2
$\begingroup$

My data was over-dispersed (dispersion coefficient over 5), so i have fitted negative binomial model.

Coefficients:
              Estimate Std. Error z value Pr(>|z|)    
(Intercept)  2.0985089  0.5845392   3.590 0.000331 ***
age         -0.0007965  0.0193064  -0.041 0.967092    
treatment   -0.5011593  0.2405658  -2.083 0.037228 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for Negative Binomial(1.499) family taken to be 1)

    Null deviance: 71.217  on 57  degrees of freedom
Residual deviance: 66.875  on 55  degrees of freedom
AIC: 341.12

When I include an interaction, the regression coefficients change completely, although they are not significant.

Coefficients:
              Estimate Std. Error z value Pr(>|z|)  
(Intercept)    1.51361    0.83920   1.804   0.0713 .
age            0.01914    0.02826   0.677   0.4981  
treatment      0.60748    1.12199   0.541   0.5882  
age:treatment -0.03893    0.03850  -1.011   0.3119  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for Negative Binomial(1.5315) family taken to be 1)

    Null deviance: 72.238  on 57  degrees of freedom
Residual deviance: 66.874  on 54  degrees of freedom
AIC: 342.18

How should I treat the interaction effect?

$\endgroup$

1 Answer 1

1
$\begingroup$

In the model adjusting for only age and treatment, the interpretation of the treatment coefficient was a log relative risk in treated versus untreated of the same age. After the interaction is added, the interpretation of the treatment is a log relative risk comparing two people who are of age 0. This is nonsensical of course and shouldn't be interpreted.

Even when the treatment by age interaction is not statistically significant, these extrapolations usually cause difficult to interpret effects. To get an interpretable coefficient you can either use post estimates or standardize age by subtracting a suitable number like 50 or 60 so that the interpretation of the treatment coefficient is an expected difference in treatment comparing people are, say, 50 or 60 years old.

The main effect for treatment is no longer statistically significant after adding an interaction term for a couple reasons: 1) there are more parameters in the model 2) when treatment effect is allowed to be non-constant with age, it's much more variable, and so the projected trend at a fixed age is more variable (this will not be fixed by subtracting 50 or 60).

$\endgroup$
1
  • $\begingroup$ If I'm not mistaken, there should not be a "not" in the first sentence of the second paragraph? $\endgroup$
    – AlexK
    Commented May 13, 2019 at 3:16

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.