# Standardized survival probabilities and contrasts between hierarchical units in multilevel survival models

## TL;DR

This paper introduces a new method to compare survival outcomes across hospitals or regions using standardized survival probabilities in multilevel models.

## Contribution

The paper proposes a novel approach to obtain standardized survival probabilities by combining regression standardization with random effects predictions.

## Key findings

- Standardized survival probabilities allow fair comparisons between hierarchical units like hospitals or surgeons.
- The method provides interpretable and potentially causal measures for comparing survival outcomes.
- The approach is demonstrated using bladder cancer patient data with a three-level hierarchical structure.

## Abstract

In the medical literature, in which time-to-event (such as time to death or disease recurrence) outcomes are commonly studied, hierarchical data is frequently encountered with patients nested within hospitals or regions. Multilevel hierarchical mixed-effects survival models are routinely used in these settings to accommodate the correlation between study subjects belonging to the same cluster and any potential unobserved heterogeneity. However, these analyses usually focus on fixed effects while marginalizing over the random effects, with fully conditional or marginal (on the random effects) post-estimation predictions.

In this work, we combine regression standardization over the observed covariates with posterior predictions of the random effects to obtain standardized survival probabilities. These predictions quantify how the entire study population would have fared under the performance of each cluster and can be used to obtain fair comparisons between hierarchical units. Compared to other common approaches, such as the median hazard ratio, this proposal yields quantities that are easier to interpret and that, under certain assumptions, can have a causal interpretation.

We illustrate the new methodology in practice using data on bladder cancer patients with a three-level hierarchical structure composed of patients nested within surgeons and centers. Then, we illustrate a variety of standardized survival predictions benchmarking, e.g., best/average/worst surgeons and centers, surgeons within a center, or centers directly — all from a single and unified modeling framework.

We introduced an analytical approach that can be used to quantify and fairly compare the differences between hierarchical units using easily interpretable measures such as (standardized) survival probabilities and contrasts thereof.

The online version contains supplementary material available at 10.1186/s12874-026-02782-8.