Statistical Methods of Meta-Analysis for Count Data with Rare Events

在计数数据的Meta分析中，典型的影响指标是风险比、优势比和风险差异。计数数据影响指标的Meta分析如下。计算每个成分研究的效果度量(部分在对数尺度上)，并伴随着相关方差的估计。然后假设近似正态分布成立，然后应用荟萃分析工具，就好像这些工具实际上是从正态分布产生的。如果成分研究的样本量和事件量都很大，这种方法可能是合理的。然而，在罕见事件的情况下，这显然是有缺陷的，在根本没有事件的极端情况下，其中一些影响度量变得不确定，所有的方差估计都不确定或没有意义。引入平滑常量将有助于避免未定义的估计，但会引入偏差。因此，该项目的主要主题是使用适合于数据的计数性质的方法，在这种情况下，包括零事件在内的罕见事件不仅没有问题，而且是事件规模的组成部分。所考虑的模型类别是混合泊松模型(针对风险比和风险差异)和混合Logistic回归(针对优势比)。这里，研究效应被视为正态分布的随机效应，它与适当的计数分布、泊松(针对风险比率和风险差异)和二项(针对优势比)混合在一起。对于风险比率和风险差异，考虑了一种特别有趣的方法。利用以事件边缘为条件的试验组中计数的条件分布是二项分布的事实，仅包含感兴趣的参数作为基线(控制组)参数被剔除。因此，推理可以只关注感兴趣的参数。在这些模型中，作为感兴趣的主要参数的异质性方差被提供为随机效应分布的方差。这种方法将与传统的方法进行比较，如DerSimoun-Laird，REML等。作为传统卡方异质性检验的一种替代方法，研究了一种通过将随机效应分布的方差设置为零来检验同质性零假设的似然比检验。混合泊松和Logistic回归方法将进一步推广，以允许在研究水平上纳入协变量。此外，将在混合效应模型中探讨在比较的一组中遗漏数值的问题。详细的模拟工作将调查和比较各种方法，最后将提供包含所建议方法的R包。

Typical effect measures in meta-analysis of count data are the risk ratio, the odds ratio and risk difference. Meta-analysis of effect measures of count data proceeds as follows. The effect measure is calculated for each component study (partly on the log-scale) accompanied by an estimate of the associated variance. It is then assumed that an approximate normality holds and the tools of meta-analysis are then applied as if these where actually arising from a normal distribution. This approach may be justifiable if both sizes, sample and event sizes, of the component studies are large. However, this becomes evidently flawed in the case of rare events, in the extreme case of no events at all, where some effect measures become undefined and all variance estimates undefined or meaningless. Introduction of smoothing constants will help to avoid undefined estimates but introduce bias instead. Hence, the main theme of the project is to use approaches that are appropriate for the count character of the data and where rare events including zero events are causing not only no problem but are an integral part of the event scale. The model classes considered are the mixed Poisson (for the risk ratio and risk difference) and the mixed logistic regression (for the odds ratio). Here, the study effect is treated as a normally distributed random effect, which is mixed with the appropriate count distribution, the Poisson (for the risk ratio and risk difference) and binomial (for the odds ratio). For the risk ratio and risk difference a particular interesting approach is considered. Using the fact that the conditional distribution of the counts in the experimental group, conditional on the margin of the events, is a binomial distribution, only the parameter of interest are contained as the baseline (control group) parameter get eliminated. Hence, inference can focus on the parameter of interest alone. In these models, the heterogeneity variance, which is the major parameter of interest, is provided as variance of the random effects distribution. This approach will be compared with conventional approaches such as DerSimonian-Laird, REML among others. As an alternative to the conventional chi-square heterogeneity test, a likelihood ratio test is investigated which tests the null hypothesis of homogeneity by setting the variance of the random effects distribution to zero. The mixed Poisson and logistic regression approach will be further generalized to allow inclusion of covariates on study level. In addition, the problem of missing values in one of the groups under comparison will be approached in the mixed effects modelling. Detailed simulation work will investigate and compare the various approaches and, finally, R-packages will be provided which contain the proposed methodology.