Jackson Dan, White Ian R, Price Malcolm, Copas John, Riley Richard D
1 MRC Biostatistics Unit, Cambridge, UK.
2 Department of Public Health, Epidemiology & Biostatistics, University of Birmingham, Birmingham, UK.
Stat Methods Med Res. 2017 Dec;26(6):2853-2868. doi: 10.1177/0962280215611702. Epub 2015 Nov 6.
Multivariate and network meta-analysis have the potential for the estimated mean of one effect to borrow strength from the data on other effects of interest. The extent of this borrowing of strength is usually assessed informally. We present new mathematical definitions of 'borrowing of strength'. Our main proposal is based on a decomposition of the score statistic, which we show can be interpreted as comparing the precision of estimates from the multivariate and univariate models. Our definition of borrowing of strength therefore emulates the usual informal assessment. We also derive a method for calculating study weights, which we embed into the same framework as our borrowing of strength statistics, so that percentage study weights can accompany the results from multivariate and network meta-analyses as they do in conventional univariate meta-analyses. Our proposals are illustrated using three meta-analyses involving correlated effects for multiple outcomes, multiple risk factor associations and multiple treatments (network meta-analysis).
多变量和网状荟萃分析有可能通过感兴趣的其他效应的数据来增强对某一效应估计均值的说服力。这种增强说服力的程度通常是通过非正式评估来衡量的。我们提出了“增强说服力”的新数学定义。我们的主要提议基于得分统计量的分解，我们证明这可以解释为比较多变量模型和单变量模型估计的精度。因此，我们对增强说服力的定义模仿了通常的非正式评估。我们还推导了一种计算研究权重的方法，并将其嵌入到与我们的增强说服力统计量相同的框架中，这样百分比研究权重就可以像在传统单变量荟萃分析中那样，伴随多变量和网状荟萃分析的结果一同呈现。我们通过三项荟萃分析来说明我们的提议，这三项荟萃分析涉及多个结局的相关效应、多个风险因素关联以及多种治疗方法（网状荟萃分析）。
