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

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 meta-analysis. 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.