# Calculating OR and IRR for a zero-inflated negative binomial model from estimates

I used the PSCL package to run a zero-inflated negative binomial model on some count data I have.

This package gives the following output:

for the zero part of the model:

Estimate    Std_Error   Z   Pr(>|z|)
(Intercept) 0.1198  0.8619  0.139   0.8895
Sex[notna]  0.6769  0.3358  2.016   0.0438
MedUse[notna]   -0.5436 0.4384  -1.2401 0.2149
sqrt(DisDurMonths[notna])   -0.2033 0.0333  -6.1059 0
Group[notna]    0.1198  0.2941  0.4073  0.6838
BMI[notna]  -0.0058 0.0118  -0.4948 0.6208
Marker_vh_1_1108138_A   -0.1676 0.1659  -1.0105 0.3123


for the count part of the model:

Estimate    Std_Error   z   value   Pr(>|z|)
(Intercept) 0.0449  0.3736  0.1201  0.9044
Sex[notna]  0.0745  0.1085  0.6869  0.4921
MedUse[notna]   0.1596  0.2721  0.5868  0.5573
sqrt(DisDurMonths[notna])   0.0528  0.009   5.8955  0
Group[notna]    0.3628  0.1388  2.6144  0.0089
BMI[notna]  -9e-04  0.0052  -0.1723 0.8632
Marker_vh_1_1108138_A   -0.0011 0.0601  -0.0175 0.986
Log(theta)  1.5946  0.2089  7.6337  0


Based on these data, I am trying to calculate the OR for the zero part of the model for Marker_vh_1_1108138_A, and the IRR for the count model for Marker_vh_1_1108138_A.

Based on various sources and slides like this one I have started to piece together how to calculate an IRR, however, I have a lot of uncertainties as to whether I am doing this correctly. Specifically, I want to ask:

For the above output, would IRR = e^-0.0011 for Marker_vh_1_1108138_A?

Or do I need to include the intercept IRR= e^(-0.0011 + 0.0449)?

Or do I need to include any of the other Betas in order to calculate the IRR for just Marker_vh_1_1108138_A?

If the possible values for Marker_vh_1_1108138_A are 0,1, and 2, does this mean that the rate of Y is e^-0.0011 different per 1 unit increase in the number of Marker_vh_1_1108138_A?

Are the calculations similar for the OR in such a model?

• If you just want the point estimates then exp(coef(...)) can be used. To obtain standard errors and test statistics via the delta method, there are various generic implementations for this, e.g., deltaMethod() in package car. – Achim Zeileis Jan 21 '16 at 23:12