I have approximately 20 median values (overall survival in months) which were obtained from different populations groups (but they shared similar characteristics). Each population group has a unique size (e.g. 52 patients) and a corresponding median overall survival. I do not have individual patient level data.
I would like to obtain a value which best represents a measure of central tendency for patients with this characteristics across all populations. I wanted to know if doing a weighted average of medians would be my best option (each median is weighted by its corresponding number of patients). Additionally, I am wondering if it is possible to calculate a 95% CI and what method would best be used?