Understanding interactions using -clogit_

[Richard Rovin]

I have a 1:4 matched dataset. One case (a brain tumor that responded to an experimental treatment) matched to four controls (a brain tumor that did not respond). Two continuous variables of interest are test (the level of a serum biomarker; this is a unit-less ratio, range 0.05-0.50) and ses (socioeconomic status, range 1-100). I want to know if test is simply a proxy for ses, or is test an independent predictor of response. I therefore look for an interaction of ses on test. Using -clogit- I find:

clogit response c.test##c.ses, group(pairid) or
note: 6 groups (24 obs) dropped because of all positive or
      all negative outcomes.

Iteration 0:   log likelihood = -1874.6946  
Iteration 1:   log likelihood = -1874.6418  
Iteration 2:   log likelihood = -1874.6418  

Conditional (fixed-effects) logistic regression

                                                Number of obs     =      5,825
                                                LR chi2(3)        =       3.67
                                                Prob > chi2       =     0.2995
Log likelihood = -1874.6418                     Pseudo R2         =     0.0010

------------------------------------------------------------------------------
    response | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        test |   .1709451    .255565    -1.18   0.237     .0091264    3.201941
         ses |   .9962459   .0070151    -0.53   0.593      .982591    1.010091
             |
c.test#c.ses |   1.015837   .0245912     0.65   0.516     .9687646    1.065197
------------------------------------------------------------------------------

So, I interpret this to mean there is no statistically significant interaction of ses on test. I then look at -margins- and -marginsplot-

quietly margins, at(ses=(1(10)100) test = (0.05(0.05)0.5))

. marginsplot, noci 

Graphically, there appears to be an interaction.

Any help with interpretation would be much appreciated.

Best
Richard

[Clyde Schechter]

These are interesting results, but they are not the way to explore whether test is simply a proxy for ses. To do that you simply run the model three times, once with ses and test both included, and then a second time with just ses (adding the condition -if e(sample)- to make sure you don't have any new observations sneaking into the estimation sample), and a third time with just test (again adding -if e(sample)-).

If test has an appreciably non-zero coefficient in the third model, but a close to zero coefficient in the second model, then test is just a proxy for ses.

As for the results you do have, yes, there appears to be a strong interaction effect here. The effect of ses on outcome clearly differs strongly according to the value of test. When test has higher values, increasing ses is associated with increasing probabilities of outcome = 1, whereas at small values of test, increasing ses is associated with decreasing probabilities of outcome = 1. We can see also that regardless of ses, higher values of test are associated with lower probabilities of outcome = 1. And we can also see that at low values of ses, the value of test makes an appreciable difference in the outcome probability, whereas at high values of ses the outcome probability is much less dependent on the value of test.

[Richard Rovin]

Clyde Schechter Thank you

I was not familiar with the -if e(sample)- concept, so I am not certain if this is correct:

 clogit response test ses, group(pairid)
note: 6 groups (24 obs) dropped because of all positive or
      all negative outcomes.

Iteration 0:   log likelihood =  -1874.904  
Iteration 1:   log likelihood = -1874.8534  
Iteration 2:   log likelihood = -1874.8534  

Conditional (fixed-effects) logistic regression

                                                Number of obs     =      5,825
                                                LR chi2(2)        =       3.25
                                                Prob > chi2       =     0.1973
Log likelihood = -1874.8534                     Pseudo R2         =     0.0009

------------------------------------------------------------------------------
    response |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        test |  -.8966724   .6643839    -1.35   0.177    -2.198841    .4054961
         ses |   .0005846   .0021938     0.27   0.790    -.0037151    .0048843
------------------------------------------------------------------------------

. clogit response ses if e(sample), group(pairid)

Iteration 0:   log likelihood = -1875.8442  
Iteration 1:   log likelihood = -1875.7625  
Iteration 2:   log likelihood = -1875.7625  

Conditional (fixed-effects) logistic regression

                                                Number of obs     =      5,825
                                                LR chi2(1)        =       1.43
                                                Prob > chi2       =     0.2322
Log likelihood = -1875.7625                     Pseudo R2         =     0.0004

------------------------------------------------------------------------------
    response |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         ses |    .002201   .0018423     1.19   0.232    -.0014099    .0058119
------------------------------------------------------------------------------

. clogit response test if e(sample), group(pairid)

Iteration 0:   log likelihood = -1874.9063  
Iteration 1:   log likelihood =  -1874.889  
Iteration 2:   log likelihood =  -1874.889  

Conditional (fixed-effects) logistic regression

                                                Number of obs     =      5,825
                                                LR chi2(1)        =       3.17
                                                Prob > chi2       =     0.0748
Log likelihood =  -1874.889                     Pseudo R2         =     0.0008

------------------------------------------------------------------------------
    response |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        test |  -.9929148   .5574013    -1.78   0.075    -2.085401    .0995717
------------------------------------------------------------------------------

And I'd appreciate help interpreting.

Thanks in advance
Richard

[Clyde Schechter]

Yes, that's correct.

The coefficient of test in the third model, -0.993 (to three places) is only modestly changed when it appears in the first model beside ses, -0.897. It shrinks in magnitude a bit, but only about 10%, and each of the two is well within the confidence limits of the other. So this implies that the explanatory power of test is largely separate from that of ses. Certainly you would not say that test is a proxy for ses here. That said, the effect is not very large in either case, and the confidence intervals around it are pretty wide. So I would say that the data simply don't provide all that much information about the effect of test one way or another.

[Richard Rovin]

Thank you so much!
Richard