Calculating confidence intervals

In an instrumental variable study, I have the point estimate of the outcome (a health outcome) and the corresponding confidence interval. I also have the mean of the instrument and the range (number of health worker visits in a year in a given population). I have to calculate how the confidence interval would change given a change in the instrument. That is, how the health outcome would change if the number of visits by the health worker changed. Can someone please guide me on how I can calculate this?

 

Scott,

Please forgive me, but I do not think it is possible to calculate. Sure you can show an equation. Yet it would not be true in reality. (Perhaps a mathematician will help you here regardless). I can not. Yet I can explain to you what I mean philosophically.

You may have 1,000 "visits". Yet if they are not good nurses, or doctor's. Or perhaps they are lazy or, foggy headed that day. Then the health outcome will be negative.

You may have only 1 "visit". Yet if they are good nurses, or doctor's, then the health outcome will be positive.

It is a philosophical flaw in humanities understanding, that we apply numbers to "living" or conscious things. Numbers, expressions, and equations can only be applied to non-conscious things. There are many examples to this. Especially within the concept of probability.

I know this is not the answer you were looking for. Yet I hope you enjoyed it.