Relative risk from nlcom different from regression output

[Robbie Dembo]

Hi,

I have a similar question to one posed a few years ago in this thread. I am running an adjusted poisson model with a binary outcome and a binary-by-binary interaction term (the log binomial model wouldn't converge). The outcome is medication adherence and the interaction is between a dichotomous measure of stigma and a dichotomous measure of medication norms. The output from the model shows a significant multiplicative interaction. To present the interaction, I am trying to obtain the effect of stigma on the relative risk of medication adherence within the "strata" of the medication norms variable; or, what is the effect of stigma given the presence of medication norms, and what is the effect of stigma given the absence of adherence norms. I used nlcom to obtain these RRs, although in the thread cited above, Martin Buis raises concerns with this approach. Below is the output. See the bold for the results I am comparing. I would like to be able to show that the confidence intervals for the RRs given the presence of norms and the absence of norms do not overlap (and thus, there is a significant multiplicative interaction) but the results from nlcom seem a little off. The RR of the interaction from the model and from nlcom are similar but the confidence intervals and p value are different. Is there a different way to do this?

Many thanks,
Robbie

. poisson medbi i.hidebi3##i.adnorm2 i.yrcat2 depr23 crack fdhivbi famhivbi pknowbi, irr vce(robust) 

Iteration 0:   log pseudolikelihood = -192.43444  
Iteration 1:   log pseudolikelihood = -192.42429  
Iteration 2:   log pseudolikelihood = -192.42428  

Poisson regression                              Number of obs     =        221
                                                Wald chi2(10)     =      29.94
                                                Prob > chi2       =     0.0009
Log pseudolikelihood = -192.42428               Pseudo R2         =     0.0355

-------------------------------------------------------------------------------------
                    |               Robust
              medbi |        IRR   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------------+----------------------------------------------------------------
            hidebi3 |
         Very much  |   .3475176   .1568795    -2.34   0.019     .1434564    .8418482
                    |
            adnorm2 |
          Adherent  |    1.29926   .1346596     2.53   0.012     1.060412    1.591906
                    |
    hidebi3#adnorm2 |
Very much#Adherent  |   3.161404   1.635853     2.22   0.026     1.146648    8.716255
                    |
             yrcat2 |
         10-19 yrs  |   1.037215   .1438793     0.26   0.792     .7903014    1.361272
         20+ years  |    .960983   .1323098    -0.29   0.773     .7337039    1.258666
                    |
             depr23 |    .791829   .1188083    -1.56   0.120     .5900851    1.062547
              crack |   .7794588   .0881733    -2.20   0.028     .6244595     .972931
            fdhivbi |   .8665909   .1037859    -1.20   0.232      .685285    1.095865
           famhivbi |    1.09182   .1187786     0.81   0.419     .8821638    1.351304
            pknowbi |     .87816   .0974026    -1.17   0.241     .7065797    1.091405
              _cons |   .7569053   .1165931    -1.81   0.071     .5596585     1.02367
-------------------------------------------------------------------------------------
Note: _cons estimates baseline incidence rate.

. margins, at(adnorm2=(0 1) hidebi3=(0 1)) predict(pr()) post

Predictive margins                              Number of obs     =        221
Model VCE    : Robust

Expression   : Predicted number of events, predict(pr())

1._at        : hidebi3         =           0
               adnorm2         =           0

2._at        : hidebi3         =           0
               adnorm2         =           1

3._at        : hidebi3         =           1
               adnorm2         =           0

4._at        : hidebi3         =           1
               adnorm2         =           1

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         _at |
          1  |   .5785924   .0410927    14.08   0.000     .4980522    .6591326
          2  |   .7517419   .0563219    13.35   0.000      .641353    .8621309
          3  |    .201071   .0894456     2.25   0.025     .0257609    .3763811
          4  |   .8258964   .1967121     4.20   0.000     .4403478    1.211445
------------------------------------------------------------------------------

. est sto m4

. 
.         *RRs stratified by norms
.         *RR for stigma given no norms
.         nlcom _b[3._at]/_b[1._at]

       _nl_1:  _b[3._at]/_b[1._at]

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |   .3475176   .1568795     2.22   0.027     .0400394    .6549958
------------------------------------------------------------------------------

.         
.         *RR for stigma given norms
.         nlcom _b[4._at]/_b[2._at]

       _nl_1:  _b[4._at]/_b[2._at]

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |   1.098644   .2726728     4.03   0.000     .5642146    1.633072
------------------------------------------------------------------------------

.         
.         *Ratio of RRs
.         nlcom (_b[4._at]/_b[2._at])/(_b[3._at]/_b[1._at])

       _nl_1:  (_b[4._at]/_b[2._at])/(_b[3._at]/_b[1._at])

------------------------------------------------------------------------------
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _nl_1 |   3.161404   1.635853     1.93   0.053     -.044808    6.367616
------------------------------------------------------------------------------

[Maarten Buis]

To understand the difference between the two see: https://www.stata.com/support/faqs/s...cs/delta-rule/

[Robbie Dembo]

Thanks Maarten. I read the post but am not sure how to manually get the CIs for relative risks after running the model in a way that would be consistent with the model results and not the nlcom results. I am trying to get the CIs for the effect of stigma (hidebi3) on adherence within the strata of norms (adnorm2). Since there is the interaction, the RR and CI for the "hidebi3" term is the effect of stigma given no norms, so that one is taken care of. What I need now is the effect of stigma (hidebi3) given the presence of norms (adnorm2=1). Any suggestions?

Thanks so much,
Robbie