Discussion of ‘A selective review of statistical methods using calibration information from similar studies’

Combining information from similar studies has attracted substantial attention and continues to become increasingly important to assemble quality evidence in comparative effectiveness research. To my knowledge, this is the first paper to systematically review classical and up-to-date methods on how different statistical methods, such as meta-analysis, empirical likelihood (EL), renewal estimation and incremental inference, can be applied to incorporate information from multiple sources. This review paper succinctly presents both basic and advanced issues and will be greatly beneficial for researchers who are interested in this field. Because of the wide array of related methods, this paper consists of cohesive but relatively independent sections. Although it is a review paper, the focus and contents are quite different from those of original papers. For example, an optimal combination of two estimators from two independent studies is derived by two methods from different perspectives: a linear combination with the smallest asymptotic variance and the maximum likelihood method. Another example is how to select a more efficient way to synthesize auxiliary information from other studies. In Section 5 of the review paper, two different sets of constraints, in which one involves parameter of interest and the other does not, have been presented and compared in terms of efficiency improvement. Both statistical intuition and theoretical justification are provided, which help readers create a better way to combine aggregate information for improved efficiency in practice. Such insightful discussions are not easily found elsewhere. The paper also nicely derives the conclusion that, similar to parametric-likelihood-based meta-analysis, the calibration methods (e.g., EL and generalized method of moments (GMM)) based on aggregate information have no efficiency loss compared to these methods using all individual data. Such deep insight into these methods greatly promotes their use for information calibration, since it is always challenging to obtain individual-level data. As stated in the title, this review paper mainly focuses on statistical methods using calibration information from similar studies. One crucial assumption of these methods is homogeneity between the cohort with individual data (e.g., target cohort) and these similar studies (e.g., external sources).When the calibration information from the external sources are not comparable with those of the target cohort, such calibration methods may result in severe bias in estimation and misleading conclusions (Chen et al., 2021; Huang et al., 2016). One way to address this issue is to test the comparability by comparing calibration information between the target cohort and external sources before combining such information. Using the setup in Section 4 of the reviewpaper as an example, assume that the auxiliary information from external sources is the mean of Y by subgroups (e.g., subgroups determined by covariates such as age and gender),