how to report Odds ratio for interactions terms separately for male and female in binary logistic regression

[anam ali]

Dear Statalist

I ran logistic regression on an AMI (acute myocardial infarction) dataset of 9 variables using Stata version 14.2. Following is the multivariable adjusted model, query is mentioned right below the table.

logistic mortality i.Gender age_10 ib(2).AMI_type ib(0).Diabetes ib(0).dyslipidemia_1 ib(0).Hypertension Discharge_Year ib(0).PTCAPCI c.age_10#Gender b(2).AMI_type#Gender

Logistic regression Number of obs = 11,673
LR chi2(10) = 672.86
Prob > chi2 = 0.0000
Log likelihood = -3355.4983 Pseudo R2 = 0.0911


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

Gender
Female 3.306906 1.418547 2.79 0.005 1.426547 7.665802
age_10 1.591416 .0581228 12.72 0.000 1.481479 1.709511

AMI_type
STEMI 2.462539 .2253916 9.85 0.000 2.058137 2.946402

Diabetes
Yes 1.258716 .0857974 3.38 0.001 1.101305 1.438626

dyslipidemia_1
Yes .3368114 .0333947 -10.98 0.000 .2773259 .4090564

Hypertension
Yes .9556454 .0715644 -0.61 0.545 .8251896 1.106725
Discharge_Year .9769054 .0059796 -3.82 0.000 .9652556 .9886958

PTCAPCI
Yes .4894141 .0390456 -8.96 0.000 .4185694 .5722497

Gender#c.age_10
Female .842007 .0506165 -2.86 0.004 .748422 .9472942

AMI_type#Gender
STEMI#Female 1.393794 .1925035 2.40 0.016 1.063249 1.827099

_cons 1.12e+18 1.38e+19 3.38 0.001 3.91e+07 3.21e+28


Can someone please guide how can I obtain the Odds ratio for interaction terms separately for Male and Female. Its a very important query I am unable to find answer for my supervisor at work really wants me to find answer for this please can someone help. Thanks in advance

[Maarten Buis]

lincom would probablt be the easiest option. Alternatively, you could consider https://www.stata-journal.com/articl...article=st0250

[Cansu Oymak]

1) generate "female" binary variable taking value of 1 if F and 0 if M.
2) generate "male" binary variable taking value of 1 if M and 0 if M.
1.1.) generate interaction term as femala_age=female*age_10 (do it for males as well if you wish )
2.1) generate interaction term as female_ami=female*AMI_type (do it for males as well if you wish)

In your regression model,


logistic mortality i.male i.female female_age (male_age) female_ami (male_ami) x3 x4 x5.....

then compute the marginal effects.

Dear Statalist

I ran logistic regression on an AMI (acute myocardial infarction) dataset of 9 variables using Stata version 14.2. Following is the multivariable adjusted model, query is mentioned right below the table.

logistic mortality i.Gender age_10 ib(2).AMI_type ib(0).Diabetes ib(0).dyslipidemia_1 ib(0).Hypertension Discharge_Year ib(0).PTCAPCI c.age_10#Gender b(2).AMI_type#Gender

Logistic regression Number of obs = 11,673
LR chi2(10) = 672.86
Prob > chi2 = 0.0000
Log likelihood = -3355.4983 Pseudo R2 = 0.0911


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

Gender
Female 3.306906 1.418547 2.79 0.005 1.426547 7.665802
age_10 1.591416 .0581228 12.72 0.000 1.481479 1.709511

AMI_type
STEMI 2.462539 .2253916 9.85 0.000 2.058137 2.946402

Diabetes
Yes 1.258716 .0857974 3.38 0.001 1.101305 1.438626

dyslipidemia_1
Yes .3368114 .0333947 -10.98 0.000 .2773259 .4090564

Hypertension
Yes .9556454 .0715644 -0.61 0.545 .8251896 1.106725
Discharge_Year .9769054 .0059796 -3.82 0.000 .9652556 .9886958

PTCAPCI
Yes .4894141 .0390456 -8.96 0.000 .4185694 .5722497

Gender#c.age_10
Female .842007 .0506165 -2.86 0.004 .748422 .9472942

AMI_type#Gender
STEMI#Female 1.393794 .1925035 2.40 0.016 1.063249 1.827099

_cons 1.12e+18 1.38e+19 3.38 0.001 3.91e+07 3.21e+28


Can someone please guide how can I obtain the Odds ratio for interaction terms separately for Male and Female. Its a very important query I am unable to find answer for my supervisor at work really wants me to find answer for this please can someone help. Thanks in advance

[anam ali]

Dear Cansu Oymak thank you for your reply

I am a little confused as to how to generate:

1) generate "female" binary variable taking value of 1 if F and 0 if M.
2) generate "male" binary variable taking value of 1 if M and 0 if M

when the gender variable being used in the analysis is coded as 0 for male and 1 for female??

[anam ali]

Cansu Oymak I did the following for female and male please let me know if its right or wrong

. generate female= 1 if Gender == 1
(7,990 missing values generated)

. tab female

female | Freq. Percent Cum.
------------+-----------------------------------
1 | 3,683 100.00 100.00
------------+-----------------------------------
Total | 3,683 100.00

. replace female= 0 if female ==.
(7,990 real changes made)

. generate male= 1 if Gender == 1
(7,990 missing values generated)

. replace male = 0 if male ==.
(7,990 real changes made)

. tab male

male | Freq. Percent Cum.
------------+-----------------------------------
0 | 7,990 68.45 68.45
1 | 3,683 31.55 100.00
------------+-----------------------------------
Total | 11,673 100.00

. tab female

female | Freq. Percent Cum.
------------+-----------------------------------
0 | 7,990 68.45 68.45
1 | 3,683 31.55 100.00
------------+-----------------------------------
Total | 11,673 100.00

[Cansu Oymak]

Yes. This is what I have just suggested. For dummy variable "female" you can analyze females only and you can use interaction terms using age or ami. Please note that stata does not provide marginal effects for interaction terms if you type like this i.dummy#c.continous or i.dummy#i.dummy. Instead, you only get the coefs. To overcome this problem, please generate your interaction terms manually. Then, you can get odds ratios or marginal effects.

[anam ali]

Cansu Oymak but isn't this wrong because the total of the male is 11,673 and female is also 11,673 and even when I analyzed them in a model without interactions female gets omitted and it gives OR for male, and marginal effects give predicted probabilities but I want Odds ratio ??

. logistic mortality i.male i.female age_10 ibn.AMI_type ib(0).Diabetes ib(0).dyslipidemia_1 ib(0).Hypertension Discharge_Year ib(0).PTCAP
> CI, noconstant
note: 1.female omitted because of collinearity

Logistic regression Number of obs = 11,673
Wald chi2(9) = 4343.89
Log likelihood = -3364.0709 Prob > chi2 = 0.0000

--------------------------------------------------------------------------------
mortality | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
---------------+----------------------------------------------------------------
1.male | 1.22991 .0849395 3.00 0.003 1.074207 1.408181
1.female | 1 (omitted)
age_10 | 1.510117 .0442539 14.07 0.000 1.425824 1.599392
|
AMI_type |
STEMI | 3.97e+18 4.87e+19 3.49 0.000 1.46e+08 1.08e+29
NSTEMI | 1.43e+18 1.76e+19 3.41 0.001 5.12e+07 4.01e+28
|
Diabetes |
Yes | 1.284302 .087296 3.68 0.000 1.124112 1.467319
|
dyslipidemia_1 |
Yes | .3373005 .0333973 -10.98 0.000 .2778028 .4095409
|
Hypertension |
Yes | .9654826 .0723664 -0.47 0.639 .8335734 1.118266
Discharge_Year | .9769106 .0059752 -3.82 0.000 .9652692 .9886923
|
PTCAPCI |
Yes | .4892884 .039026 -8.96 0.000 .4184778 .5720809
--------------------------------------------------------------------------------

[anam ali]

Dear Maarten Buis thank you so much for the reply I tried the lincom command but I got OR for female only which I am already getting in the multivariable-adjusted model I wanted Odds ratio for both male and female separately do you have any comment

lincom 0.Gender + 0.Gender#c.age_10, or

( 1) [mortality]0b.Gender + [mortality]0b.Gender#co.age_10 = 0

------------------------------------------------------------------------------
mortality | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 1 (omitted)
------------------------------------------------------------------------------

. lincom 1.Gender + 1.Gender#c.age_10, or

( 1) [mortality]1.Gender + [mortality]1.Gender#c.age_10 = 0

------------------------------------------------------------------------------
mortality | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) | 2.784438 1.032236 2.76 0.006 1.346429 5.758265
------------------------------------------------------------------------------

[anam ali]

Dear Sir Clyde Schechter can you please help with my query if possible would be extremely grateful for your time and efforts

[Maarten Buis]

Here is an example:

.

. // open example data
. sysuse nlsw88, clear
(NLSW, 1988 extract)

.
. // prepare the data
.
. gen byte black = race == 2 if !missing(race)

. label variable black "respondent's race"

. label define black 0 "not black" ///
>                    1 "black"

. label value black black

.
. gen byte urban = c_city + smsa

. label define urban 2 "central city" ///
>                    1 "suburban"     ///
>                    0 "rural"

. label value urban urban

. label variable urban "urbanicity"

.
. gen grade_c = grade - 12
(2 missing values generated)

. label var grade_c "current grade completed (centered at 12)"

.
. logit never_married i.black##c.grade_c i.urban i.south, or

Iteration 0:   log likelihood = -750.35422  
Iteration 1:   log likelihood = -700.91937  
Iteration 2:   log likelihood = -695.33561  
Iteration 3:   log likelihood = -695.32636  
Iteration 4:   log likelihood = -695.32636  

Logistic regression                             Number of obs     =      2,244
                                                LR chi2(6)        =     110.06
                                                Prob > chi2       =     0.0000
Log likelihood = -695.32636                     Pseudo R2         =     0.0733

---------------------------------------------------------------------------------
  never_married | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
          black |
         black  |   3.782607   .6961037     7.23   0.000     2.637223     5.42545
        grade_c |   1.239818   .0474363     5.62   0.000     1.150245    1.336367
                |
black#c.grade_c |
         black  |   .7904653   .0446505    -4.16   0.000     .7076223     .883007
                |
          urban |
      suburban  |   .9448063   .1903419    -0.28   0.778     .6365882    1.402255
  central city  |   1.894218   .3631246     3.33   0.001     1.300928    2.758078
                |
        1.south |   .6305354   .0982841    -2.96   0.003     .4645465    .8558344
          _cons |   .0553448   .0105848   -15.13   0.000     .0380438    .0805137
---------------------------------------------------------------------------------
Note: _cons estimates baseline odds.

. lincom grade_c + 1.black#c.grade_c, or

 ( 1)  [never_married]grade_c + [never_married]1.black#c.grade_c = 0

------------------------------------------------------------------------------
never_marr~d | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         (1) |   .9800335   .0410871    -0.48   0.630      .902724    1.063964
------------------------------------------------------------------------------

The normal logit model give you the estimate of grade when someone is white. With lincom you can get the estimate of grade for people who are black.

You can get the same estimates using

. logit never_married ibn.black i.black#c.grade_c i.urban i.south, or nocons

Iteration 0:   log likelihood = -1555.4223  
Iteration 1:   log likelihood = -709.08567  
Iteration 2:   log likelihood = -695.64862  
Iteration 3:   log likelihood = -695.32652  
Iteration 4:   log likelihood = -695.32636  
Iteration 5:   log likelihood = -695.32636  

Logistic regression                             Number of obs     =      2,244
                                                Wald chi2(7)      =     851.87
Log likelihood = -695.32636                     Prob > chi2       =     0.0000

---------------------------------------------------------------------------------
  never_married | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
          black |
     not black  |   .0553448   .0105848   -15.13   0.000     .0380438    .0805137
         black  |   .2093476   .0446847    -7.33   0.000     .1377784    .3180933
                |
black#c.grade_c |
     not black  |   1.239818   .0474363     5.62   0.000     1.150245    1.336367
         black  |   .9800335   .0410871    -0.48   0.630      .902724    1.063964
                |
          urban |
      suburban  |   .9448063   .1903419    -0.28   0.778     .6365882    1.402255
  central city  |   1.894218   .3631246     3.33   0.001     1.300928    2.758078
                |
        1.south |   .6305354   .0982841    -2.96   0.003     .4645465    .8558344
---------------------------------------------------------------------------------

This is discussed in the Stata Tip I linked to earlier in #2

[anam ali]

Dear Maarten Buis since you mentioned the normal logit model give you the estimate of grade when someone is white how is it giving for white because as per the example in the model it is giving OR for black while taking white as reference category even the interaction consist of black, yes I can see with lincom the estimate is for grade for people who are black. Also, the lincom is giving OR for the interaction term which is mentioned in the model, which is lincom grade_c + 1.black#c.grade_c, or and not giving OR for not black category.
This is exactly what's happening with me as you can see in #1 my interaction term is giving OR for females not for males so when I use lincom it is giving OR for females only and for males it is getting omitted mentioned in #8. Please let me know where I am making a mistake would be extremely thankful.


Also, the part where you mentioned I can get an estimate using the following method I did that please review:

When I remove age_10 and AMI type from the model I get ORs for male and female separately for interaction terms, but why is OR for gender variable coming in this form (male:1.12e+18, female:3.70e+18) ?? I also want OR for age_10 and AMI type as well in my model what to do about that please suggest


. logit mortality ibn.Gender ib(0).Diabetes ib(0).dyslipidemia_1 ib(0).Hypertension Discharge_Year ib(0).PTCAPCI c.age_10#Gender b(2).AMI_type#Gender,or nocons

Iteration 0: log likelihood = -8091.107
Iteration 1: log likelihood = -3464.0954
Iteration 2: log likelihood = -3359.1581
Iteration 3: log likelihood = -3355.5102
Iteration 4: log likelihood = -3355.4983
Iteration 5: log likelihood = -3355.4983

Logistic regression Number of obs = 11,673
Wald chi2(11) = 4324.04
Log likelihood = -3355.4983 Prob > chi2 = 0.0000

---------------------------------------------------------------------------------
mortality | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
----------------+----------------------------------------------------------------
Gender |
Male | 1.12e+18 1.38e+19 3.38 0.001 3.91e+07 3.21e+28
Female | 3.70e+18 4.55e+19 3.48 0.000 1.30e+08 1.06e+29
|
Diabetes |
Yes | 1.258716 .0857974 3.38 0.001 1.101305 1.438626
|
dyslipidemia_1 |
Yes | .3368114 .0333947 -10.98 0.000 .2773259 .4090563
|
Hypertension |
Yes | .9556454 .0715644 -0.61 0.545 .8251896 1.106725
Discharge_Year | .9769054 .0059796 -3.82 0.000 .9652556 .9886958
|
PTCAPCI |
Yes | .4894141 .0390456 -8.96 0.000 .4185693 .5722497
|
Gender#c.age_10 |
Male | 1.591416 .0581228 12.72 0.000 1.481479 1.709511
Female | 1.339983 .0649256 6.04 0.000 1.218587 1.473473
|
AMI_type#Gender |
STEMI#Male | 2.462539 .2253916 9.85 0.000 2.058137 2.946402
STEMI#Female | 3.432272 .38052 11.12 0.000 2.761931 4.265308
---------------------------------------------------------------------------------


ORs for male and female don't get generated when age_10 and AMI type

logit mortality ibn.Gender age_10 ib(2).AMI_type ib(0).Diabetes ib(0).dyslipidemia_1 ib(0).Hypertension Discharge_Year ib(0).PTCAPCI c.age_10#Gender b(2).AMI_type#Gender, or nocons

note: 1.Gender#c.age_10 omitted because of collinearity
note: 1.AMI_type#1.Gender omitted because of collinearity
Iteration 0: log likelihood = -8091.107
Iteration 1: log likelihood = -3464.0954
Iteration 2: log likelihood = -3359.1581
Iteration 3: log likelihood = -3355.5102
Iteration 4: log likelihood = -3355.4983
Iteration 5: log likelihood = -3355.4983

Logistic regression Number of obs = 11,673
Wald chi2(11) = 4324.04
Log likelihood = -3355.4983 Prob > chi2 = 0.0000

---------------------------------------------------------------------------------
mortality | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval]
----------------+----------------------------------------------------------------
Gender |
Male | 1.12e+18 1.38e+19 3.38 0.001 3.91e+07 3.21e+28
Female | 3.70e+18 4.55e+19 3.48 0.000 1.30e+08 1.06e+29
|
age_10 | 1.339983 .0649256 6.04 0.000 1.218587 1.473473
|
AMI_type |
STEMI | 3.432272 .38052 11.12 0.000 2.761931 4.265308
|
Diabetes |
Yes | 1.258716 .0857974 3.38 0.001 1.101305 1.438626
|
dyslipidemia_1 |
Yes | .3368114 .0333947 -10.98 0.000 .2773259 .4090563
|
Hypertension |
Yes | .9556454 .0715644 -0.61 0.545 .8251896 1.106725
Discharge_Year | .9769054 .0059796 -3.82 0.000 .9652556 .9886958
|
PTCAPCI |
Yes | .4894141 .0390456 -8.96 0.000 .4185693 .5722497
|
Gender#c.age_10 |
Male | 1.187639 .0713938 2.86 0.004 1.055638 1.336145
Female | 1 (omitted)
|
AMI_type#Gender |
STEMI#Male | .7174662 .0990926 -2.40 0.016 .5473158 .9405132
STEMI#Female | 1 (omitted)
---------------------------------------------------------------------------------

.

[Joseph Coveney]

_cons 1.12e+18 1.38e+19 3.38 0.001 3.91e+07 3.21e+28


. . . my supervisor at work really wants me to find answer for this . . .

If I were your supervisor at work, I'd be more interested in your investigating further into what's behind that.

It would certainly warrant checking the data, work flow &c. before anyone gets too hung up about sex differences in ST segment elevation in the EKG.