# Network meta analysis without standard deviations

I am trying to compute Cohen's in some studies that I gathered in a Systematic Literature Review.

Unfortunately, almost none of them report the standard deviation (nor df/t, or something for back-computing Cohen's d). Thus, I cannot neither compute Cohen's nor calculate the standard error of each study.

However, the studies commonly report the means and the sample sizes.

I was thinking about using the response ratio (mean1/mean2) as the effect size, and weighting each study according to its sample size (instead of its standard error as usual).

Question 1: do you know any reference where they have done exactly that, and where they acknowledge to have obtained similar results to those with standard error weighting?

Question 2: do you know whether it is posible doing that with network meta analysis in R? I have studies comparing A vs B, and studies comparing A vs C.

• Sample size can be a reliable weighting factor only for categorical variables, but you might proceed with using point effect estimates and sample sizes nonetheless, with a hypothesis-generating scope. You can surely use them as you suggest in R with netmeta or mvmeta packages. – Joe_74 Sep 27 '18 at 10:53

In principle weighting by the sample size makes sense for a difference between groups (or for Cohen's D), if you assume the standard deviation to be the same across studies. This is because the SD of the sampling distribution of a difference between two means in both groups is $$\sqrt{\text{SD}_1^2/n_1+\text{SD}_2^2/n_2}$$ and if $$n_1=n_2=N/2$$ and $$\text{SD}_1=\text{SD}_2=\text{SD}$$, then that simplifies $$\text{SD} \sqrt{4/N}$$. So, to get inverse variance weights, you would want something close to $$N/(4\times\text{SD}^2)$$. If the SD is the same in all trials and the trials have 1:1 allocation, then weighting by N gets you very close (there's of course issues like the SD being estimated in practice etc.) to inverse variance weights.