A Bayesian hierarchical surrogate outcome model for multiple sclerosis

Abstract

The development of novel therapies in multiple sclerosis (MS) is one area where a range of surrogate outcomes are used in various stages of clinical research. While the aim of treatments in MS is to prevent disability, a clinical trial for evaluating a drugs effect on disability progression would require a large sample of patients with many years of follow-up. The early stage of MS is characterized by relapses. To reduce study size and duration, clinical relapses are accepted as primary endpoints in phase III trials. For phase II studies, the primary outcomes are typically lesion counts based on magnetic resonance imaging (MRI), as these are considerably more sensitive than clinical measures for detecting MS activity. Recently, Sormani and colleagues in 'Surrogate endpoints for EDSS worsening in multiple sclerosis' provided a systematic review and used weighted regression analyses to examine the role of either MRI lesions or relapses as trial level surrogate outcomes for disability. We build on this work by developing a Bayesian three-level model, accommodating the two surrogates and the disability endpoint, and properly taking into account that treatment effects are estimated with errors. Specifically, a combination of treatment effects based on MRI lesion count outcomes and clinical relapse was used to develop a study-level surrogate outcome model for the corresponding treatment effects based on disability progression. While the primary aim for developing this model was to support decision-making in drug development, the proposed model may also be considered for future validation. Copyright © 2016 John Wiley & Sons, Ltd.

Predictive probability of success using surrogate endpoints

“…Since the individual patient data from the published clinical trials are rarely available, we focused on a method using aggregated data . However, this approach usually requires to make assumptions regarding the between‐endpoint correlations within each trial, almost never published, and to perform sensitivity analyses accordingly . The availability of individual patient data resolves this problem, because, then, a two‐stage model can be used where the within‐trial dependence between the endpoints is first estimated from the patient observations.…”

“…Their posterior means and 95% credible intervals are presented in Table , for the one‐surrogate models and the two‐surrogate model. The results of the model using relapse as surrogate endpoint (with those of another model assuming a structural relationship between the endpoints, not used here for simplicity) were already presented in the work of Pozzi et al, with slight differences due to sampling only. It can be noted that the MRI lesion counts and the annualized relapse rate, taken separately, are good predictors of the disability progression with parameters b significantly different from 0.…”

“…Let denote the estimated treatment differences on the M surrogate endpoints in the trial i , and their sampling variance. The within‐trial model in Equation could be extended to …”

“…As indicated before, it is very unlikely that these values are reported in the publications, but plausible values and range of values could be assumed . Using vectorized notations G i = ( γ 1 i ,…, γ M i ) and B = ( b 1 ,…, b M ), and assuming fixed effects for G i , the linear model to describe the relationship between the endpoints becomes The generalization where G i are random effects is described in the work of Bujkiewicz et al Some additional assumptions could also be made on the structural relationships between the endpoints, for example, that the treatment effect on the final endpoint is independent from the effect on some surrogate endpoints conditionally on some others, see the works of Pozzi et al and Bujkiewicz et al, for more details.…”

“…The relationship between the endpoints, using the meta‐analytic approach described in Section 2.3, has been previously published in the work of Pozzi et al, based on the data from the work of Sormani et al We translated the Winbugs code from the work of Pozzi et al in Stan, in order to use the most up‐to‐date software for Bayesian inference, but the data of the meta‐analysis (Appendix , Table C1) are strictly identical to those of the original publication, with a correlation fixed at 0.05 between the estimated treatment effects on the surrogate and final endpoints within each study, as in their main analysis.…”