Meta-analysis to the rescue - improved weighting methods for the statistical analysis of multi environment crop variety trials

多环境试验（MET）在植物育种和正式作物品种试验中发挥着关键作用。MET通常通过线性混合模型进行分析。目前统计分析的最佳实践是根据试验的精度对其进行加权。在信息加权方面，目前还存在一些未解决的问题。在此，我们主要关注以下五个问题：(1)基于MET线性混合模型的加权最小二乘基因型均值估计可能导致基因型之间的差异估计超出了个体试验中相应差异估计的范围。(2)当变异系数较大时，试验往往被丢弃，这是一种极端的加权形式。对于丢弃试验没有一致的阈值，甚至不清楚丢弃试验是否能提高精度。(3)对于一些试验，特别是对于长期数据，没有可用的方差信息来加权是很常见的。目前还没有确定的方法来处理MET分析中的权重缺失问题。(4)不同试验的权重可能与基因型-环境相互作用模式相关，从而影响效应大小，在这种情况下，加权分析可能导致结果偏倚。(5)不同类型的试验可能产生不一致的结果。例如，农场试验的结果可能与车站试验的结果不同。目前还没有确定的方法来检测这种不一致，以及在不一致的情况下对MET中的信息进行加权组合。本项目建议使用最近的荟萃分析结果来解决这五个问题。荟萃分析的方法主要是在医学统计领域发展起来的，包括许多方法来总结来自同一类型研究问题的多个已发表试验的证据。大多数已建立的荟萃分析方法的关键组成部分是根据精度对试验进行加权，因此有许多已建立的荟萃分析方法可用于解决MET中的这些问题。然而，到目前为止，这个机会还没有被探索，因为在过去的几十年里，一方面荟萃分析和另一方面分析MET的方法在很大程度上是在脱节的道路上发展的。在这里，我们将以自己最近的工作为基础，建立两个研究方向之间的密切联系。最近这项工作的一个关键发现是，元分析可以基于与MET非常相似的模型。这些联系允许采用元分析方法来分析MET，从而开发出上述五个权重相关问题的解决方案。该项目的主要重点将放在品种试验上，但我们也将探索新开发的元分析方法在农业科学和医学的其他领域的应用。

Multi-environment trials (MET) play a key role in plant breeding and official crop variety testing. MET are routinely analysed by linear mixed models. Current best practice in the statistical analysis involves weighting of trials based on their precision. There are currently several unresolved problems related to weighting of information in MET. Here, we focus on the following five problems: (1) Weighted least squares estimates of genotype means based on a linear mixed model for MET may lead to estimates of differences among genotypes which are outside of the range of corresponding difference estimates in the individual trials. (2) Trials are often discarded when having a large coefficient of variation, which constitutes an extreme form of weighting. There is no agreed threshold for discarding trials, and it is not even clear that discarding trials improves precision. (3) It is quite common, especially with long-term data, that for some trials no variance information is available for weighting. There is currently no established method to deal with this missing-weight problem in MET analyses. (4) The weights for different trials may be correlated with the genotype-environment interaction pattern and hence the effect size, in which case a weighted analysis may lead to biased results. (5) Different types of trial may yield inconsistent results. For example, on-farm trials may lead different results than on-station trials. There is no established method for detecting such inconsistencies and for weighted combination of information in MET under inconsistency.This project proposes to use recent results from meta-analysis to approach these five problems. Methods of meta-analysis were mainly developed in the domain of medical statistics and comprise a host of methods to summarize the evidence from multiple published trials on the same type of research question. A key component of most established methods of meta-analysis is weighting of trials according to precision and hence there are many established methods of meta-analysis that can be used to solve these problems in MET. This opportunity has so far not been explored, however, because meta-analysis on the one hand and methods for analysis of MET on the other hand have evolved on largely disconnected paths over the past decades. Here, we will build on recent own work establishing the close connection between the two lines of research. A key finding of that recent work is that meta-analysis can be based on models that are very similar to models used for MET. These connections allow adapting methods of meta-analysis to the analysis of MET and thus developing solutions to the five weighting-related problems named above. The main focus of the project will be on variety trials, but we will also explore applications of newly developed methodology for meta-analysis in other areas of the agricultural sciences as well as in medicine.