Comparison of Mortality Risk With Different Surgeon and Hospital Operative Volumes Among Individuals Undergoing Pancreatectomy by Emulating Target Trials in US Medicare Beneficiaries

Key Points Question How can past studies of the volume-outcomes association in surgery be interpreted and how might future research on these questions generate valid results? Findings In this cohort study that emulated 4 hypothetical target trials among 9136 Medicare beneficiaries undergoing pancreatectomy for malignancy, mortality was higher for higher volumes only when target trials with poorly defined interventions were emulated. Meaning The target trial framework demonstrated in this study may be useful for volume-outcomes researchers who are not willing to make unrealistic assumptions in their studies.

eFigure 1. Acyclic Graphs eFigure 1A. Causal directed acyclic graph for Hypothetical Trial #1 (assignment to surgeon volume only), in which the compound intervention is randomly assigned and precedes the relevant version of surgeon. Node denotes a patient's assignment to a surgeon with a specific operative volume, ( ) denotes a patient's selection of a particular surgeon with the specified operative volume , denotes covariates associated with both the particular surgeon selected and mortality, and represents mortality at the end of follow-up. eFigure 1B. Causal directed acyclic graph for Hypothetical Trial #2 (assignment to surgeon volume and hospital volume), in which the compound intervention denotes a random joint assignment of surgeon volume and hospital volume; denotes the hospital volume component of R; denotes the surgeon volume component of R; ( ) denotes a patient's selection of a particular hospital with the specified operative volume , ( ) denotes an patient's selection of a particular surgeon with the specified operative volume , 1 denotes covariates associated with both the particular hospital selected and mortality, 2 denotes covariates associated with both the particular surgeon selected and mortality, and denotes mortality at the end of follow-up. This supplemental material has been provided by the authors to give readers additional information about their work. eFigure 1C. Causal directed acyclic graph for Hypothetical Trial #3 (dynamic assignment to surgeon volume and hospital volume, accounting for travel distance), in which the compound intervention denotes a random joint assignment of surgeon volume and hospital volume; denotes the hospital volume component of R; denotes the surgeon volume component of R; ( ) denotes a patient's selection of a particular hospital with the specified operative volume , ( ) denotes a patient's selection of a particular surgeon with the specified operative volume , denotes travel time from the nearest surgeon with volume ≥ and hospital with volume ≥ ; 1 denotes covariates associated with both the particular hospital selected and mortality, 2 denotes covariates associated with both the particular surgeon selected and mortality, and denotes mortality at the end of follow-up. eFigure 1D. Causal directed acyclic graph for Hypothetical Trial #4 (dynamic assignment to surgeon volume and hospital volume, accounting for travel distance and multiple treatment versions), in which the compound intervention denotes a random joint assignment of surgeon volume and hospital volume; denotes the hospital volume component of R; denotes the surgeon volume component of R; ( ) denotes a patient's selection of a particular hospital with the specified operative volume , ( ) denotes an patient's selection of a particular surgeon with the specified operative volume , denotes travel time from the nearest surgeon with volume ≥ and hospital with volume ≥ ; and denotes mortality at the end of follow-up. This supplemental material has been provided by the authors to give readers additional information about their work.

Analysis of Target Trials #1-4
Under full adherence to randomization, the intention to treat and per protocol effects are equivalent and could be estimated under each intervention arm non-parametrically or by fitting the following logistic model:

Emulation of Analysis of Target Trials #1 and #2
The regression model used to emulate the analysis of the target trials is similar to Equation (1), but with the addition of baseline covariates to emulate randomization: One way to estimate the conditional mean in Equation (3) is by fitting the following logistic model: We could then compute Equation (3) by computing the population sample average of each covariate pattern.

Emulation of Analysis of Target Trial #3
Given the dynamic regime, the Equation (4) above must be modified:

Emulation of Analysis of Target Trial #4
This supplemental material has been provided by the authors to give readers additional information about their work.