Bayesian hypothesis testing with frequentist characteristics in clinical trials

Design and monitoring of clinical trials with an interim analysis and a negative binomial endpoint

There are very rich publications devoted to group sequential design, adaptive design and trial monitoring for continuous, binary and time to event endpoints. Many authors also discuss fixed design, blinded sample size re-estimation design and group sequential design for studies with a negative binomial outcome. Nonetheless, literature is sparse in adaptive design for a trial with a negative binomial endpoint. The features of such an endpoint in a flexible trial design setting remains inadequately understood. In this research, we seek to bridge this knowledge gap by offering a thorough examination of utilizing data components from a two-stage adaptive design for unblinded conditional power calculation and corresponding sample size re-estimation. We also provide expression for calculating the probability of meeting the futility criterion to determine the appropriate timing for the interim analysis. To evaluate the performance of the design, we conduct simulations to assess its operation characteristics. Finally, we provide a helpful and illustrative example to demonstrate the practical applications of the methods.

Bayesian kinetic modeling for tracer-based metabolomic data

BACKGROUND

Stable Isotope Resolved Metabolomics (SIRM) is a new biological approach that uses stable isotope tracers such as uniformly [Formula: see text]-enriched glucose ([Formula: see text]-Glc) to trace metabolic pathways or networks at the atomic level in complex biological systems. Non-steady-state kinetic modeling based on SIRM data uses sets of simultaneous ordinary differential equations (ODEs) to quantitatively characterize the dynamic behavior of metabolic networks. It has been increasingly used to understand the regulation of normal metabolism and dysregulation in the development of diseases. However, fitting a kinetic model is challenging because there are usually multiple sets of parameter values that fit the data equally well, especially for large-scale kinetic models. In addition, there is a lack of statistically rigorous methods to compare kinetic model parameters between different experimental groups.

RESULTS

We propose a new Bayesian statistical framework to enhance parameter estimation and hypothesis testing for non-steady-state kinetic modeling of SIRM data. For estimating kinetic model parameters, we leverage the prior distribution not only to allow incorporation of experts' knowledge but also to provide robust parameter estimation. We also introduce a shrinkage approach for borrowing information across the ensemble of metabolites to stably estimate the variance of an individual isotopomer. In addition, we use a component-wise adaptive Metropolis algorithm with delayed rejection to perform efficient Monte Carlo sampling of the posterior distribution over high-dimensional parameter space. For comparing kinetic model parameters between experimental groups, we propose a new reparameterization method that converts the complex hypothesis testing problem into a more tractable parameter estimation problem. We also propose an inference procedure based on credible interval and credible value. Our method is freely available for academic use at https://github.com/xuzhang0131/MCMCFlux .

CONCLUSIONS

Our new Bayesian framework provides robust estimation of kinetic model parameters and enables rigorous comparison of model parameters between experimental groups. Simulation studies and application to a lung cancer study demonstrate that our framework performs well for non-steady-state kinetic modeling of SIRM data.

Utilization of treatment effect on a surrogate endpoint for planning a study to evaluate treatment effect on a final endpoint

To design a phase III study with a final endpoint and calculate the required sample size for the desired probability of success, we need a good estimate of the treatment effect on the endpoint. It is prudent to fully utilize all available information including the historical and phase II information of the treatment as well as external data of the other treatments. It is not uncommon that a phase II study may use a surrogate endpoint as the primary endpoint and has no or limited data for the final endpoint. On the other hand, external information from the other studies for the other treatments on the surrogate and final endpoints may be available to establish a relationship between the treatment effects on the two endpoints. Through this relationship, making full use of the surrogate information may enhance the estimate of the treatment effect on the final endpoint. In this research, we propose a bivariate Bayesian analysis approach to comprehensively deal with the problem. A dynamic borrowing approach is considered to regulate the amount of historical data and surrogate information borrowing based on the level of consistency. A much simpler frequentist method is also discussed. Simulations are conducted to compare the performances of different approaches. An example is used to illustrate the applications of the methods.

The use of local and nonlocal priors in Bayesian test-based monitoring for single-arm phase II clinical trials

Bayesian sequential monitoring is widely used in adaptive phase II studies where the objective is to examine whether an experimental drug is efficacious. Common approaches for Bayesian sequential monitoring are based on posterior or predictive probabilities and Bayesian hypothesis testing procedures using Bayes factors. In the first part of the paper, we briefly show the connections between test-based (TB) and posterior probability-based (PB) sequential monitoring approaches. Next, we extensively investigate the choice of local and nonlocal priors for the TB monitoring procedure. We describe the pros and cons of different priors in terms of operating characteristics. We also develop a user-friendly Shiny application to implement the TB design.

Trial monitoring via a futility criterion for interim results on a count data endpoint and a continuous endpoint

Assumptions made at design stage regarding the true treatment effect, background event rate and other factors may not always hold. Thus, long-term and large-scale studies may be designed with an interim analysis in order that the trials may be stopped early due to futility to save resource. There are many considerations of trial conducts for this type of trials. In this paper, we use a mock study to illustrate systematically the thinking and procedures for trial monitoring with a futility criterion for the interim results on a count data endpoint and a continuous endpoint. We focus on the discussions of blinded trial monitoring, the probability of meeting the futility criterion, conditional power/probability of success, Bayesian inference, potential delayed treatment effect and subgroup analysis. The experience should be applicable to future studies with similar features.