Conference Agenda

Introduction: The dawn of personalized medicine comes with new challenges in the design of clinical trials. Especially in the development of gene-specific cancer therapy, drugs may be tissue-agnostic, which means that the same drug can be applied in diseases of different organs. So-called basket trial designs are a useful tool for investigating such drugs: In a single trial, one therapy is investigated in several strata defined by different diseases or disease subtypes. This eases the organizational burden compared to the conduct of several trials, and furthermore it offers a statistical benefit: information borrowing can be used to share response information between the strata. This may leverage the oftentimes small sample sizes in the strata to increase power while keeping type-I error inflation and bias reasonably low. In biometrical research, a variety of frequentist and Bayesian techniques were suggested to implement borrowing in basket trials. These designs often come with tuning parameters to adjust the amount of borrowing. However, the optimal choice of these parameters is subject to current research.

Methods: We suggest a utility-based framework for optimizing borrowing in basket trial designs. As an example, we consider a Bayesian basket trial design by Fujikawa et al. (Biom J, 2020;62(2):330–8) which is based on the beta-binomial model. We demonstrate the use of utility functions for defining a compromise between successfully detecting strata with high response rates (“active strata”) while rejecting strata with low response rates (“inactive strata”). Applying numerical optimization algorithms, these utility functions can be used to find optimal tuning parameters for the borrowing.

Results and conclusion: We conducted an extensive comparison study showing that utility-based optimization is a feasible approach for optimizing information borrowing in basket trial designs. Our approach successfully achieves a compromise between increasing per-stratum power while keeping type-I error inflation moderate. In our study, we also compared the use of grid search to different optimization algorithms and will discuss their performance. Our framework is not unique to Fujikawa’s design and may hence be used for planning basket trial designs in general. Finally, we will also discuss the extension of utility functions to tune sample size and interim analyses, thus allowing simultaneous planning of all aspects of basket trial design in a single framework.

Background:
There has been growing interest in leveraging external control data to augment a randomized control group data in clinical trials and enable more informative decision making. In recent years, the quality and availability of real-world data have improved steadily as external controls. However, information borrowing by directly pooling such external controls with randomized controls may lead to biased estimates of the treatment effect. Dynamic borrowing methods under the Bayesian framework have been proposed to better control the false positive error. However, the numerical computation and, especially, parameter tuning, of those Bayesian dynamic borrowing methods remain a challenge in practice.

Method:
We present a frequentist interpretation of a Bayesian commensurate prior borrowing approach and describe intrinsic challenges associated with this method from the perspective of optimization. Motivated by this observation, we propose a new dynamic borrowing approach using adaptive lasso. The treatment effect estimate derived from this method follows a known asymptotic distribution, which can be used to construct confidence intervals and conduct hypothesis tests. The proposed approach only needs to solve two convex optimizations problems and thus is easy to implement and computationally efficient. Extensive Monte Carlo simulations were conducted under different settings to evaluate the type I error, power, bias, standard deviation, mean square error (MSE) of treatment effect estimates and effective sample size (ESS).

Results:
We observed highly competitive performance of adaptive lasso compared to Bayesian approaches, in terms of statistical power, bias, MSE, and ESS. An illustration example using actual trial data also suggested the adaptive lasso produces similar estimates as the Bayesian approaches, yet with much less computation time and resources. Methods for parameter tuning are also thoroughly discussed based on results from the stimulation studies.

Conclusion:
We have developed a novel frequentist dynamic borrowing method based on the adaptive lasso methodology. This approach boosts the accuracy of treatment effect estimation by borrowing information from external controls. It is easy to implement, runs substantially faster than Bayesian approaches, and allows frequentist asymptotic inference. While it is theoretically impossible to have an estimator that always outperforms a Bayesian estimator (and vise versa), we have demonstrated through extensive simulations that with appropriate choices of tuning parameters, the operating characteristics of our approach is highly competitive compared to conventional Bayesian approaches.

Background:

Basket trials examine the efficacy of a single intervention simultaneously in several patient subgroups, called baskets. They are currently mostly applied in oncology, where the assignment to the baskets is based on matching medical characteristics such as a common mutation. This can result in small sample sizes within baskets that are also likely to differ. Several designs for the analysis of basket trials have been proposed in the literature that share information across baskets to increase power. Most designs utilise Bayesian methods, such as hierarchical modelling and model averaging. The recently proposed power prior design uses empirical Bayes methods to increase the computational efficacy compared to fully Bayesian designs. This design incorporates data from all baskets using a weighted likelihood that shares information according to the similarity of the individual baskets. However, if the sample sizes differ, there is a risk that the information from the small baskets will be overlaid by that from the large baskets.

Methods:

We extend the power prior design by applying a weighting method, previously suggested for sharing information from historical data, that accounts for unequal sample sizes by limiting the amount of information shared between baskets. The new weights take the pairwise ratio of sample sizes per basket into account, such that the effective sample size that is shared per basket cannot exceed the sample size of the basket of interest. Using a simulation study, we systematically compare the power prior design with previously suggested weights and the new information-limiting weighting method to other Bayesian basket trial designs with respect to the expected number of correct decisions, type 1 error rates and power. We consider a range of different scenarios with different true response probabilities and sample sizes across baskets.

Results:

The results of the simulation study show that the new information-limiting weights improve the results of the original power prior design. In terms of the expected number of correct decisions, the improved power prior design performs slightly better than the competing designs in all sample size scenarios. In scenarios with some active and some inactive baskets, the inflation of the type 1 error rates is less severe than with unlimited sharing.

Conclusion:

The proposed basket trial design shows promising performance in the investigated scenarios and is computationally less expensive than fully Bayesian designs. It can therefore be considered for the analysis of basket trials with unequal sample sizes.

Basket trials are a new class of trial designs that evaluate a common treatment across multiple related conditions. These trials allow for more efficient analysis by leveraging information from different subtrials; however, methods typically assume a common endpoint. In immune-mediated inflammatory disease trials, different clinical trial endpoints are often used, making direct information sharing between subtrials in a basket setting less justifiable. However, in these diseases, the response to treatment is often mediated through a common inflammatory biomarker. For example, in trials investigating the safety and efficacy of Ustekinumab for Ulcerative Colitis, clinical remission was the primary endpoint, whereas in trials of the same drug for Rheumatoid Arthritis, the primary endpoint was the disease activity score. These trials also collected data on C-reactive protein, which may mediate the treatment effect on clinical outcomes. It is plausible that borrowing information on the clinical outcome treatment effect via the mediator would enhance the efficiency of the analysis. We develop methodology that borrows information on the mediator in basket trials with distinct responder outcomes.

We propose a Bayesian hierarchical model that assumes the treatment affects an outcome both directly and indirectly through an intervening mediator variable. The model allows for borrowing of information between subtrials, with the extent of borrowing determined by the prior distributions of the parameters for the mediation effect. Since the outcomes are assumed to be different, there is no sharing of information on the direct treatment effect on the outcome; the only sharing occurs through the mediator. We investigate the operating characteristics of the model using a simulation study and apply it to real data from Ustekinumab trials.

We compared the new approach with logistic regression on a binary outcome that shares information on the response outcome, across multiple simulation scenarios. In scenarios with a mediation effect, we observed an increase in power and a reduction in the width of credible intervals for log odds ratios provided by the new model. In many scenarios, the new model achieved a decrease in bias and mean squared error, as well as an increase in precision for the estimates. The type I error rate was well controlled.

Numerical results suggest that sharing information on the mediation effect can improve the precision of estimates and increase power compared to a standard approach. Further work will explore the most effective mechanism for sharing information between the subtrials through suitable prior distributions of the parameters.

Introduction

External information borrowing can help improving clinical trial efficiency and is therefore often considered in situations where the sample size that can realistically be recruited is limited, as, e.g., pediatric or rare disease trials. When dealing with a two-arm trial, external information is often available for the control arm, leading to so-called ‘hybrid-control’ designs. The Bayesian approach borrows such external information by adopting an informative prior distribution for the control arm mean. A potential issue of this procedure is that external and current information may conflict, but such inconsistency may not be predictable a priori. Robust prior choices are typically proposed to limit extreme worsening of operating characteristics in these situations. However, trade-offs are still present and in general no power gains are possible if strict control of type I error (TIE) rate is desired. In this context, principled justifications for TIE rate inflation can be of interest.

Methods

Building on Calderazzo et al. (2024), we propose an interpretable approach for external information borrowing in this context. The method is built by eliciting explicit caps on TIE rate inflation and power loss based on regions of pre-defined conflict. The method does not rely on a prior specification, and is developed for both normal and binomial outcomes by exploiting relationships between frequentist and Bayesian test decisions thresholds.

Results

The method provides a direct and easily interpretable link between conflict assumptions and test error rates behavior. We additionally show connections of the approach to alternative robust borrowing methods, which can aid their interpretability. The long run behavior (including Bayesian average TIE rate and power) is evaluated via simulations, showing comparable performance to alternative dynamic borrowing methods, such as the robust mixture prior.

Conclusions

Robust external information borrowing typically depends on the choice or estimation of specific borrowing parameters. We provide a rationale for robust incorporation of external information which is directly linked to TIE rate inflation, thus helping interpretability of such borrowing parameters.

Calderazzo, S., Wiesenfarth, M., & Kopp-Schneider, A. (2024). Robust incorporation of historical information with known type I error rate inflation. Biometrical Journal, 66(1), 2200322.