Letter to the Editor about the article “C-reactive protein and fracture risk: an updated systematic review and meta-analysis of cohort studies through the use of both frequentist and Bayesian approaches”

Abstract

We read with interest the recent article by Mun et al. [1] who conducted an updated systematic review and meta-analysis of cohort studies to explore the association between highsensitivity C-reactive protein (hs-CRP) and osteoporotic fracture risk. Findings of this study are important as they suggested a significant association between a high level of hs-CRP increased risk of osteoporotic fracture. However, we identified issues related to the Bayesian methods and model selection that require attention to appropriately interpret the findings of the study. First, the authors applied both Bayesian and frequentist approaches to generate and compare effect estimates. This is unusual considering both methods to generate same-effect estimates as they are fundamentally different in their nature. Compared to the frequentist approach, Bayesian methods considered that the data and model parameters are random quantities, and the likelihood function is considered as defining the probability of the data given values of the model parameters [2]. Then, prior distributions may be specified for model parameters since they are considered as unknown random quantities based on evidence external to the study. Further, prior probability density functions for all model parameters are combined with the likelihood function to obtain the joint posterior probability density function. Second, design and reporting of the Bayesian method was not well documented in this report as suggested in the literature [3]. No justification was provided for conducting Bayesian meta-analysis, selection and type of the prior distribution, and model diagnostics (such as model convergence etc.). Transparency in methodological design and analytics for Bayesian methods is essential to checking the robustness of the findings. Therefore, the lack of any mention of the use of such instructions, even though the study follows the core principles, raises the question of the credibility of their findings. Third, it is recommended to present and elaborate analysis report including relevant tables, figures, assumption checks, and background information related to Bayesian methods [4]. However, the authors did not present their findings in such manner. It is also important to submit their analysis codes related to Bayesian methods (i.e. prior sensitivity, analysis, and diagnostics) so others can reproduce the same results with the same data. Fourth, the authors selected the random-effect model based on the significance of Cochran’s Q test (p < 0.01). However, it is not recommended to decide on the basis of a significant Q that we should choose a random-effect model; rather, the authors should have considered the differences in the way studies were conducted and study characteristics [5]. Fifth, the authors did not present meta-analysis results of the random-effect model with the prediction interval which is a common practice to allow more informative inferences in meta-analyses [6, 7]. The prediction interval reflects the expected range of true effects in similar future studies over different settings. We believe that the authors will address the points raised, and the overall purpose of the presented points will only to improve the conduct and reporting of Bayesian methods in meta-analysis and serve to benefit the researchers at large.