component odds ratios for logistic regression with interaction using lincom

[Hanna Leicht]

Hello,

being new to the derivation of component odds ratios for a logistic regression with an interaction term and the lincom command, I'd be grateful for feedback to make sure that I've understood the idea and that I'm using lincom correctly.

In a simplified version of my model, I'm evaluating the effect of age (in four categories), sex and the interaction age*sex on risk of postoperative bleeding:

. label list sex age
sex:
0 male
1 female
age:
1 10-19 yrs
2 20-29 yrs
3 30-39 yrs
4 40+ yrs

Here is the model:

. logistic rbleed age##sex

Logistic regression Number of obs = 20,957
LR chi2(7) = 225.07
Prob > chi2 = 0.0000
Log likelihood = -6120.3964 Pseudo R2 = 0.0181


rbleed Odds Ratio Std. Err. z P>z [95% Conf. Interval]

age_cat
20-29 yrs 1.730926 .1701694 5.58 0.000 1.427565 2.098752
30-39 yrs 1.398721 .1532218 3.06 0.002 1.128462 1.733706
40+ yrs 1.057445 .1531469 0.39 0.700 .796124 1.404543

sex
female .6967148 .0710717 -3.54 0.000 .5704587 .8509144

age_cat#sex
20-29 yrs#female .6128676 .0768577 -3.90 0.000 .4793142 .7836336
30-39 yrs#female .7652589 .1145742 -1.79 0.074 .5706462 1.026242
40+ yrs#female .7862151 .1587033 -1.19 0.233 .5293221 1.167785

_cons .103046 .0085828 -27.28 0.000 .0875253 .121319


Looking at two examples, am I right in assuming that this is the lincom command / component OR for the comparison of females/30-39 yrs old vs. females/10-19 yrs old:

. lincom 3.age_cat + 1.sex + 3.age_cat#1.sex - (1.age_cat + 1.sex + 1.age_cat#1.sex)

( 1) - [rbleed]1b.age_cat + [rbleed]3.age_cat - [rbleed]1b.age_cat#1o.sex + [rbleed]3.age_cat#1.sex = 0

rbleed Odds Ratio Std. Err. z P>z [95% Conf. Interval]

(1) 1.070384 .109242 0.67 0.505 .8763287 1.307411

...and that this is the component OR for the comparison of females vs. males aged 20-29 yrs?

. lincom 2.age_cat + 1.sex + 2.age_cat#1.sex - 2.age_cat

( 1) [rbleed]1.sex + [rbleed]2.age_cat#1.sex = 0

rbleed Odds Ratio Std. Err. z P>z [95% Conf. Interval]

(1) .4269939 .0311467 -11.67 0.000 .3701106 .4926198


Thanks
Hanna

[Clyde Schechter]

am I right in assuming that this is the lincom command / component OR for the comparison of females/30-39 yrs old vs. females/10-19 yrs old:

. lincom 3.age_cat + 1.sex + 3.age_cat#1.sex - (1.age_cat + 1.sex + 1.age_cat#1.sex)

Yes, that's correct.

...and that this is the component OR for the comparison of females vs. males aged 20-29 yrs?

. lincom 2.age_cat + 1.sex + 2.age_cat#1.sex - 2.age_cat

Yes, that is correct. But you can simplify it. Notice that 2.age_cat appears with both a positive and negative sign, so these cancel out. You could just do it as

lincom 1.sex + 2.age_cat#1.sex

In fact, if you look at your output carefully, you will see that -lincom- itself made this simplification before it did your calculations.

[Hanna Leicht]

Dear Clyde,

thanks very much, that's really most helpful!

Best regards
Hanna