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July 4, 2024

The authors discussed the use of the standardized mortality ratio (SMR) to compare survival across centers, especially in the context of U.S. kidney transplant center evaluation.  The SMR is calculated based on indirect standardization methods in general but the authors aimed for a different measure that was model based and allowed for center effects and was also not affected by proportional hazards.  Also, using weighting methods to handle covariate imbalance was discussed.  They, therefore, adapted prognostic score class weighting into survival outcomes.  They, therefore, created a prognostic score and conditioned on it to de-confound the relationship between failure times and center memberships.

In the prognostic score section, each person’s survival estimate was weighted. They used a weighted Nelson-Aalen survival estimator and then created a center weighted version.  They then ran simulations and compared the true SMR to their center SMR which was estimated under the Cox model and also estimated under an Additive model. They also used a real data application that had data on U.S. kidney transplant centers with respect to 1-year graft survival. Both applications seemed suitable. Per their discussion, they did discuss their no-effect modification assumption and their need to adjust for effect modifiers, which they had not done so this was in the realm of future work.  The article was a worthwhile endeavor on taking into account center effects. It was still not clear though the advantage of doing this through their SMR measure over other methods, to which they did not really compare

Written by,


Usha Govindarajulu, PhD


Keywords: survival analysis, SMR, prognostic scores, center effects, Cox model



Lee Y, Reese PP, Tran AH, and Schaubel DE (2024). “Prognostic score-based methods for estimating center effects based on survival probability: Application to post-kidney transplant survival” Statistics in Medicine, 43(16): 3036-3050.