On the normalized power prior

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.

Bayesian methods: a potential path forward for sepsis trials

BACKGROUND

Given the success of recent platform trials for COVID-19, Bayesian statistical methods have become an option for complex, heterogenous syndromes like sepsis. However, study design will require careful consideration of how statistical power varies using Bayesian methods across different choices for how historical data are incorporated through a prior distribution and how the analysis is ultimately conducted. Our objective with the current analysis is to assess how different uses of historical data through a prior distribution, and type of analysis influence results of a proposed trial that will be analyzed using Bayesian statistical methods.

METHODS

We conducted a simulation study incorporating historical data from a published multicenter, randomized clinical trial in the US and Canada of polymyxin B hemadsorption for treatment of endotoxemic septic shock. Historical data come from a 179-patient subgroup of the previous trial of adult critically ill patients with septic shock, multiple organ failure and an endotoxin activity of 0.60-0.89. The trial intervention consisted of two polymyxin B hemoadsorption treatments (2 h each) completed within 24 h of enrollment.

RESULTS

In our simulations for a new trial of 150 patients, a range of hypothetical results were observed. Across a range of baseline risks and treatment effects and four ways of including historical data, we demonstrate an increase in power with the use of clinically defensible incorporation of historical data. In one possible trial result, for example, with an observed reduction in risk of mortality from 44 to 37%, the probability of benefit is 96% with a fixed weight of 75% on prior data and 90% with a commensurate (adaptive-weighting) prior; the same data give an 80% probability of benefit if historical data are ignored.

CONCLUSIONS

Using Bayesian methods and a biologically justifiable use of historical data in a prior distribution yields a study design with higher power than a conventional design that ignores relevant historical data. Bayesian methods may be a viable option for trials in critical care medicine where beneficial treatments have been elusive.

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 parameterδ ∈ [ 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 withδ = 0 $\delta = 0$ andδ = 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.