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Application of the Parametric g-Formula to Characterizing Counterfactual Time-to-Event Disability Progression Outcomes in Multiple Sclerosis

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Abstract

Disentangling the effects of disease activity associated with focal inflammation, e.g., as characterized by relapses, and other pathophysiological processes leading to disability progression in multiple sclerosis (MS) is of central importance. This is because it will provide an enhanced understanding of the pathology of MS, and may have implications for treating patients. Recently, this endeavor has lead researchers to characterize progression independent of relapse activity (PIRA), which has been defined as a counterfactual outcome representing disability progression without relapses. To date, several methods based on data pre-processing have been proposed to characterize PIRA, e.g., censoring onset of disability progression at onset of relapses. However, these methods can be subject to severe bias if relapse-progression confounders are present and lead to highly imprecise inference if most of the data is unused. In this article, we perform simulations to demonstrate that, unlike these methods, the parametric g-computation formula can provide unbiased inference on PIRA in the presence of relapse-progression confounders. Additionally, we utilize new results on the g-computation formula to estimate treatment effects that provide complementary information, and require less extrapolation to be estimated than the treatment effect on PIRA. Finally, we apply our proposed methodology to two phase 3 studies of MS to highlight the benefits and additional insights that it generates over standard methods.

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Data availability

For eligible studies, qualified researchers may request access to individual patient level clinical data through a data request platform. At the time of writing, this request platform is Vivli. https://vivli.org/ourmember/roche/. For up-to-date details on Roche’s Global Policy on the Sharing of Clinical Information and how to request access to related clinical study documents, see here: https://www.roche.com/innovation/process/clinical-trials/data-sharing/

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Acknowledgements

The authors would like to thank Gian-Andrea Thanei, Hans-Martin Schneble and Claude Berge for insightful discussions and reviewing a previous version of this article.

Author information

Authors and Affiliations

  1. Roche Products Ltd, Welwyn Garden City, UK

    Sean Yiu

  2. F. Hoffmann-La Roche Ltd, Basel, Switzerland

    Qing Wang & Francois Mercier

  3. Impulze GmbH, Zurich, Switzerland

    Frank Dahlke

  4. Denali Therapeutics, South San Francisco, CA, USA

    Fabian Model

Authors
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  2. Qing Wang
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  3. Francois Mercier
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  4. Frank Dahlke
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  5. Fabian Model
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Corresponding author

Correspondence to Sean Yiu.

Supplementary Information

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Appendix

Appendix

In this Appendix, we show how (3) can be derived from (2) for the two visit setting. Namely,

$$\begin{aligned} \begin{aligned}&\text {pr}(T(a,\overline{\varvec{L(a)}},\overline{\varvec{0}})> t)\\&\quad =\int _{v}\int _{l_1}\text {pr}(T>t\mid T>1,R_1=0,l_1,\varvec{v},A=a)f(l_1\mid T>1, \varvec{v},A=a)\,dl_1\\&\quad \quad \text {pr}(T>1\mid \varvec{v},A=a)f(\varvec{v})\,d\varvec{v}\\&\quad =\int _{\varvec{v}}E_{L_1}\{\text {pr}(T>t\mid T>1,R_1=0,L_1,\varvec{v},A=a)\mid T>1, \varvec{v},A=a\}\\&\quad \quad \text {pr}(T>1\mid \varvec{v},A=a)f(\varvec{v})\,d\varvec{v}\\&\quad =E_{\varvec{V}}[E_{L_1}\{\text {pr}(T>t\mid T>1,R_1=0,L_1,\varvec{V},A=a)\mid T>1, \varvec{V},A=a\}\\&\quad \quad \text {pr}(T>1\mid \varvec{V},A=a)] \end{aligned} \end{aligned}$$

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Yiu, S., Wang, Q., Mercier, F. et al. Application of the Parametric g-Formula to Characterizing Counterfactual Time-to-Event Disability Progression Outcomes in Multiple Sclerosis. Stat Biosci (2024). https://doi.org/10.1007/s12561-024-09426-9

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