I have a dataset of median survival time and their confidence intervals. One way of pooling these medians using meta-analysis requires an estimate of the standard error of the median / variance of the median of the raw data. I am assuming the unseen raw data are skewed since they are survival data. However, if I assume the sampling distribution of medians is normal (for a large sample size), is it reasonable to estimate the standard error of the median from the confidence intervals e.g. (Upperbound CI - lowerbound CI) / (2*1.96) ?
One reason I am hesitant is that the confidence intervals for the medians are asymmetric around the median value and so I'm not sure whether this would make sense. Any guidance would be very much appreciated.