The Meta-Analytic-Predictive Priors Generation and Comparisons
Staying abreast of the rapid pace of clinical development means adopting innovative or computationally intensive designs like Bayesian methods. These methods allow for the incorporation of prior knowledge, in terms of either expert opinion from clinicians or historical data, in statistical inference. Thus, they have the additional advantage of being able to work with real-world data (generally, real-world data has a lot of missing data) without the need to impute missing values. These kinds of models are also flexible enough to work with temporal data. This helps ease the reliance on large sample approximations that are often required for frequentist methods and generally results in greater efficiency in study design.
In this edition of The Informative Bayesian by Pantelis Vlachos, we learn about information borrowing to form a prior distribution. In a Bayesian framework, borrowing from historical data is equivalent to considering informative priors. These priors can be derived as meta-analytic predictive (MAP) priors or using patient-level data.
East Alloy provides the meta-analytic predictive (MAP) approach for deriving an informative prior from historical data in a way that accounts for between-trial heterogeneity. This is done with the use of a hierarchical model. In particular, the MAP prior is derived using a random effects meta-analysis model which is typically used to synthesize the evidence on the comparative effectiveness of two treatments.
The meta-analysis accounts for between-trial heterogeneity and leads to discounting of the historical information. As with any meta-analysis, special consideration should be given to the examination of the characteristics of the historical trials included in the meta-analysis. In order to ensure that the selected historical controls are comparable to those in the new trial, quantitative descriptions of the trial population (subject demographics, baseline characteristics) and qualitative features (concomitant medication), should be first examined. In addition, the assumption for the between-trial heterogeneity needs to be reasonable as the number of historical trials is typically small and uncertainty needs to be accounted for.
The MAP prior is then derived from a random-effect meta-analysis of historical data via Markov Chain Monte Carlo (MCMC) algorithms. MCMC methods are necessary as analytical derivation of the MAP prior is typically not possible. This posterior MCMC sample will represent the MAP prior with a parametric mixture distribution using the expectation maximization (EM) algorithm. The EM algorithm, which begins with a fixed number of mixture components, is used to find a way to express parametrically the numerical representation of the MAP prior. The number of mixture components to be used can either be manually specified or determined automatically based on information criteria measures.
One can also increase robustness of the parametric MAP by adding a weakly-informative prior component to the mixture derived from the previous steps. The degree of how informative the MAP prior is can be assessed with its effective sample size which gives a rough guide by how much the sample size can be reduced when using the respective frequentist power calculation as a reference.
East Alloy – Verified Innovation for Generating Meta-analytic Predictive Priors
Cytel’s East AlloyTM, a web-native extension of East, makes it practical and sustainable to adopt innovative and computationally-intensive designs. This software aims at enhancing your company’s intelligence by using an intuitive graphical interface to proficiently design innovative clinical trials informed by prior data. The MAP approach in East Alloy enables reduction of within-study placebo-treated number of subjects and increase of study power. It allows easy communication of prior information through parametric mixture density which leads to fast and accurate analytical procedures to evaluate properties of trial designs.
Watch this space to learn more about the Bayesian capabilities offered by East Alloy.
Pantelis illustrates a framework for incorporation of historical data in terms of informative priors, in an on demand webinar. Click the button to watch the webinar and access the presentation.
About Pantelis Vlachos
Pantelis is Principal/Strategic Consultant for Cytel, Inc. based in Geneva. He joined the company in January 2013. Before that, he was a Principal Biostatistician at Merck Serono as well as a Professor of Statistics at Carnegie Mellon University for 12 years. His research interests lie in the area of adaptive designs, mainly from a Bayesian perspective, as well as hierarchical model testing and checking although his secret passion is Text Mining. He has served as Managing Editor of the journal “Bayesian Analysis” as well as editorial boards of several other journals and online statistical data and software archives.