 And in this presentation, I'm going to be giving an overview of the meta-median package. This is an R package that can be used to meta-analyze studies that report the median of the outcome. I'm gonna begin with going over the context of where this package can be used. So I'm gonna consider the setting where we have an aggregate data meta-analysis that has a continuous outcome, say the age. And in this type of setting, I'm gonna consider that sum, or perhaps even all of the primary studies, report the sample median of the outcome. One case where this very commonly occurs is when data are skewed, so authors may choose to report the median. But this happens in all sorts of settings. There's a few statistical challenges that one faces when meta-analyzing this type of data. Standard statistical methods for performing meta-analysis of continuous data often assume that the primary studies report the sample mean and the standard deviation of the outcome. And where median's become a bit problematic is that studies rarely report the standard error of the median. And these sort of, these standard errors are needed to compute the weights in an inverse variance weighted meta-analysis. Another challenge is that some studies may report the mean and other studies may report the median. And now we have the case where different studies are reporting different outcome measures and we need a single outcome measure for standard methods. So these challenges have resulted in lots of statistical, lots of developments in the statistical literature over the last few decades. One group of methods we're gonna refer to as mean-based methods. And we're later gonna talk about median-based methods, but for these mean-based methods, the approach can be described as follows. We first impute the sample means and estimates of their standard errors from all studies that report the median. Then we're gonna apply standard methods based on either the sample means or the imputed sample means. And so this is going to be estimating a pooled mean or perhaps a pooled difference of means for two group studies. For performing this first step of imputing the sample means and their standard errors, there's been a huge amount of estimators that have been proposed in recent years and particularly over the last five years or so has been well over, I think, a dozen papers. And they typically consider that studies report the median of the outcome and possibly that either the minimum and maximum values or the first and third quartiles of the outcome or perhaps both. So these are denoted by scenarios S1, S2 and S3. In all three of these scenarios, they're assuming we have the sample size as well, which we're denoting by N. So the advantage of these mean-based methods are that they're applicable in very general meta-analytic settings. There has been proposed a few median-based methods. These are a bit more case-specific, but in any case, we can describe them as follows. All of these have been proposed fairly recently. So the median of the different, the median of median's method or for two group data, it's gonna be the median of the difference of median's method. This is an approach that completely avoids having to estimate the standard error of the medians. There's been a few approaches that try to estimate the standard error of the medians and then apply standard meta-analytic inverse variance weighted methods. And so this quantile matching estimation, which we're denoting by QE, this approach uses a parametric estimator. There was a paper that followed shortly after, which uses a non-parametric estimator of the standard errors, but the idea is quite similar. The meta-median package implements both these mean-based methods and these median-based methods. The mean-based methods are implemented in the meta-mean function. The median-based methods are implemented in the meta-median function. There's a few example data sets to play around with when getting familiar with the methods. These three data sets are from a recently performed meta-analysis that aim to identify risk factors for a severe course of COVID-19. They contain data on different variables and they're comparing COVID-19 survivors and non-survivors. So the dat.age data set has data on the age of these COVID-19 patients, which I'm gonna be focusing on this data set throughout this presentation. And one other thing to note about the structure of the package is that a number of these approaches eventually use inverse variance type weighting to perform meta-analysis. And so internally in our package, we're gonna apply the metaphor package to perform the pooling step. And note that the object that's returned by many of the functions in the meta-median package, they return the object that's returned by the metaphor package. So this enables data analysts to use a lot of the functionalities that are available in the metaphor package that many may be familiar with, such as generating force plots and funnel plots and testing small study effects and all these types of subsequent analyses that users may wanna perform who are familiar with the metaphor package. Okay, so the main functions in the meta-median package require users to supply a data set. And so in this data set, the rows are gonna correspond to the primary studies and the columns are gonna correspond to the summary statistics. So for instance, in the example data set, I show the first three rows for the first seven columns. So they contain the optionally, they contain the author name of the primary study and the different columns here contain the sample size, the median and all sorts of other summary statistics for the first group. This is the group of non-survivors and their additional columns for the group of survivors which is noted by G2 for group two. The meta-mean function has a few main arguments. So it has the input data set, of course. And then the next argument, which is noted by your mean method, this is the method that's gonna be used to impute the means from medians. And the next argument, SE method, this is gonna be the method for estimating the standard error of these imputed means. There's a couple different options. The naive option, this uses the imputed standard deviation divided by the square root of the sample size. This is an approach that has traditionally been used in the literature very recently. I've explored with a few colleagues a parametric bootstrap of a parametric bootstrap approach. The idea being that this may help better incorporate the variability of these imputed means. We'll explore that in a very recent paper. Now for the outcome measure that's gonna be used in the meta-analysis, this depends on how the input data set is structured. So when the input data set consists of just one group studies, it's gonna meta-analyze the mean of the outcome. When the input data set consists of two group studies, such as in our example, it's gonna meta-analyze the difference of means across the two groups. So at the bottom of the slide here, you have an example where we're implying the meta-mean function, supplying the input data set, specifying one of these mean-based methods. And then I'm using the bootstrap standard error estimator for the within-study standard errors. The output is perhaps very familiar for those who use the metaphor package. This is the object that's returned by the RMA function in the metaphor package. And this is indicating a pooled estimate of 12.8. So this corresponds to the difference of means between survivors and non-survivors. So this is indicating that the non-survivors are 12.8. The average age is 12.8 years larger in the non-survivor group. The meta-mean function is, the user interface is quite similar. We have an input data set. We have the different median-based methods are specified by the median method argument. And once again, the structure of the input data set is gonna determine what type of outcome measure that's gonna be used in the meta-analysis. So at the bottom of the slide here, we have an example of using the meta-median function where I'm supplying the same input data set, the age data set, and I'm applying one of the QE median-based method. And here the output is, the structure of the output is the same. And here we're getting a pooled estimate of 13.2 years. So this is the difference of medians now instead of the difference of means. So this is saying that the median age is 13.2 years larger in the non-survivor group compared to the survivor group. All right, so in summary, the meta-median package allows data analysts to apply several of these mean-based methods as well as these median-based methods to perform meta-analysis in this setting. And our hope is that this package will help facilitate data analysts applying several of these different methods and perhaps evaluating how their conclusions may change depending on the choice of method. And then one reminder is that this is integrated in the metaphor workflow, so it enables you to use these functions you may be familiar with in the metaphor package such as generating force plots very easily after using the meta-median package to obtain a fitted model here. To access the package, the released version is available on CRAN, the development version is available on GitHub, and we just released today a pre-print describing the meta-median package it's available on Archive here on the bottom of the slide here. So thank you very much.