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

多环境试验（MET）在植物育种和官方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。目前统计分析中的最佳做法是根据试验的精确度对其进行加权。目前有几个尚未解决的问题，有关加权信息在MET。（1）基于MET线性混合模型的基因型均值的加权最小二乘估计可能导致基因型间差异的估计超出个体试验中相应差异估计的范围。(2)当变异系数较大时，试验通常被丢弃，这构成了加权的极端形式。对于丢弃试验没有商定的阈值，甚至不清楚丢弃试验是否会提高精度。(3)这是很常见的，特别是长期数据，对于一些试验没有方差信息可用于加权。目前还没有既定的方法来处理MET分析中的这种失重问题。(4)不同试验的权重可能与基因型-环境相互作用模式相关，因此与效应大小相关，在这种情况下，加权分析可能导致偏倚结果。(5)不同类型的试验可能会产生不一致的结果。例如，农场试验可能导致与站上试验不同的结果。目前还没有确定的方法来检测这种不一致性和加权组合的信息在MET下unconsistent.This项目建议使用最近的结果从荟萃分析接近这五个问题。荟萃分析的方法主要是在医学统计学领域发展起来的，包括一系列方法来总结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一个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，一方面是荟萃分析，另一方面是MET分析方法在很大程度上是在不相关的道路上发展的。在这里，我们将建立在最近自己的工作建立两条研究线之间的密切联系。最近这项工作的一个关键发现是，荟萃分析可以基于与MET所用模型非常相似的模型。这些连接允许调整方法的荟萃分析的MET分析，从而开发解决方案，上述五个加权相关的问题。该项目的主要重点将是品种试验，但我们也将探索新开发的方法在农业科学和医学的其他领域的荟萃分析的应用。

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.