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Article History

Received: 25 January 2025

Accepted: 15 December 2025

First Online: 11 February 2026

Declarations

:

: A.H.B., Z.L., J.S., A.L., and D.A. have all received research funding from Boehringer Ingelheim through Occam research Ltd, Avalon Health Economics, and Acaster Lloyd Consulting. V.W.-J. and S.A. are employees of Boehringer Ingelheim Intl. GmbH.

: A version of the model written in the R statistical software [ ] can be downloaded from .

: A data availability statement is provided four lines below in its own headed section? We only used data avaioable in the literature which has been referenced.

: A.L., W.V.J., and A.B. conceived the study. A.B., J.S., and Z.L. undertook the modeling, and all authors provided substantial input into the interpretation of the work as presented. AB drafted the manuscript and all authors were involved in critical review across many iterations before providing final approval for the submitted version. All authors agree to take responsibility for the manuscript contents. The author(s) meet criteria for authorship as recommended by the International Committee of Medical Journal Editors (ICMJE).

: Not applicable.

: Not applicable.

: All authors have consented to publication.