[Clyde Schechter]

Then the coefficient of that prevalence variable (which you say is given as a percentage) is the expected difference in the change from t-1 to t (of whatever that dependent variable is the change of) associated with a 1 percentage point difference in the disease prevalence.

[Michael Schuster]

Clyde Schechter Thank you for your answer! Just to make sure I understood you correctly. So then the coefficient (lets say beta) is to be understood in a way that a change in disease prevalence by 1 percentage point results in a change by beta in my dependent variable (delta from t-1 to t)?

[Clyde Schechter]

Almost. Kill the "results in" and "change in"--that's causal language, and unless you are dealing with an experiment (which I doubt, because how do you experimentally manipulate the prevalence of a disease) you cannot make any causal claims here. The correct phrases are "is associated with" and "difference in," respectively.

[Michael Schuster]

Clyde Schechter Thank you very much! I'm sorry if I ask you two more questions now, but the answers would help me a lot.

What is the interpretation if my independent variable stays the same but,
1. if my dependent variable is not a delta from t-1 to t, but a growth rate, so my delta just divided by the value in t?
2. if my dependent variable is another variable expressed as a percentage?

[Clyde Schechter]

1. It's a little difficult to phrase this in general terms. So I'll take a specific example and you can adapt it to your actual circumstances. Suppose your dependent variable is the rate of growth of a child, measured in cm/year. Then beta is the expected difference in the child's rate of growth (denominated in cm/year) associated with a 1 percentage point difference in the independent variable.

2. Beta is the expected number of percentage points difference in whatever the dependent variable is a percentage of associated with a 1 percentage point difference in the independent variable.