Conference Agenda

Background: Surrogate endpoints are increasingly being utilised in clinical trials and for regulatory and reimbursement decision-making, as they can allow for the treatment effects to be measured more quickly than final clinical outcomes. However, surrogate endpoints should be validated before they are used to inform healthcare decision-making, to ensure that the putative surrogate endpoint is truly predictive of the treatment benefit on the final outcome. Traditionally, the strongest level of evidence for a surrogate relationship would be obtained from a meta-analysis of treatment effects on the surrogate endpoint and final outcome utilising all clinical trial data in the relevant clinical setting. However, in several disease areas genetic biomarkers are predictive of treatment effect and thus may also impact surrogacy relationships. Potential differences in the surrogate relationships across biomarker groups can be investigated via subgroup analysis using standard meta-analytic methods for surrogate endpoint validation. However, this could result in insufficient data to make robust conclusions about the strength of the surrogate relationship, as subgroup analyses tend to be under-reported.

Methods: We propose an extension to bivariate random-effects meta-analysis (BRMA) to allow for treatment effects to vary across biomarker subgroups by assuming systematic differences in treatment effects (on both outcomes) between biomarker-positive and biomarker-negative patient subgroups. The systematic differences estimated from studies reporting treatment effects in both biomarker subgroups is then used to interpolate treatment effects in the biomarker-positive subgroup from studies only reporting treatment effects in the mixed population. The true treatment effects in the biomarker-positive population from all the trials are then used to estimate the surrogate relationship in the biomarker-positive subgroup.

Results: The standard and proposed models when applied to an illustrative example in non-small cell lung cancer (NSCLC) did not provide strong evidence for surrogacy in biomarker-positive patients. However, the proposed model reduced the width of the credible intervals for the surrogacy parameters by up to 75% (when using limited clinical trial data available early in the drug development) compared to the standard BRMA model applied to subgroups.

Conclusions: The developed method can improve precision of the estimates of surrogacy parameters compared to using the BRMA model for subgroups alone. The improvement in precision of the surrogacy parameters was particularly notable at the early drug development stage when data from only few clinical trials were available. We carried out a simulation study, which confirmed the improved precision of the surrogacy parameters achieved via the extended BRMA model.

With the growing availability of large-scale longitudinal studies, such as the UK Biobank and NO.MS dataset [1], there is an increasing need for scalable predictive models that can accommodate long-term outcomes and perform causal inference in longitudinal settings. Bayesian Additive Regression Trees (BART) has gained popularity in causal inference due to its flexibility, scalability, built-in uncertainty estimation, and ability to capture complex, non-linear relationships and interactions without explicit parametric assumptions [2]. However, existing BART-based causal inference models, such as Bayesian Causal Forests (BCF), assume independent outcomes, making them unsuitable for longitudinal settings, where repeated measures within individuals are inherently correlated. Motivated by the NO.MS dataset, which is the largest and most comprehensive dataset on Multiple Sclerosis (MS), comprising more than 34,000 subjects with up to 15 years follow-up, we develop BCFLong, a flexible hierarchical model that preserves BART’s strengths while extending it for longitudinal data analysis. Inspired by BCF, we decompose the mean structure into prognostic and treatment effects, and introduce individual-specific random effects, including random intercepts and time-dependent slope. Additionally, to account for heterogeneous variability across individuals, we implement a sparsity-inducing horseshoe prior on the random effects, which adaptively shrinks small coefficients while preserving meaningful signals. This hierarchical structure balances flexibility and regularization, enabling BCFLong to adapt to varying levels of complexity in fixed and random effects.

Simulation results show that BCFLong outperforms traditional BCF, significantly improving predictive accuracy and treatment effect estimation in the presence of temporal correlation and individual-level variability, while remaining robust to sparsity in the random effects. We then showcased our model on the NO.MS dataset. Here, BCFLong significantly improved predictive performance and effectively captured clinically meaningful longitudinal patterns in brain volume change, which would have otherwise remained undetected, demonstrating the importance of accounting for within-individual correlations.

These findings demonstrate BCFLong’s ability to enhance treatment effect estimation and outcome modelling in longitudinal large-scale studies. By integrating random effects with a sparsity-inducing prior, BCFLong provides a robust and interpretable framework for analysis of longitudinal data, with applications to healthcare and beyond.

[1] Ann-Marie Mallon et al. (2021). Advancing data science in drug development through an innovative computational framework for data sharing and statistical analysis. BMC Medical Research Methodology 21, 1–11.

[2] Chipman, H. A., George, E. I., & McCulloch, R. E. (2010). BART: Bayesian additive regression trees. The Annals of Applied Statistics, 4(1), 266-298.

Group sequential designs are increasingly adopted in clinical research to enable interim analyses and potential early stopping for efficacy or lack of benefit. While these adaptations improve trial efficiency and ethical considerations, they introduce a selection bias that alters the final inference: by adopting the Bayesian perspective, Flournoy and Tarima (2023) show how failing to account for interim decisions in the model results in biased inference and credible intervals that are overly optimistic in the direction of the decision made. Conversely, properly accounting for interim decisions in the likelihood model reflects the additional uncertainty in the posterior estimates. Drawing on information theory, we adopt a Bayesian entropy-based measure to quantify this cost of adaptation at each interim phase, and show how this can be used for post-hoc evaluation of interim decisions, with a particular focus on the trial's final decision. Similarly to what Tarima and Flournoy (2024) found using Fisher information, we find that the closer the observed statistic to the decision boundary, the higher this cost of adaptation, reflecting the limited evidence supporting the decision made. We illustrate the use of the proposed measure in a retrospective evaluation of a multi-stage group sequential trial. By comparing alternative decision boundaries and prior specifications, we show how this measure can enhance the understanding of trial results and inform the design of future adaptive studies. Finally, we present an expected version of this metric to guide clinicians in choosing decision boundaries in a pre-experimental phase. This guidance may complement traditional strategies based on type-I error control, such as those provided by Pocock or O'Brien-Fleming boundaries, by offering insights into the potential loss of information on the treatment effect at each interim phase.

Flournoy, N., & Tarima, S. (2023). Posterior alternatives with informative early stopping. Statistical Papers, 64(4), 1329-1341.

Tarima, S., & Flournoy, N. (2024). The cost of sequential adaptation and the lower bound for mean squared error. Statistical Papers, 65(9), 5529-5553.

Background:

In clinical and epidemiological studies, there is growing interest in examining the role of within-individual variability (WIV) patterns in longitudinal biomarker data, as emerging evidence suggests that WIV may offer valuable insights and improve predictive power for disease risk and progression. Joint models for longitudinal and time-to-event data (JM) provide a statistically rigorous framework for inferring potential associations between biomarker WIV and clinical outcomes and performing dynamic risk predictions informed by WIV. However, WIV measures themselves can be challenging to estimate reliably, and inferential results can be sensitive to model setting. A motivating example arises when WIV is characterized by biological variability in terms of curvature or wiggliness patterns in the underlying biomarker trajectory [1,2]. Existing findings underscore the need for further research.

Methods:

Motivated by Wang et al. [1,2], we investigated novel modelling strategies for trajectory-based biomarker WIV within the JM context. We propose the use of two state-of-the-art semiparametric approaches to model biomarker WIV: one based on penalized orthogonal P-splines and the other on functional principal component analysis (FPCA). We compare them with a standard spline-based approach used in Wang et al. [1,2]. For all approaches, we formulated the JM within a Bayesian framework due to its advantages in modelling and computation. Using a Monte Carlo simulation study, we empirically assessed the estimation performance of these approaches under various model settings.

Results:

In general, the association of trajectory-based WIV with a time-to-event outcome is challenging to estimate robustly under realistic data settings. Among the three approaches, the standard method is the least robust and suffers from convergence issues as models become more complex, while FPCA tends to provide less bias for most parameters across scenarios. When the focus is on prediction, the FPCA-based approach demonstrates the best overall performance, achieving predictive accuracy close to that of the true model across all scenarios. Results from a real-data comparative analysis using data from the Danish cystic fibrosis registry are also anticipated.

Conclusion:

Estimating the association of trajectory-based WIV with a time-to-event outcome is challenging and requires careful model consideration and interpretation of results. Overall, FPCA appears to be a promising approach for use in JM, particularly when the focus is on prediction.

References:

[1] Wang et al. Biostatistics 2024

[2] Wang et al. Ann. Appl. Stat. 2024

Reference-based imputation (RBI) methods, proposed by Carpenter et al. (2013), are widely used to handle missing data after the occurence of intercurrent events (ICEs) in randomized clinical trials. These methods assume no data collection after the ICE. Conventionally, the variance for reference-based estimators was obtained using Rubin's rules but this is biased compared to the repeated sampling variance of the point estimator, due to uncongeniality. Repeated sampling variance estimators were proposed as an alternative to variance estimation for reference-based estimators. However, these have a property that they decrease as the proportion of ICEs increases. Currently, no frequentist or Bayesian framework method has been developed under which Rubin's variance estimator provides correct inference.

White et al. (2019) introduced a causal model incorporating the concept of a `maintained treatment effect` post-ICE, showing that reference-based estimators are special cases within this framework. Building on this framework, we propose using a prior distribution for the maintained effect parameter to account for uncertainty about the reference-based assumption using the Bayesian framework. The proposed Bayesian causal model (BCM) provides inference for reference-based estimators that explicitly reflects our uncertainty about how much treatment effects are maintained following the occurrence of ICEs.

A simulation study compared the BCM with existing RBI methods. The analysis used 5000 simulations, incorporating the BCM with fixed and prior distributions on the maintained effect parameter k₀. Results showed that incorporating a prior distribution on the maintained treatment effect parameter increased posterior variance, particularly in high ICE scenarios, reflecting the impact of the greater uncertainty about the reference-based assumptions. When uncertainty in k₀ was introduced, posterior standard deviation increased with higher ICE rates, aligning with the principle that treatment effect uncertainty should grow as missing data proportions rise.

Application of the method requires pre-specification of the prior distribution for the maintained treatment effect. This mandates careful clinical considerations about the likely impact of ICEs on post-ICE outcomes. The approach can also be used for sensitivity analyses, enabling assessment across varying prior assumptions.

J. R. Carpenter, J. H. Roger, and M. G. Kenward. Analysis of longitudinal trials with protocol deviation: a framework for relevant, accessible assumptions, and inference via multiple imputation. J Biopharm Stat, 23(6):1352–71, 2013. doi: 10.1080/10543406.2013.834911.

Ian White, Royes Joseph, and Nicky Best. A causal modelling framework for referencebased imputation and tipping point analysis in clinical trials with quantitative outcome.
Journal of Biopharmaceutical Statistics, 30(2):334–350, 2020. doi: 10.1080/10543406.2019.1684308.