by Nawaraj Bhattarai
I have been working on a survival (time to event) analysis using the Hospital Episode Statistics (HES) data for a while now. Kaplan Meier (KM), also known as product limit estimate, is the commonly used statistical method for the analysis of survival data [1]. However, the Kaplan Meier method is not a suitable method for such analyses when competing events are present in the data. A competing event is defined as an event which prevents occurrence of the primary event of interest. Patients who die, who have no information on occurrence of the event of interest or who are lost to follow up in the study period are censored; censoring simply means that nothing is known about them after the censoring time. The KM method assumes that there would be an equal chance of observing the event of interest for censored patients as those who are not censored. However, this assumption may be incorrect where there is no chance of occurrence of the event of interest. For example, where readmission to hospital is an event of interest, the death of a patient serves as a competing event. A patient who dies is no longer at risk of readmission to the hospital, regardless of the observation period. Failure to account for competing events in the survival analysis generally leads to overestimation of the cumulative incidence of the event of interest [2-6].
A cumulative incidence function (CIF)[7] regression model, also known as a sub-distribution hazard model, accounts for competing events by altering the risk set and is the preferred alternative to the KM method [2,6]. Functions for competing risks analyses exist for common statistical software. A recent tutorial publication [6] by Austin and colleagues introduces readers to statistical methods for survival analysis in the presence of competing events and provide the R and SAS codes used in their examples. Hein Putter’s tutorial [8] is another useful resource which guides researchers through competing risk and multi-state model analyses using the mstate package in R.
In conclusion, the KM method has pitfalls when used for survival analysis if competing events are present in the data. Evidence suggests researchers be aware of any competing events present in their survival data and ensure that an appropriate statistical method, such as those mentioned earlier, is used for survival analysis.
References
1. Putter H, Fiocco M, Geskus RB. Tutorial in biostatistics: competing risks and multi-state models. Statistics in Medicine 2007;26(11):2389-430.
2. Satagopan JM, Ben-Porat L, Berwick M, et al. A note on competing risks in survival data analysis. Br J Cancer 2004;91(7):1229-35.
3. Keurentjes JC, Fiocco M, Schreurs BW, et al. Revision surgery is overestimated in hip replacement. Bone and Joint Research 2012;1(10):258-62.
4. Leslie WD, Lix LM, Wu X. Competing mortality and fracture risk assessment. Osteoporosis International 2013;24(2):681-88.
5. Berry SD, Ngo L, Samelson EJ, et al. Competing Risk of Death: An Important Consideration in Studies of Older Adults. Journal of the American Geriatrics Society 2010;58(4):783-87.
6. Austin PC, Lee DS, Fine JP. Introduction to the Analysis of Survival Data in the Presence of Competing Risks. Circulation 2016;133(6):601-09.
7. Coviello V, Boggess M. Cumulative incidence estimation in the presence of competing risks. Stata Journal 2004;4(2):103-12.
8. Putter H. Tutorial in biostatistics: Competing risks and multi-state models. Analyses using the mstate package, 2016. https://cran.rproject.org/web/packages/mstate/vignettes/Tutorial.pdf.