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# st: Testing for effect modification in Stata

 From Amal Khanolkar To "statalist@hsphsun2.harvard.edu" Subject st: Testing for effect modification in Stata Date Tue, 5 Mar 2013 15:02:48 +0000

```Hello all,

This isn't a real Stata question per se but I'm hoping that someone could tell me if I'm thinking all the right path and if not, what I could do to make the analysis below more meaningful:

My hypothesis is that parental smoking effects certain outcomes in their children and that this effect is modified by ethnicity.

1. My first instinct was linear running regression models (my outcome Y is continuous) stratified by ethnicity as follows (adjusted for confounders):

eststo clear
eststo: xi: regress Y  i.smoke ib3.magecat ib2.education i.famsit_new2 ib2.MBMI4 if multibirth==1 & ethnicity_bi2==1, vce (robust)
eststo: xi: regress Y  i.smoke ib3.magecat ib2.education i.famsit_new2 ib2.MBMI4 if multibirth==1 & ethnicity_bi2==2, vce (robust)
eststo: xi: regress Y  i.smoke ib3.magecat ib2.education i.famsit_new2 ib2.MBMI4 if multibirth==1 & ethnicity_bi2==3, vce (robust)
esttab, ci

2. The model results do indicate that the effect of the exposure (smoking) on the outcome does indeed vary by ethnic group, or that the effect is much smaller in ethnic group 3 compared to the other two ethnic groups.:

esttab, ci

------------------------------------------------------------------------------------------
(1)                       (2)                       (3)
Y                          Y                         Y
------------------------------------------------------------------------------------------
_Ismoke1_3                   -163.2***                 -121.4***                 -61.69***
[-166.3,-160.1]           [-137.6,-105.2]           [-83.33,-40.05]

_Ismoke1_4                   -224.5***                 -192.8***                 -134.7***
[-228.5,-220.5]           [-213.4,-172.2]           [-168.0,-101.5]

------------------------------------------------------------------------------------------
N                           1064084                     34344                     47092
------------------------------------------------------------------------------------------
95% confidence intervals in brackets
* p<0.05, ** p<0.01, *** p<0.001

3. I then proceeded by running a regression model that includes an interaction term between ethnicity and smoking and one without followed by a likelihood ratio test:

*LRT*

xi: regress Y  i.ethnicity_bi2*i.smoke1 ib3.magecat i.education i.famsit_new i.MBMI4 if multibirth==1
est store A
xi: regress Y  i.ethnicity_bi2 i.smoke1 ib3.magecat i.education i.famsit_new i.MBMI4 if multibirth==1
lrtest A

The interactions terms for all groups tested were highly significant (p<0.0001) and so was the LRTest  (p<0.0001).

My questions are:

A. Is the above enough to demonstrate that there is indeed an effect modification by ethnic group? If not, what further statistical tests may I run?

B. If I were to run a linear regression model as the first one above, but instead of stratifying by ethnicity I adjust for it. My first thought was that this should be similar to running stratified analysis, but I am obviously wrong as one cannot interpret the Beta's in the same way??

xi: regress Y i.smoke i.ethnicity_bi2 ib3.magecat ib2.education i.famsit_new2 ib2.MBMI4 if multibirth==1, vce (robust)

Thanks for any valuable input!

Amal Khanolkar

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```