Adding median and 95% confidence interval that are reported for multiple datasets

Reply Wed 18 Nov, 2020 12:04 pm
I have three datasets say for Stage 1, Stage 2, and Stage 3 with median (95% CI) reported for all these stages.

I want to report the All stage value that is the sum of all the 3 stages.

All_Stage values = Stage 1 + Stage 2 + Stage 3 All_stage median (95% CI) = Stage 1 median (95% CI) + Stage 2 median (95% CI) + Stage 3 median (95% CI)

It is unclear if we can just add up the lower bound of CIs for Stages 1-3, or propagate the error. I don't have the sample size or mean values.

How can I estimate All_stage median (95% CI)
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Reply Wed 18 Nov, 2020 12:13 pm
Do you believe the stage values are correlated or independent? If they are correlated (say if the stage 1 value is low, the stage 2 and 3 values will be low also) then you need to have some idea of the correlation. If you think they are not correlated, then the central limit theorem will drive a tighter confidence interval on the sum of three values then the sum of the values.
Reply Wed 18 Nov, 2020 12:49 pm
So the estimates are independent in that they are from different base processes. The estimates are however determined using the same set of models, meaning if the value is "low" for one, they are low for all.

Sorry this isn't that straight forward a question because the median and CI come from different scientific studies, but sample size is unclear.
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