How to convert median survival time confidence interval to standard deviation for network meta-analysis? I am conducting a network metanalysis using mean difference and standart deviation but I have issues converting some of the data presented in the articles selected to mean and standart deviation.
The outcome is a time to an event however the delay and nature of the event makes it that all event are observed and there is ususally no censor. However some study used survival type of analysis.
Obviously if all event are observed median survival time is equal to the median but how can i convert the confidence interval of this median to something usable for the conversion to a standart deviation (range, sd itself, IQR), this is even more tricky considering that most papers to not precise which algorithm or even which software was used to calculate these confidance interval.
In a similar fashion I sometime have HR with it's confidence interval and median survival time.
I would like to know if someone encountered similar issue and found a way around it.

First, to quote this review on network meta-analysis (NMA), a way to combine information from multiple studies that involved different sets of treatments for a condition:

Since NMA is statistically complex, regardless of the model used, it is advised that one work with a trained statistician when conducting NMA.

Please do that unless you are just trying to learn about the methods at this point.
If you are using results from survival analysis, what you presumably want is standard-error (SE) estimates for treatment effects rather than standard deviation estimates. For example, functions in the netmeta package sometimes ask for standard deviations and numbers of cases, but that seems to be limited to studies with continuous outcomes. For the ultimate analysis with the netmeta() function, treatment effects and their standard errors are what's expected.
What would be best would be to express treatment effects in scales that have reasonably symmetric confidence intervals. For example, if you have hazard ratios and their confidence intervals, take natural logarithms to put those values on the log-hazard scale (which is what the survival software originally produced, anyway). With 95% confidence intervals for survival models based on an assumption of asymptotic normality in terms of the log-hazard estimates, 95% confidence intervals will be $\pm$ 1.96 time the SE around the point estimate in the log-hazard scale.
This is much trickier if you only have median survival times to work with. See this thread, for example. This thread suggests some approaches for estimating standard errors for individual median survival times, which you could use to estimate standard errors for differences between medians in a study. Note that treatment effects evaluated by differences in median survival need not be the same as those evaluated by differences in log-hazards in Cox models.
