Subanalysis

[Sam Lee]

Hello,

I have a few questions regarding interaction terms.

1. If I have my final logistic regression model below,

• use http://www.stata-press.com/data/r13/lbw3
• logistic low age lwd smoke ht ptd

Logistic regression Number of obs = 189
LR chi2(5) = 29.56
Prob > chi2 = 0.0000
Log likelihood = -102.55384 Pseudo R2 = 0.1260

------------------------------------------------------------------------------
low | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .9383918 .0332708 -1.79 0.073 .8753963 1.00592
lwd | 2.54087 .9815007 2.41 0.016 1.191724 5.417377
smoke | 1.585579 .5509269 1.33 0.185 .802469 3.132905
ht | 4.017858 2.57528 2.17 0.030 1.143957 14.1117
ptd | 4.322268 1.93573 3.27 0.001 1.796804 10.39735
_cons | .8722474 .7224864 -0.17 0.869 .1720227 4.422763
------------------------------------------------------------------------------
Note: _cons estimates baseline odds.


2. and now I want to add interaction term between smoke and lwd

• logistic low age smoke##lwd ht ptd

Logistic regression Number of obs = 189
LR chi2(6) = 32.20
Prob > chi2 = 0.0000
Log likelihood = -101.23846 Pseudo R2 = 0.1372

------------------------------------------------------------------------------
low | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
age | .9433269 .0337749 -1.63 0.103 .8793985 1.011903

smoke |
smoker | 2.263877 .9304785 1.99 0.047 1.011579 5.066477
1.lwd | 4.67193 2.53338 2.84 0.004 1.614089 13.52275
|
smoke#lwd
smoker#1 | .2850451 .2207858 -1.62 0.105 .0624602 1.30084
|
ht | 3.719531 2.426126 2.01 0.044 1.035805 13.35668
ptd | 4.002717 1.800033 3.08 0.002 1.657933 9.663683
_cons | .6733606 .5741697 -0.46 0.643 .1266002 3.581468
------------------------------------------------------------------------------
Note: _cons estimates baseline odds.

3. Can I report from my first final model that lwd (OR 2.54), ht (OR 4.08) and ptd (OR 4.32) are the risk factors for low birth, and from my second model, can I just explain about the interaction between smoke and lwd only (OR 0.28)? or should I use the second model to be my final model and report the results from the second model? if then, how should I interpret smoker 1. lwd and smoke#lwd altogether? because in the first model, smoke wasn't a significant risk factor but in the second model it is significant.

4. how to decide which interaction terms to include in a multivariate logistic regression model? which analysis should I run to choose interaction terms?

Thank you for your time and help in advance.

[Marcos Almeida]

I recommend to use - margins- followed by - marginsplot- for that matter.

[Sam Lee]

Thank you for your reply.

If I want to see the interaction effect of smoking on lwd, can I add this term like below? or should I do this -logistic low age smoke##lwd ht ptd-?

• logistic low smoke##lwd

Logistic regression Number of obs = 189
LR chi2(3) = 17.27
Prob > chi2 = 0.0006
Log likelihood = -108.70116 Pseudo R2 = 0.0736

------------------------------------------------------------------------------
low | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
smoke |
smoker | 2.972426 1.153821 2.81 0.005 1.388981 6.361009
1.lwd | 6.039216 3.116229 3.49 0.000 2.196653 16.6035
|
smoke#lwd |
smoker#1 | .1892393 .1390064 -2.27 0.023 .0448496 .7984804
|
_cons | .2207792 .0591633 -5.64 0.000 .1305743 .3733007
------------------------------------------------------------------------------
Note: _cons estimates baseline odds.

• . margins smoke#lwd, expression(exp(predict(xb)))

Adjusted predictions Number of obs = 189
Model VCE : OIM

Expression : exp(predict(xb))

------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
smoke#lwd |
nonsmoker#0 | .2207792 .0591633 3.73 0.000 .1048213 .3367371
nonsmoker#1 | 1.333333 .5879447 2.27 0.023 .1809828 2.485684
smoker#0 | .65625 .1842988 3.56 0.000 .2950309 1.017469
smoker#1 | .75 .3307189 2.27 0.023 .1018028 1.398197
------------------------------------------------------------------------------


Is this the correct way to do it? how should I interpret these margins? Could you please show me the code (step-by-step)?

Thank you,

[Marcos Almeida]

This way, I believe you've got relative odds. If this is what you wish, OK.

But there are many exemples of - margins - with interaction term in the Stata Manual. The examples 5 and 8 are what I usually use for that matter.