Bayesian joint modeling of multivariate longitudinal and survival outcomes using Gaussian copulas.

There is an increasing interest in the use of joint models for the analysis of longitudinal and survival data. While random effects models have been extensively studied, these models can be hard to implement and the fixed effect regression parameters must be interpreted conditional on the random effects. Copulas provide a useful alternative framework for joint modeling. One advantage of using copulas is that practitioners can directly specify marginal models for the outcomes of interest. We develop a joint model using a Gaussian copula to characterize the association between multivariate longitudinal and survival outcomes. Rather than using an unstructured correlation matrix in the copula model to characterize dependence structure as is common, we propose a novel decomposition that allows practitioners to impose structure (e.g., auto-regressive) which provides efficiency gains in small to moderate sample sizes and reduces computational complexity. We develop a Markov chain Monte Carlo model fitting procedure for estimation. We illustrate the method's value using a simulation study and present a real data analysis of longitudinal quality of life and disease-free survival data from an International Breast Cancer Study Group trial.

Case weighted power priors for hybrid control analyses with time-to-event data.

We develop a method for hybrid analyses that uses external controls to augment internal control arms in randomized controlled trials (RCTs) where the degree of borrowing is determined based on similarity between RCT and external control patients to account for systematic differences (e.g., unmeasured confounders). The method represents a novel extension of the power prior where discounting weights are computed separately for each external control based on compatibility with the randomized control data. The discounting weights are determined using the predictive distribution for the external controls derived via the posterior distribution for time-to-event parameters estimated from the RCT. This method is applied using a proportional hazards regression model with piecewise constant baseline hazard. A simulation study and a real-data example are presented based on a completed trial in non-small cell lung cancer. It is shown that the case weighted power prior provides robust inference under various forms of incompatibility between the external controls and RCT population.

Basket trials in oncology: a systematic review of practices and methods, comparative analysis of innovative methods, and an appraisal of a missed opportunity.

Background: Basket trials are increasingly used in oncology drug development for early signal detection, accelerated tumor-agnostic approvals, and prioritization of promising tumor types in selected patients with the same mutation or biomarker. Participants are grouped into so-called baskets according to tumor type, allowing investigators to identify tumors with promising responses to treatment for further study. However, it remains a question as to whether and how much the adoption of basket trial designs in oncology have translated into patient benefits, increased pace and scale of clinical development, and de-risking of downstream confirmatory trials. Methods: Innovation in basket trial design and analysis includes methods that borrow information across tumor types to increase the quality of statistical inference within each tumor type. We build on the existing systematic reviews of basket trials in oncology to discuss the current practices and landscape. We conceptually illustrate recent innovative methods for basket trials, with application to actual data from recently completed basket trials. We explore and discuss the extent to which innovative basket trials can be used to de-risk future trials through their ability to aid prioritization of promising tumor types for subsequent clinical development. Results: We found increasing adoption of basket trial design in oncology, but largely in the design of single-arm phase II trials with a very low adoption of innovative statistical methods. Furthermore, the current practice of basket trial design, which does not consider its impact on the clinical development plan, may lead to a missed opportunity in improving the probability of success of a future trial. Gating phase II with a phase Ib basket trial reduced the size of phase II trials, and losses in the probability of success as a result of not using innovative methods may not be recoverable by running a larger phase II trial. Conclusion: Innovative basket trial methods can reduce the size of early phase clinical trials, with sustained improvement in the probability of success of the clinical development plan. We need to do more as a community to improve the adoption of these methods.

Bayesian design of clinical trials using joint models for recurrent and terminating events.

Joint models for recurrent event and terminating event data are increasingly used for the analysis of clinical trials. However, few methods have been proposed for designing clinical trials using these models. In this article, we develop a Bayesian clinical trial design methodology focused on evaluating the effect of an investigational product (IP) on both recurrent event and terminating event processes considered as multiple primary endpoints, using a multifrailty joint model. Dependence between the recurrent and terminating event processes is accounted for using a shared frailty. Inferences for the multiple primary outcomes are based on posterior model probabilities corresponding to mutually exclusive hypotheses regarding the benefit of IP with respect to the recurrent and terminating event processes. We propose an approach for sample size determination to ensure the trial design has a high power and a well-controlled type I error rate, with both operating characteristics defined from a Bayesian perspective. We also consider a generalization of the proposed parametric model that uses a nonparametric mixture of Dirichlet processes to model the frailty distributions and compare its performance to the proposed approach. We demonstrate the methodology by designing a colorectal cancer clinical trial with a goal of demonstrating that the IP causes a favorable effect on at least one of the two outcomes but no harm on either.

Bayesian Design of Clinical Trials Using Joint Cure Rate Models for Longitudinal and Time-to-Event Data.

For clinical trial design and analysis, there has been extensive work related to using joint models for longitudinal and time-to-event data without a cure fraction (i.e., when all patients are at risk for the event of interest), but comparatively little treatment has been given to design and analysis of clinical trials using joint models that incorporate a cure fraction. In this paper, we develop a Bayesian clinical trial design methodology focused on evaluating the treatment's effect on a time-to-event endpoint using a promotion time cure rate model, where the longitudinal process is incorporated into the hazard model for the promotion times. A piecewise linear hazard model for the period after assessment of the longitudinal measure ends is proposed as an alternative to extrapolating the longitudinal trajectory. This may be advantageous in scenarios where the period of time from the end of longitudinal measurements until the end of observation is substantial. Inference for the time-to-event endpoint is based on a novel estimand which combines the treatment's effect on the probability of cure and its effect on the promotion time distribution, mediated by the longitudinal outcome. We propose an approach for sample size determination such that the design has a high power and a well-controlled type I error rate with both operating characteristics defined from a Bayesian perspective. We demonstrate the methodology by designing a breast cancer clinical trial with a primary time-to-event endpoint where longitudinal outcomes are measured periodically during follow up.

Bayesian design of clinical trials using joint models for longitudinal and time-to-event data.

Joint models for longitudinal and time-to-event data are increasingly used for the analysis of clinical trial data. However, few methods have been proposed for designing clinical trials using these models. In this article, we develop a Bayesian clinical trial design methodology focused on evaluating the treatment's effect on the time-to-event endpoint using a flexible trajectory joint model. By incorporating the longitudinal outcome trajectory into the hazard model for the time-to-event endpoint, the joint modeling framework allows for non-proportional hazards (e.g., an increasing hazard ratio over time). Inference for the time-to-event endpoint is based on an average of a time-varying hazard ratio which can be decomposed according to the treatment's direct effect on the time-to-event endpoint and its indirect effect, mediated through the longitudinal outcome. We propose an approach for sample size determination for a trial such that the design has high power and a well-controlled type I error rate with both operating characteristics defined from a Bayesian perspective. We demonstrate the methodology by designing a breast cancer clinical trial with a primary time-to-event endpoint and where predictive longitudinal outcome measures are also collected periodically during follow-up.

Bayesian adaptive basket trial design using model averaging.

In this article, we develop a Bayesian adaptive design methodology for oncology basket trials with binary endpoints using a Bayesian model averaging framework. Most existing methods seek to borrow information based on the degree of homogeneity of estimated response rates across all baskets. In reality, an investigational product may only demonstrate activity for a subset of baskets, and the degree of activity may vary across the subset. A key benefit of our Bayesian model averaging approach is that it explicitly accounts for the possibility that any subset of baskets may have similar activity and that some may not. Our proposed approach performs inference on the basket-specific response rates by averaging over the complete model space for the response rates, which can include thousands of models. We present results that demonstrate that this computationally feasible Bayesian approach performs favorably compared to existing state-of-the-art approaches, even when held to stringent requirements regarding false positive rates.

Bayesian design of biosimilars clinical programs involving multiple therapeutic indications.

In this paper, we propose a Bayesian design framework for a biosimilars clinical program that entails conducting concurrent trials in multiple therapeutic indications to establish equivalent efficacy for a proposed biologic compared to a reference biologic in each indication to support approval of the proposed biologic as a biosimilar. Our method facilitates information borrowing across indications through the use of a multivariate normal correlated parameter prior (CPP), which is constructed from easily interpretable hyperparameters that represent direct statements about the equivalence hypotheses to be tested. The CPP accommodates different endpoints and data types across indications (eg, binary and continuous) and can, therefore, be used in a wide context of models without having to modify the data (eg, rescaling) to provide reasonable information-borrowing properties. We illustrate how one can evaluate the design using Bayesian versions of the type I error rate and power with the objective of determining the sample size required for each indication such that the design has high power to demonstrate equivalent efficacy in each indication, reasonably high power to demonstrate equivalent efficacy simultaneously in all indications (ie, globally), and reasonable type I error control from a Bayesian perspective. We illustrate the method with several examples, including designing biosimilars trials for follicular lymphoma and rheumatoid arthritis using binary and continuous endpoints, respectively.

Bayesian clinical trial design using historical data that inform the treatment effect.

We consider the problem of Bayesian sample size determination for a clinical trial in the presence of historical data that inform the treatment effect. Our broadly applicable, simulation-based methodology provides a framework for calibrating the informativeness of a prior while simultaneously identifying the minimum sample size required for a new trial such that the overall design has appropriate power to detect a non-null treatment effect and reasonable type I error control. We develop a comprehensive strategy for eliciting null and alternative sampling prior distributions which are used to define Bayesian generalizations of the traditional notions of type I error control and power. Bayesian type I error control requires that a weighted-average type I error rate not exceed a prespecified threshold. We develop a procedure for generating an appropriately sized Bayesian hypothesis test using a simple partial-borrowing power prior which summarizes the fraction of information borrowed from the historical trial. We present results from simulation studies that demonstrate that a hypothesis test procedure based on this simple power prior is as efficient as those based on more complicated meta-analytic priors, such as normalized power priors or robust mixture priors, when all are held to precise type I error control requirements. We demonstrate our methodology using a real data set to design a follow-up clinical trial with time-to-event endpoint for an investigational treatment in high-risk melanoma.

Bayesian design of a survival trial with a cured fraction using historical data.

In this paper, we develop a general Bayesian clinical trial design methodology, tailored for time-to-event trials with a cured fraction in scenarios where a previously completed clinical trial is available to inform the design and analysis of the new trial. Our methodology provides a conceptually appealing and computationally feasible framework that allows one to construct a fixed, maximally informative prior a priori while simultaneously identifying the minimum sample size required for the new trial so that the design has high power and reasonable type I error control from a Bayesian perspective. This strategy is particularly well suited for scenarios where adaptive borrowing approaches are not practical due to the nature of the trial, complexity of the model, or the source of the prior information. Control of a Bayesian type I error rate offers a sensible balance between wanting to use high-quality information in the design and analysis of future trials while still controlling type I errors in an equitable way. Moreover, sample size determination based on our Bayesian view of power can lead to a more adequately sized trial by virtue of taking into account all the uncertainty in the treatment effect. We demonstrate our methodology by designing a cancer clinical trial in high-risk melanoma.