 and today I'm going to be presenting the S-Mean SDR package. This is an R package that can be used to estimate the mean and standard deviation of the outcome from studies that report the median in meta-analysis. First, I want to begin with some context in where this package can be used. We consider the setting of an aggregate data meta-analysis of a continuous outcome. In this setting, it's fairly common that some of the primary studies report the sample mean of the outcome, but other primary studies may report the sample median. This is a challenge because in standard meta-analytic methods, they require that each study contribute an estimate of the same outcome measure. There's been a number of solutions that have been proposed in the statistical literature and today I'm going to be focusing just on one of these solutions, which essentially goes as follows. You first impute the sample means and there's estimates of their standard errors from all these studies that report medians. Once doing so, you then apply standard meta-analytic methods based on these sample means or these imputed sample means from all the primary studies. There's been a number of methods that have been developed in the literature over the last, say, 20 years and this is particularly growing over the last five years on these mean and center deviation estimators and almost all of these approaches consider that a primary study will report one of the three following sets of summary statistics. So these sets of summary statistics are based on the median and either the minimum and maximum values in the sample or the first and third quartiles in the sample or both as well as the sample size. So these are known by scenarios one, two and three. Apart from considerations on estimating the mean and the standard deviation, another consideration is how do you then go to get an estimate of the standard error of these imputed means? The most common approach used in the literature is an approach which we refer to as the naive approach which uses the imputed standard deviation divided by the square root of the sample size. In some quite recent work I've explored along with some colleagues some simple approaches based on parametric bootstrap to estimate the standard error of these imputed means. And so the estimate SD package incorporates both of these types of standard error estimators as well as a few different mean and standard deviation estimators developed in the literature. In particular, the package considers these two methods. The first method we refer to as quantile matching estimation or QE for short. And this approach can be described as follows. We fit several different candidate parametric distributions for the outcome. So for instance, we consider the normal distribution of the log normal distribution or other sorts of skew distributions because these skew distributions may be reasonable when studies report the median. For each of these distributions we can estimate the parameters of these distributions by minimizing the distance between the sample quantiles and the quantiles of the distribution. We then select the distribution with the best fit. Then we use the mean and standard deviation of that distribution as our sample mean and standard deviation estimates. A couple other approaches are based on performing a type of box-cox transformation. So essentially they consider that the sample, the outcome is normally distributed after you apply a suitable box-cox transformation. The idea is that this can help allow for skew distributions. So the BC method is one that I've explored with some colleagues which essentially estimates this lambda, which is a parameter that governs the box-cox transformation by enforcing a type of symmetry in the transformed quantiles. There was another approach based on the same idea which was referred to as the MLN method and this estimates lambda by a maximum length approach. This was developed very shortly after the BC method. So to apply these types of methods in the estimate SD package we can use the main functions which are given here. The naming is the QE dot mean dot SD function applies the QE method. And then similarly we can apply the BC and MLN methods with the BC mean SD function and the MLN mean SD function. To compute estimates of the standard error based on bootstrap, we can then use the get underscore standard deviation or SE. So we'll see how these look in an example in just a couple slides. A very straightforward example I'm gonna consider is based on a real meta-analysis that was performed a few years ago. And this meta-analysis aimed to compare the age between survivors and non-survivors of COVID-19. And the primary studies in this meta-analysis often reported the median as well as the first and third quartiles as well as some other studies that reported the mean and standard deviation of age in the survivors and non-survivor groups. The example data I'm gonna consider is from the non-survivor group in one of the primary studies. And the summary data that's reported is given here in the slides where we have a median of 71 years and first and third quartiles of 64 years and 80 years respectively as well as a sample size of 84. The code for applying the QE method is given here where we can apply the QE mean SD function. And we essentially can input the Q1 median and Q3 values as follows as well as the sample size. The object that's returned has essentially contains the fitted distribution and we can print the mean and standard deviation estimates obtained from this type of approach. So here we estimate a mean of around 72.4 years and a standard deviation of approximately 12. From this fitted object, we can compute an estimate of, it's a standard error of the mean using the getSE function. And it obtains an estimate of around, a standard error of around 1.5. Then from these values, you can then perform a whatever type of meta analytic procedure, typically based on inverse variance weighting from these values. A very similar example we consider is instead of using the QE method, we can use the MLN method. The code is essentially identical replacing QE with MLN throughout. So we can fit this first line of code here, applies the MLN method to get estimates of a mean now of 72 years and a standard deviation of around 11.6. And then we can apply the parametric bootstrap standard error estimator in a similar way to get a standard error now of around 1.4. So in conclusion, the S mean SD package, it implements a few different methods to estimate the mean of an outcome and an estimate of its standard error from the studies that report the median as well as other sorts of quantiles. This can be applied to each primary study in your meta analysis individually. And the meta median package, which I have a presentation for in this conference, can apply this sort of method to all the different primary studies in your meta analysis to in one fell swoop, essentially, and also implements a number of other type of approaches that have been considered in the literature. So that may be worth checking out if you're interested. And lastly, to access the package, the released version is available on CRAN and the development version is available on GitHub. Thank you.