IRR comparison

[jykim]

Hello,

I ran nbreg for the same outcome variable with two different primary independent variables and same covariates.

 nbreg conditions var1 covar1 covar2 covar3 covar4, exposure(pop) irr

 nbreg conditions  var2  covar1 covar2 covar3 covar4, exposure(pop) irr

Is there any way that I can compare these two different primary independent variables?
Both of VAR1 and VAR2 were statistically significant. But IRR was larger for var1 than for var2.

In case results were shown as below, can I say that var1 is a better predictor for the outcome variable?

	IRR	Std.err	Z	P	95%	CI
var1	1.16	0.017	9.7	0.000	1.21	1.19
var1	1.10	0.015	6.9	0.000	1.07	1.12

Thank you.

[Richard Williams]

Why don’t you include both variables in the same equation?

[jykim]

Because var1 is the new determinant to predict the condition and var2 is the old determinant and var2 was replaced by var1, we would like to show the effect of var1 and 2 separately.
Then we would like to show that var1 is better predictor.

If we include both var1 and var2, there will be endogeneity problem as they are similar but different.

[Joseph Coveney]

I don't quite follow. Usually, the reason you can't include both in the same equation is because var1 and var2 are evaluated in separate, independent samples. That's not the case; rather, an endogeneity problem prevents it?

When you say endogeneity problem, is it that you and your colleagues tried out several candidate replacement determinants until one seemed better than var2, and now you want to show that it is better?

[Richard Williams]

I don't follow the endogeneity argument either. My argument might be that var1 and var2 are different operationalizations of the same concept. Perhaps because var1 has less random error than var2, its effects are less attenuated and hence its estimated effects are larger.

[jykim]

Thank you Joseph and Richard for your comments.

Var1 and Var2 are two different existing social determinants of health. Var 1 index seems to be more comprehensive and complex than var 2 using more factors.
As Richard said, var 1 and var2 are different operationalizations of the same concept. and I like Richard's argument. Thank you so much.