Validity of population adjustment methods for disconnected networks of evidence

网络荟萃分析（NMA）是一种方法，用于汇总来自随机对照试验（RCT）的已发表的汇总治疗效果，以获得多种治疗之间相对治疗效果的估计值。NMA通常用于决定哪些治疗是有效的或具有成本效益的，但要求RCT证据形成一个连接的比较网络（RCT中的比较图是一个连接的网络）。协变量如年龄、生物标志物状态或疾病严重程度可分为（i）与相对治疗效应相互作用的协变量（效应修饰因子）和（ii）预测结果但不与治疗效应相互作用的协变量（预后因子）。NMA假设，如果存在效应调节剂，则其分布在所有纳入的试验中相同或相似。然而，这可能不成立。最近开发了一种多水平网络元回归（ML-NMR）方法，只要可以从一个或多个RCT中获得个体患者数据，就可以放松这一假设。ML-NMR在有个体患者数据的研究中拟合个体水平治疗效应的模型，然后对于具有聚集水平数据的每项研究，将个体水平似然性整合到每项研究中效应修饰因子的联合分布上，以获得聚集水平似然性。这是实现使用copulae近似的联合分布的效果修饰符和准蒙特卡罗积分，以获得聚合级的可能性。然后，通过对效应修饰因子的相关联合分布进行积分，可以在任何感兴趣的人群（例如，其中一项纳入研究所代表的人群或英国人群）中获得估计值。到目前为止，该方法仅适用于证据网络连接的情况（RCT证据路径连接网络中的任何两种治疗）。然而，越来越常见的是，卫生保健政策制定者面临着不连贯的证据网络，其中可能包括单臂（非随机）研究。具有断开的证据网络的群体调整要求不仅考虑效应修正协变量，而且考虑所有预后因素，因为建模的是绝对结果而不是相对效应。该项目的目的是将ML-NMR方法扩展到一系列可能性的断开证据网络，包括生存结果的可能性，并探索在断开证据网络的背景下评估ML-NMR方法有效性的方法。这将包括：（i）制定ML-NMR模型的扩展，用于对绝对结果以及相对效应进行建模，而不会将偏倚引入估计的相对治疗效应中（ii）在模拟研究中评估此类方法的性能和性质（iii）开发用于评估假设有效性的样本内方法，例如交叉验证，以估计模型解释的变异比例，从而使任何无法解释的变异主要是由于遗漏的预后变量或未考虑的效应修饰因子;以及（iv）开发样本外方法，旨在通过识别给定人群中的外部研究并将ML-NMR在该外部人群中预测的绝对结果与观察到的结果进行比较来估计预测误差。

Network meta-analysis (NMA) is a method to pool published summary treatment effects from randomised controlled trials (RCTs) to obtain estimates of relative treatment effects between multiple treatments. NMA is routinely used to inform decisions as to which treatments are effective or cost-effective, but requires that the RCT evidence forms a connected network of comparisons (the map of comparisons made in RCTs is a connected network). Covariates such as age, biomarker status, or disease severity can be classified into (i) those that interact with relative treatment effects (Effect Modifiers), and (ii) those that predict outcomes but don't interact with treatment effects (Prognostic Factors). NMA assumes that, if effect modifiers are present, their distribution is the same, or similar, in all the included trials. However, this may not hold. Recently a multi-level network meta-regression (ML-NMR) method has been developed that relaxes this assumption, as long as individual patient data is available from one or more RCTs. ML-NMR fits a model for individual-level treatment effects in studies where there is individual patient data, and then for each of the studies with aggregate-level data integrates the individual-level likelihood over the joint distribution of effect modifiers in each study to obtain an aggregate-level likelihood. This is achieved using copulae to approximate the joint distribution of effect modifiers and quasi-Monte Carlo integration to obtain the aggregate-level likelihood. Estimates can then be obtained in any population of interest (for example, the population represented by one of the included studies, or the UK population) by integrating over the relevant joint distribution of effect modifiers. To date, the method has only been developed for the case where networks of evidence are connected (there is a path of RCT evidence joining any two treatments in the network). However, it is becoming more common that health care policy makers are confronted with disconnected networks of evidence which may include single-arm (non-randomised) studies. Population adjustment with disconnected networks of evidence requires that not only the effect modifying covariates are accounted for, but also all prognostic factors since absolute outcomes rather than relative effects are modelled. The aim of this project is to extend the ML-NMR method for disconnected networks of evidence for a range of likelihoods, including likelihoods for survival outcomes, and to explore methods to assess the validity of the ML-NMR method in the context of disconnected networks of evidence. This will include: (i) formulating extensions to the ML-NMR model for modelling absolute outcomes alongside relative effects, without introducing bias into the estimated relative treatment effects (ii) assessing the performance and properties of such approaches in a simulation study (iii) developing in-sample methods for assessing the validity of assumptions, such as cross-validation to estimate the proportion of variation explained by the model so that any unexplained variation will be largely due to missing prognostic variables or effect modifiers that have not been accounted for; and (iv) developing out-of-sample methods that aim to estimate prediction error by identifying external studies in a given population and comparing the absolute outcomes predicted by ML-NMR in this external population with the observed outcomes.