A scaled kernel density estimation prior for dynamic borrowing of historical information with application to clinical trial design.

Incorporating historical data into a current data analysis can improve estimation of parameters shared across both datasets and increase the power to detect associations of interest while reducing the time and cost of new data collection. Several methods for prior distribution elicitation have been introduced to allow for the data-driven borrowing of historical information within a Bayesian analysis of the current data. We propose scaled Gaussian kernel density estimation (SGKDE) prior distributions as potentially more flexible alternatives. SGKDE priors directly use posterior samples collected from a historical data analysis to approximate probability density functions, whose variances depend on the degree of similarity between the historical and current datasets, which are used as prior distributions in the current data analysis. We compare the performances of the SGKDE priors with some existing approaches using a simulation study. Data from a recently completed phase III clinical trial of a maternal vaccine for respiratory syncytial virus are used to further explore the properties of SGKDE priors when designing a new clinical trial while incorporating historical data. Overall, both studies suggest that the new approach results in improved parameter estimation and power in the current data analysis compared to the considered existing methods.

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 Mediation Analysis with Power Prior Distributions.

Bayesian methods are often suggested as a solution for issues encountered in small sample research, however, Bayesian methods often require informative priors to outperform classical methods in these settings. Specifying accurate priors with respect to the true value of the parameter of interest is challenging and inaccurate informative priors can have detrimental effects on conclusions from the statistical analysis. This paper proposes an objective procedure for creating informative priors for mediation analysis based on a historical data set; the only requirements for implementing the procedure are that the data from the current study constitute a representative sample from the population of interest, and that the historical and current data sets contain measures of the same covariates and independent variable, mediator, and outcome. The simulation study findings show that the proposed method leads to appropriate amount of borrowing from the historical data set, which leads to increases in precision and power when the historical data and current data are exchangeable, and does not induce bias when the historical and current studies are not exchangeable. The proposed method is illustrated using data from the project PROsetta Stone, and we provide rstan code for implementing the proposed method.

Dynamic borrowing through empirical power priors that control type I error.

In order for historical data to be considered for inclusion in the design and analysis of clinical trials, prospective rules are essential. Incorporation of historical data may be of particular interest in the case of small populations where available data is scarce and heterogeneity is not as well understood, and thus conventional methods for evidence synthesis might fall short. The concept of power priors can be particularly useful for borrowing evidence from a single historical study. Power priors employ a parameter γ ∈ [ 0 , 1 ] that quantifies the heterogeneity between the historical study and the new study. However, the possibility of borrowing data from a historical trial will usually be associated with an inflation of the type I error. We suggest a new, simple method of estimating the power parameter suitable for the case when only one historical dataset is available. The method is based on predictive distributions and parameterized in such a way that the type I error can be controlled by calibrating to the degree of similarity between the new and historical data. The method is demonstrated for normal responses in a one or two group setting. Generalization to other models is straightforward.

Bayesian Dynamic Borrowing of Historical Information with Applications to the Analysis of Large-Scale Assessments.

The purpose of this paper is to demonstrate and evaluate the use of Bayesian dynamic borrowing (Viele et al, in Pharm Stat 13:41-54, 2014) as a means of systematically utilizing historical information with specific applications to large-scale educational assessments. Dynamic borrowing via Bayesian hierarchical models is a special case of a general framework of historical borrowing where the degree of borrowing depends on the heterogeneity among historical data and current data. A joint prior distribution over the historical and current data sets is specified with the degree of heterogeneity across the data sets controlled by the variance of the joint distribution. We apply Bayesian dynamic borrowing to both single-level and multilevel models and compare this approach to other historical borrowing methods such as complete pooling, Bayesian synthesis, and power priors. Two case studies using data from the Program for International Student Assessment reveal the utility of Bayesian dynamic borrowing in terms of predictive accuracy. This is followed by two simulation studies that reveal the utility of Bayesian dynamic borrowing over simple pooling and power priors in cases where the historical data is heterogeneous compared to the current data based on bias, mean squared error, and predictive accuracy. In cases of homogeneous historical data, Bayesian dynamic borrowing performs similarly to data pooling, Bayesian synthesis, and power priors. In contrast, for heterogeneous historical data, Bayesian dynamic borrowing performed at least as well, if not better, than other methods of borrowing with respect to mean squared error, percent bias, and leave-one-out cross-validation.

An adaptive power prior for sequential clinical trials - Application to bridging studies.

During drug evaluation trials, information from clinical trials previously conducted on another population, indications or schedules may be available. In these cases, it might be desirable to share information by efficiently using the available resources. In this work, we developed an adaptive power prior with a commensurability parameter for using historical or external information. It allows, at each stage, full borrowing when the data are not in conflict, no borrowing when the data are in conflict or "tuned" borrowing when the data are in between. We propose to apply our adaptive power prior method to bridging studies between Caucasians and Asians, and we focus on the sequential adaptive allocation design, although other design settings can be used. We weight the prior information in two steps: the effective sample size approach is used to set the maximum desirable amount of information to be shared from historical data at each step of the trial; then, in a sort of Empirical Bayes approach, a commensurability parameter is chosen using a measure of distribution distance. This approach avoids elicitation and computational issues regarding the usual Empirical Bayes approach. We propose several versions of our method, and we conducted an extensive simulation study evaluating the robustness and sensitivity to prior choices.