Probit regression results.

Objective
To evaluate the underlying mechanism of the volume-outcome relationship, namely learning-by-doing and scale economies in patients with sepsis.
Design and study setting
Retrospective cohort study of adult patients with sepsis between 1 January 2010 and 31 December 2016 in 231 intensive care units (ICUs) in the UK.
Participants
The patient was the primary unit of analysis. Patient and ICU characteristics were included for risk adjustment. Demographic and clinical data were extracted from the Intensive Care National Audit and Research Centre (ICNARC) Case Mix Programme database.
Study design
We used the lags of quarterly sepsis volume in the ICU as a measure of the learning-by-doing effect.
Outcome measure
The outcome of hospital mortality after ICU admission for sepsis was assessed using a multilevel probit regression model of patients nested in ICUs over quarters.
Data collection/extraction methods
Critically ill patients with sepsis were identified by the Sepsis-3 consensus criteria.
Results
Our study identified a cohort of 273001 patients with sepsis admitted to 231 ICUs in the UK. Our study finds that in comparison with contemporaneous volume, lagged volume had a stronger association with acute hospital mortality. This implies that the dynamic learning-by-doing effect is more important than the static economies of scale effect. This finding was consistent across alternate specifications of learning-by-doing.
Conclusions
The study provides evidence that the underlying mechanism for the volume-outcome relationship is learning-by-doing and not the static economies of scale. ICUs caring for patients with sepsis tend to improve by experience.