Bayesian hierarchical model for dose-finding trial incorporating historical data.

The Multiple Comparison Procedure and Modelling (MCPMod) approach has been shown to be a powerful statistical technique that can significantly improve the design and analysis of dose-finding studies under model uncertainty. Due to its frequentist nature, however, it is difficult to incorporate information into MCPMod from historical trials on the same drug. BMCPMod, a recently introduced Bayesian version of MCPMod, is designed to take into account historical information on the placebo dose group. We introduce a Bayesian hierarchical framework capable of incorporating historical information on an arbitrary number of dose groups, including both placebo and active ones, taking into account the relationship between responses of these dose groups. Our approach can also model both prognostic and predictive between-trial heterogeneity and is particularly useful in situations where the effect sizes of two trials are different. Our goal is to reduce the necessary sample size in the dose-finding trial while maintaining its target power.

A model-based approach for historical borrowing, with an application to neovascular age-related macular degeneration.

Bayesian historical borrowing has recently attracted growing interest due to the increasing availability of historical control data, as well as improved computational methodology and software. In this article, we argue that the statistical models used for borrowing may be suboptimal when they do not adjust for differing factors across historical studies such as covariates, dosing regimen, etc. We propose an alternative approach to address these shortcomings. We start by constructing a historical model based on subject-level historical data to accurately characterize the control treatment by adjusting for known between trials differences. This model is subsequently used to predict the control arm response in the current trial, enabling the derivation of a model-informed prior for the treatment effect parameter of another (potentially simpler) model used to analyze the trial efficacy (i.e. the trial model). Our approach is applied to neovascular age-related macular degeneration trials, employing a cross-sectional regression trial model, and a longitudinal non-linear mixed-effects drug-disease-trial historical model. The latter model characterizes the relationship between clinical response, drug exposure and baseline covariates so that the derived model-informed prior seamlessly adapts to the trial population and can be extrapolated to a different dosing regimen. This approach can yield a more accurate prior for borrowing, thus optimizing gains in efficiency (e.g. increasing power or reducing the sample size) in future trials.

On efficient posterior inference in normalized power prior Bayesian analysis.

The power prior has been widely used to discount the amount of information borrowed from historical data in the design and analysis of clinical trials. It is realized by raising the likelihood function of the historical data to a power parameter δ ∈ [ 0 , 1 ] $\delta \in [0, 1]$ , which quantifies the heterogeneity between the historical and the new study. In a fully Bayesian approach, a natural extension is to assign a hyperprior to δ such that the posterior of δ can reflect the degree of similarity between the historical and current data. To comply with the likelihood principle, an extra normalizing factor needs to be calculated and such prior is known as the normalized power prior. However, the normalizing factor involves an integral of a prior multiplied by a fractional likelihood and needs to be computed repeatedly over different δ during the posterior sampling. This makes its use prohibitive in practice for most elaborate models. This work provides an efficient framework to implement the normalized power prior in clinical studies. It bypasses the aforementioned efforts by sampling from the power prior with δ = 0 $\delta = 0$ and δ = 1 $\delta = 1$ only. Such a posterior sampling procedure can facilitate the use of a random δ with adaptive borrowing capability in general models. The numerical efficiency of the proposed method is illustrated via extensive simulation studies, a toxicological study, and an oncology study.

Bayesian Method of Borrowing Study-Level Historical Longitudinal Control Data for Mixed-Effects Models with Repeated Measures.

Bringing historical control information into a new trial appropriately holds the promise of more efficient trial design with more accurate estimates, increased power, and fewer patients allocated to inefficacious control group, provided the historical control data are sufficiently similar to the concurrent control. Interest has been growing over the past few decades in leveraging historical clinical trial on the control arm. However, most of the current historical borrowing methods focus on incorporating patient-level historical control information at only one time point. In this work, we propose a Bayesian hierarchical Mixed effect Models for Repeated Measures to incorporate aggregated study-level longitudinal historical control estimates into the concurrent trial that collected repeated longitudinal data. The simulation study demonstrates that, as compared to one time point data analysis approach, leveraging longitudinal historical control data produces greater power enhancement and mitigates the power loss when the missing data under missing at random mechanism is present. Our work also helps fill the gap of lack of methods borrowing historical longitudinal control data from the published summarized estimates when patient-level control data are not available.

Incorporating historical control information in ANCOVA models using the meta-analytic-predictive approach.

The meta-analytic-predictive (MAP) approach is a Bayesian meta-analytic method to synthesize and incorporate information from historical controls in the analysis of a new trial. Classically, only a single parameter, typically the intercept or rate, is assumed to vary across studies, which may not be realistic in more complex models. Analysis of covariance (ANCOVA) is often used to analyze trials with a pretest-posttest design, where both the intercept and the baseline effect (coefficient of the outcome at baseline) affect the estimated treatment effect. We extended the MAP approach to ANCOVA, to allow for variation in the intercept and the baseline effect across studies, and possibly also correlation between these parameters. The method was illustrated using data from the Alzheimer's Disease Cooperative Study (ADCS) and assessed with a simulation study. In the ADCS data, the proposed multivariate MAP approach yielded a prior effective sample size of 79 and 58 for the intercept and the baseline effect respectively and reduced the posterior standard deviation of the treatment effect by 12.6%. The result was robust to the choice of prior for the between-study variation. In the simulations, the proposed approach yielded power gains with a good control of the type I error rate. Ignoring the between-study correlation of the parameters or assuming no variation in the baseline effect generally led to less power gain. In conclusion, the MAP approach can be extended to a multivariate version for ANCOVA, which may improve the estimation of the treatment effect.

Incorporating historical controls in clinical trials with longitudinal outcomes using the modified power prior.

Several dynamic borrowing methods, such as the modified power prior (MPP), the commensurate prior, have been proposed to increase statistical power and reduce the required sample size in clinical trials where comparable historical controls are available. Most methods have focused on cross-sectional endpoints, and appropriate methodology for longitudinal outcomes is lacking. In this study, we extend the MPP to the linear mixed model (LMM). An important question is whether the MPP should use the conditional version of the LMM (given the random effects) or the marginal version (averaged over the distribution of the random effects), which we refer to as the conditional MPP and the marginal MPP, respectively. We evaluated the MPP for one historical control arm via a simulation study and an analysis of the data of Alzheimer's Disease Cooperative Study (ADCS) with the commensurate prior as the comparator. The conditional MPP led to inflated type I error rate when there existed moderate or high between-study heterogeneity. The marginal MPP and the commensurate prior yielded a power gain (3.6%-10.4% vs. 0.6%-4.6%) with the type I error rates close to 5% (5.2%-6.2% vs. 3.8%-6.2%) when the between-study heterogeneity is not excessively high. For the ADCS data, all the borrowing methods improved the precision of estimates and provided the same clinical conclusions. The marginal MPP and the commensurate prior are useful for borrowing historical controls in longitudinal data analysis, while the conditional MPP is not recommended due to inflated type I error rates.

Challenges and potential strategies utilizing external data for efficacy evaluation in small-sized clinical trials.

In clinical trials for diseases with very small patient populations, trial investigators may encounter recruitment difficulties. It can be challenging to conduct clinical trials with enough power to detect a treatment effect, and randomization may not be feasible due to timeline, budget, and ethical concerns. To bring breakthrough therapies to the market quickly, it is important to come up with efficient approaches to utilizing individual patient data through improved study design and sound statistical methods. Emerging topics in this area include the use of Bayesian approaches to flexibly incorporate prior information into the current clinical trials, the use of historical controls to efficiently conduct trials that will reduce the number of subjects recruited and ease ethical considerations, and the use of innovative study designs, such as a platform design, to improve the efficiency and speed of the medical therapy development progress. In this paper, we describe three scenarios which highlight some of the challenges encountered in small-sized clinical trial development and provide potential statistical approaches to overcome the aforementioned challenges.

Utilizing shared internal control arms and historical information in small-sized platform clinical trials.

Recruitment of patients in concurrent control arms can be very challenging for clinical trials for pediatric and rare diseases. Innovative approaches, such as platform trial designs, including shared internal control arm(s), can potentially reduce the needed sample size, improving the efficiency and speed of the drug development program. Furthermore, historical borrowing, which involves leveraging information from control arms in previous relevant clinical trials, may further enhance a clinical trial's efficiency. In this paper, we discuss platform trials highlighting their advantages and limitations. We then compare various strategies that borrow historical data or information, such as pooling data from different studies, analyzing data from studies separately, test-then-pool, dynamic pooling, and Bayesian hierarchical modeling, which focuses on the meta-analytic-predictive (MAP) prior. We further propose a procedure to illustrate the feasibility of utilizing historical controls under a platform setting and describe the statistical performance of our method via simulations.