The Annals of Applied Statistics

Bayesian aggregation of average data: An application in drug development

Sebastian Weber, Andrew Gelman, Daniel Lee, Michael Betancourt, Aki Vehtari, and Amy Racine-Poon

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Abstract

Throughout the different phases of a drug development program, randomized trials are used to establish the tolerability, safety and efficacy of a candidate drug. At each stage one aims to optimize the design of future studies by extrapolation from the available evidence at the time. This includes collected trial data and relevant external data. However, relevant external data are typically available as averages only, for example, from trials on alternative treatments reported in the literature. Here we report on such an example from a drug development for wet age-related macular degeneration. This disease is the leading cause of severe vision loss in the elderly. While current treatment options are efficacious, they are also a substantial burden for the patient. Hence, new treatments are under development which need to be compared against existing treatments.

The general statistical problem this leads to is meta-analysis, which addresses the question of how we can combine data sets collected under different conditions. Bayesian methods have long been used to achieve partial pooling. Here we consider the challenge when the model of interest is complex (hierarchical and nonlinear) and one data set is given as raw data while the second data set is given as averages only. In such a situation, common meta-analytic methods can only be applied when the model is sufficiently simple for analytic approaches. When the model is too complex, for example, nonlinear, an analytic approach is not possible. We provide a Bayesian solution by using simulation to approximately reconstruct the likelihood of the external summary and allowing the parameters in the model to vary under the different conditions. We first evaluate our approach using fake data simulations and then report results for the drug development program that motivated this research.

Article information

Source
Ann. Appl. Stat., Volume 12, Number 3 (2018), 1583-1604.

Dates
Received: July 2017
Revised: October 2017
First available in Project Euclid: 11 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1536652966

Digital Object Identifier
doi:10.1214/17-AOAS1122

Mathematical Reviews number (MathSciNet)
MR3852689

Keywords
Meta-analysis hierarchical modeling Bayesian computation pharmacometrics Stan

Citation

Weber, Sebastian; Gelman, Andrew; Lee, Daniel; Betancourt, Michael; Vehtari, Aki; Racine-Poon, Amy. Bayesian aggregation of average data: An application in drug development. Ann. Appl. Stat. 12 (2018), no. 3, 1583--1604. doi:10.1214/17-AOAS1122. https://projecteuclid.org/euclid.aoas/1536652966


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Supplemental materials

  • Supplement: Program sources. Source code of R and Stan programs of simulation studies and drug-disease model.