Statistical issues in survival analysis (Part XVVVVV)

October 9, 2024

The authors have discussed some issues in survival analysis in relation to Kaplan-Meier curves. They then came up with alternative ways to design, analyze, and interpret the results of the trials that compare preventive surgery with medical management.  The authors focused on an analysis from a surgical study with follow-up for stroke or death from the Carotid and Middle Cerebral Artery Occlusion Surgery Study (CMOSS), which was a multicenter, randomized, open-label, outcome-assessor blinded clinical trial conducted in 13 Chinese centers between 2013 and 2020.

They mentioned the authors admitted not having proportional hazards so then reported relative risks. They then disagreed with the analysis and interpretation of the CMOSS trial and said the authors should have known that they would have lack of proportional hazards when they proposed using Cox proportional hazards regression for their trial which was designed to test whether there was an immediate surgical risk to prevent future strokes.  The authors then went on to describe the Kaplan-Meier (KM) curve, how it was originally designed and allows for the patients to be ordered by serial time, time according to their position in the series of patients included in the study).  Also, patients can be censored due to loss of followup or death from another cause, or study ending with patient still alive. They then go on to point out this analysis makes sense for oncology trials where death is an outcome but not for preventative surgery and management where a different type of outcome is needed.  They caution against just visual inspection of KM curves, which is why tests like the log-rank test and the Cox proportional hazards regression were developed in order to compare survival between two groups.  However for the CMOSS trial with the combined endpoint of stroke recurrence and death, there was supposedly violation of proportional hazards due to crossing curves.

The authors then offered some solutions to the problem, like starting the survival analysis after the 30 day peri-operative period, for then the crossing curves issue would be avoided. Then the analysis would be for the post-operative period.  But what would happen to the variability from the peri-operative period?  The authors had seemed to indicate they would offer alternate strategies but they only offer changing the time scale of analysis.  The authors did not seem aware of more sophisticated methods like restricted mean survival time analysis, or a combination of semi-parametric and longitudinal analysis to handle the multiple recurrences.  Perhaps had the authors known of these other techniques then there whole article would have been different.

Written by,

Usha Govindarajulu, PhD

Keywords: survival, Kaplan-Meier, crossing curves, log-rank test, Cox model

References

Darsaut TE, Rheaume AR, Chagnon M, Raymond J. (2024). “The use and abuse of survival analysis and Kaplan-Meier curves in surgical trials.” Neurochirurgie, Volume 70, Issue 4, 101567,ISSN 0028-3770, https://doi.org/10.1016/j.neuchi.2024.101567.(https://www.sciencedirect.com/science/article/abs/pii/S0028377024000389)

https://www.medcalc.org/manual/images/kaplan-meier-curves.png