Statistics and Its Interface

Volume 13 (2020)

Number 4

A CD-based mapping method for combining multiple related parameters from heterogeneous intervention trials

Pages: 533 – 549



Yang Jiao (Department of Statistics, Rutgers University, Piscataway, New Jersey, U.S.A.)

Eun-Young Mun (Department of Health Behavior and Health Systems, University of North Texas Health Science Center, Fort Worth, Tx., U.S.A.)

Thomas A. Trikalinos (Department of Health Services, Policy and Practice, Brown University, Providence, Rhode Island, U.S.A.)

Minge Xie (Department of Statistics, Rutgers University, Piscataway, New Jersey, U.S.A.)


Effect size can differ as a function of the elapsed time since treatment or as a function of other key covariates, such as sex or age. In evidence synthesis, a better understanding of the precise conditions under which treatment does work or does not work well has been highly valued. With increasingly accessible individual patient or participant data (IPD), more precise and informative inference can be within our reach. However, simultaneously combining multiple related parameters across heterogeneous studies is challenging because each parameter from each study has a specific interpretation within the context of the study and other covariates in the model. This paper proposes a novel mapping method to combine study-specific estimates of multiple related parameters across heterogeneous studies, which ensures valid inference at all inference levels by combining sample-dependent functions known as Confidence Distributions (CD). We describe the “CD-based mapping method” and provide a data application example for a multivariate random-effects meta-analysis model. We estimated up to 13 study-specific regression parameters for each of 14 individual studies using IPD in the first step, and subsequently combined the study-specific vectors of parameters, yielding a full vector of hyperparameters in the second step of metaanalysis. Sensitivity analysis indicated that the CD-based mapping method is robust to model misspecification. This novel approach to multi-parameter synthesis provides a reasonable methodological solution when combining complex evidence using IPD.


multi-parameter synthesis, multivariate random-effects meta-analysis, mapping matrix, combining confidence density functions, individual patient data, individual participant data

The project described was supported by the National Institute on Alcohol Abuse and Alcoholism (NIAAA) [R01 AA019511 to EYM] and in part by the National Science Foundation (NSF) [DMS1513483 and DMS1737857 to MX].

The content is solely the responsibility of the authors and does not necessarily represent the official views of the NIAAA, the National Institutes of Health, or the NSF.

Received 18 November 2019

Accepted 1 April 2020

Published 31 July 2020