Fair, risk-adjusted survival comparisons across hospitals and surgeons
A new method — and an open Stata command — for comparing survival between hierarchical units while adjusting for who they treat.
The published work
The challenge
Comparing survival outcomes between hospitals, surgical units, or regions is a routine need — for benchmarking providers, monitoring quality, and informing health-system decisions. But naïve comparisons are unfair: units treat different patients.
A centre that takes on sicker, higher-risk cases can look worse than one that doesn't, even when its care is better. A credible comparison has to adjust for that case mix while respecting the hierarchical structure of the data — patients nested within surgeons, nested within centres — and handle censored survival data correctly.
The approach
Alessandro Gasparini — then at Red Door Analytics — and Michael Crowther, with co-author Justin Schaffer, developed a method that combines regression standardisation with posterior prediction of the random effects in a multilevel survival model.
From a single fitted model it produces standardised survival probabilities that answer a clear question: how would the entire study population have fared under the performance of a given cluster? Because every cluster is evaluated over the same common case mix, differences in patient risk are accounted for and the comparison becomes fair and interpretable. The work was published in BMC Medical Research Methodology.
What it enables
Demonstrated on a three-level dataset of patients nested within surgeons nested within centres, the approach supports — all from one unified model — benchmarking the best, average, and worst providers; comparing surgeons within a centre; comparing centres directly; and computing contrasts between any two units, each with appropriate uncertainty and correct handling of censoring.
Why it matters
This is exactly the kind of risk-adjusted, higher-level comparison that hospital and regional benchmarking, quality monitoring, and health-system research rely on.
It is also a clean illustration of how the merlin family is built: multilevel survival estimation in the engine, with standardisation and prediction layered cleanly on top — the same machinery available in R and Stata.
The software
The method ships with an accompanying Stata command, released openly on Red Door Analytics' GitHub — so the approach isn't only a paper, it's a tool teams can run on their own data.