Can confidence intervals or uncertainty intervals provide information on replication? Let's say I'm looking at a forest plot from a meta-analysis. I notice that most of the width of the confidence intervals are fairly consistent and the point estimates are all on one side (showing a benefit). Is it possible to use these trends to inform us on what future trials with the same research question will be? (I don't know how else to ask this)
 A: Confidence intervals always rely on the data that was at hand at the time of analysis and are not necessarily applicable to future studies.
If nothing changes in the world and you make the same measurements as the original study made, your mean value is likely to lie within the confidence bounds. However, if the situation changed in ways that are factored into the model, your data will deviate from the original study.
For example: If I count people at the beach every day in August, I get a mean and a CI and any other person counting people in August will likely come to a mean that lies within the confidence interval. That is not to say, however, that someone counting in January will get a mean within these bounds.
But if I counted people on the beach every month and present a model with estimated means for each month, anyone counting in any month may come to a mean within the bounds for this month.
If, however, I collected this data from 2000 to 2018 and someone counts people at the beach in April 2020, the mean will not lie within confidence bounds of the month April as I never counted during a pandemic and this situation is novel.
So, whether or no the confidence interval in a study informs you about the expected outcome of your own study depends on the context in which the original study was undertaken, whether th same conditions apply to your case and whether changed parameters are factored into the original study. Whether this applies to your particular case, I do not know as the question was quite vague.
