplan EK, Meier P. Nonparametric estimation from incomplete observations. J Am Stat Assoc 1958;53(282):457-81.CrossRefGoogle Scholar
- 2.Savage IR. Contributions to the theory of rank order statistics: The two sample case. Ann Math Stat 1956;27(3):590-615.CrossRefGoogle Scholar
- 3.Cox DR. Regression models and life-tables. J R Stat Soc Ser B (Methodol) 1972;34(2):187-220.Google Scholar
- 4.Xu Y-Z, Cha Y-M, Feng D, Powell BD, Wise HJ, Hua W, et al. Impact of myocardial scarring on outcomes of cardiac resynchronization therapy: Extent or location? J Nucl Med 2012;53(1):47-54.PubMedCrossRefGoogle Scholar
- 5.Bourque JM, Velazquez EJ, Tuttle RH, Shaw LK, O’Connor CM, Borges-Neto S. Mortality risk associated with ejection fraction differs among resting nuclear perfusion findings. J Nucl Cardiol 2007;14(2):165-73.PubMedCrossRefGoogle Scholar
- 6.Hachamovitch R, Berman DS. The use of nuclear cardiology in clinical decision making. Semin Nucl Med 2005;35(1):62-72.PubMedCrossRefGoogle Scholar
- 7.Nakata T, Miyamoto K, Doi A, Sasao H, Wakabayashi T, Kobayashi H, et al. Cardiac death prediction and impaired cardiac sympathetic innervation assessed by MIBG in patients with failing and nonfailing hearts. J Nucl Cardiol 1998;5(6):579-90.PubMedCrossRefGoogle Scholar
- 8.Duvall WL, Wijetunga MN, Klein TM, Razzouk L, Godbold J, Croft LB, et al. The prognosis of a normal stress-only Tc-99m myocardial perfusion imaging study. J Nucl Cardiol 2010;17(3):370-7.PubMedCrossRefGoogle Scholar
- 9.Hachamovitch R, Hayes S, Friedman JD, Cohen I, Shaw LJ, Germano G, et al. Determinants of risk and its temporal variation in patients with normal stress myocardial perfusion scans: What is the warranty period of a normal scan? J Am Coll Cardiol 2003;41(8):1329-40.PubMedCrossRefGoogle Scholar
- 10.Acampa W, Evangelista L, Petretta M, Liuzzi R, Cuocolo A. Usefulness of stress cardiac single-photon emission computed tomographic imaging late after percutaneous coronary intervention for assessing cardiac events and time to such events. Am J Cardiol 2007;100(3):436-41.PubMedCrossRefGoogle Scholar
- 11.Petretta M, Acampa W, Evangelista L, Daniele S, Ferro A, Cuocolo A. Impact of inducible ischemia by stress SPECT in cardiac risk assessment in diabetic patients: Rationale and design of a prospective multicenter trial. J Nucl Cardiol 2008;15(1):100-4.PubMedCrossRefGoogle Scholar
- 12.Daniele S, Nappi C, Acampa W, Storto G, Pellegrino T, Ricci F, et al. Incremental prognostic value of coronary flow reserve with single-photon emission computed tomography. J Nucl Cardiol 2011;18(4):612-9.PubMedCrossRefGoogle Scholar
- 13.Acampa W, Petretta M, Cuocolo R, Daniele S, Cantoni V, Cuocolo A. Warranty period of normal stress myocardial perfusion imaging in diabetic patients: A propensity score analysis. J Nucl Cardiol 2014;21(1):50-6.PubMedCrossRefGoogle Scholar
- 14.Kalbfleisch JD, Prentice RL. The statistical analysis of failure time data. 2nd ed. Hoboken: John Wiley and Sons; 2002.CrossRefGoogle Scholar
- 15.Klein JP, Moeschberger ML. Survival analysis: Techniques for censored and truncated data. New York: Springer; 2003.Google Scholar
- 16.Akaike H. A new look at the statistical model identification. IEEE Trans Autom Control 1974;19(6):716-23.CrossRefGoogle Scholar
- 17.Schwarz GE. Estimating the dimension of a model. Ann Stat 1978;6(2):461-4.CrossRefGoogle Scholar