To describe the difference in relative risk instead of absolute risk reduction after logistic regress

[Tom Hsiung]

Hi,

I just made a logistic regression. Of the independent remained after the forward selection, I used 'margins' to get the confidence interval of the absolute risk difference. However, I would like to get another output of relative risk.

 logistic firsttherapeuticinrreached i.nonaaornonanona i.ageforttest i.af i.ttesttargetinr

Logistic regression                             Number of obs     =        187
                                                LR chi2(4)        =      25.32
                                                Prob > chi2       =     0.0000
Log likelihood = -84.409294                     Pseudo R2         =     0.1304

--------------------------------------------------------------------------------------------
firsttherapeuticinrreached | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------------------+----------------------------------------------------------------
         1.nonaaornonanona |   .1526829    .073589    -3.90   0.000     .0593656    .3926867
             1.ageforttest |   2.916752   1.356175     2.30   0.021     1.172531    7.255625
                      1.af |   .3494673    .161598    -2.27   0.023     .1411888    .8649931
          1.ttesttargetinr |   2.409212    1.35103     1.57   0.117     .8026778    7.231175
                     _cons |   4.008227   1.200546     4.64   0.000     2.228436    7.209492
--------------------------------------------------------------------------------------------

. margins i.nonaaornonanona

Predictive margins                              Number of obs     =        187
Model VCE    : OIM

Expression   : Pr(firsttherapeuticinrreached), predict()

---------------------------------------------------------------------------------
                |            Delta-method
                |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
nonaaornonanona |
             0  |   .8367911   .0286637    29.19   0.000     .7806114    .8929709
             1  |   .4675317   .0984477     4.75   0.000     .2745778    .6604856
---------------------------------------------------------------------------------

. margins r.nonaaornonanona

Contrasts of predictive margins
Model VCE    : OIM

Expression   : Pr(firsttherapeuticinrreached), predict()

---------------------------------------------------
                |         df        chi2     P>chi2
----------------+----------------------------------
nonaaornonanona |          1       12.88     0.0003
---------------------------------------------------

-----------------------------------------------------------------
                |            Delta-method
                |   Contrast   Std. Err.     [95% Conf. Interval]
----------------+------------------------------------------------
nonaaornonanona |
      (1 vs 0)  |  -.3692594   .1028906     -.5709214   -.1675975
-----------------------------------------------------------------

.

Tom

[Phil Bromiley]

I'm not sure exactly what you want, but I would look harder at the margins statement documentation and the contrast option. You can specify a wide variety of outputs in margins.

[Tom Hsiung]

I'm not sure exactly what you want, but I would look harder at the margins statement documentation and the contrast option. You can specify a wide variety of outputs in margins.

I don't need the odds ratio. Instead, I need the risk ratio.

Tom

[Tom Hsiung]

I used the help to find this:

help logistic

Title

[R] logistic -- Logistic regression, reporting odds ratios


Syntax

logistic depvar indepvars [if] [in] [weight] [, options]

help logit

Title

[R] logit -- Logistic regression, reporting coefficients


Syntax

logit depvar [indepvars] [if] [in] [weight] [, options]


So how to get the

Logistic regression, reporting relative risk? Much appreciated!

[Rich Goldstein]

us poisson instead of logistic, be sure to use the "irr" option; another alternative is to use glm with family(binomial) and link(log)

[Andrea Discacciati]

us poisson instead of logistic, be sure to use the "irr" option; another alternative is to use glm with family(binomial) and link(log)

To follow up on Rich's excellent suggestion, I would use robust SEs if I chose the Poisson model.

[Tom Hsiung]

So there is no direct way to report the relative risk by a single logistic regress syntax?

and by the way, the

margins i.variable

shows the absolute risk

the

margins r.variable

show the absolute risk difference

Correct?

Tom

[Tom Hsiung]

I read from some ebooks at made a test, see below. Interesting.

. logit firsttherapeuticinrreached i.nonaaornonanona i.ageforttest i.af i.ttesttargetinr

Iteration 0:   log likelihood = -97.068543  
Iteration 1:   log likelihood = -85.364098  
Iteration 2:   log likelihood = -84.413247  
Iteration 3:   log likelihood = -84.409295  
Iteration 4:   log likelihood = -84.409294  

Logistic regression                             Number of obs     =        187
                                                LR chi2(4)        =      25.32
                                                Prob > chi2       =     0.0000
Log likelihood = -84.409294                     Pseudo R2         =     0.1304

--------------------------------------------------------------------------------------------
firsttherapeuticinrreached |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------------------+----------------------------------------------------------------
         1.nonaaornonanona |  -1.879392   .4819725    -3.90   0.000    -2.824041   -.9347431
             1.ageforttest |   1.070471   .4649608     2.30   0.021     .1591643    1.981777
                      1.af |  -1.051345   .4624124    -2.27   0.023    -1.957657   -.1450337
          1.ttesttargetinr |   .8792999   .5607765     1.57   0.117    -.2198018    1.978402
                     _cons |   1.388349   .2995205     4.64   0.000     .8012998    1.975398
--------------------------------------------------------------------------------------------

.

. mlogit firsttherapeuticinrreached i.nonaaornonanona i.ageforttest i.af i.ttesttargetinr

Iteration 0:   log likelihood = -97.068543  
Iteration 1:   log likelihood = -85.364098  
Iteration 2:   log likelihood = -84.413247  
Iteration 3:   log likelihood = -84.409295  
Iteration 4:   log likelihood = -84.409294  

Multinomial logistic regression                 Number of obs     =        187
                                                LR chi2(4)        =      25.32
                                                Prob > chi2       =     0.0000
Log likelihood = -84.409294                     Pseudo R2         =     0.1304

-----------------------------------------------------------------------------------
firsttherapeuti~d |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
0                 |
1.nonaaornonanona |   1.879392   .4819725     3.90   0.000     .9347431    2.824041
    1.ageforttest |  -1.070471   .4649608    -2.30   0.021    -1.981777   -.1591643
             1.af |   1.051345   .4624124     2.27   0.023     .1450337    1.957657
 1.ttesttargetinr |  -.8792999   .5607765    -1.57   0.117    -1.978402    .2198018
            _cons |  -1.388349   .2995205    -4.64   0.000    -1.975398   -.8012998
------------------+----------------------------------------------------------------
1                 |  (base outcome)
-----------------------------------------------------------------------------------

.

. mlogit firsttherapeuticinrreached i.nonaaornonanona i.ageforttest i.af i.ttesttargetinr, rrr

Iteration 0:   log likelihood = -97.068543  
Iteration 1:   log likelihood = -85.364098  
Iteration 2:   log likelihood = -84.413247  
Iteration 3:   log likelihood = -84.409295  
Iteration 4:   log likelihood = -84.409294  

Multinomial logistic regression                 Number of obs     =        187
                                                LR chi2(4)        =      25.32
                                                Prob > chi2       =     0.0000
Log likelihood = -84.409294                     Pseudo R2         =     0.1304

-----------------------------------------------------------------------------------
firsttherapeuti~d |        RRR   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
0                 |
1.nonaaornonanona |   6.549521   3.156689     3.90   0.000     2.546559    16.84478
    1.ageforttest |   .3428471   .1594105    -2.30   0.021     .1378241    .8528562
             1.af |   2.861498   1.323192     2.27   0.023     1.156079    7.082714
 1.ttesttargetinr |   .4150734   .2327634    -1.57   0.117     .1382901     1.24583
            _cons |   .2494868   .0747264    -4.64   0.000      .138706    .4487453
------------------+----------------------------------------------------------------
1                 |  (base outcome)
-----------------------------------------------------------------------------------

.

[Tom Hsiung]

However, it looks like that RRR by syntax -mlogit- = Odds ratio by syntax -logistic-

Note that 1/2.546559 = 0.3926867, and 1/16.84478 = 0.0593656. It's a same thing. However, we know that RRR and Odds ratio are not the same thing!

. logistic firsttherapeuticinrreached i.nonaaornonanona i.ageforttest i.af i.ttesttargetinr

Logistic regression                             Number of obs     =        187
                                                LR chi2(4)        =      25.32
                                                Prob > chi2       =     0.0000
Log likelihood = -84.409294                     Pseudo R2         =     0.1304

--------------------------------------------------------------------------------------------
firsttherapeuticinrreached | Odds Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------------------+----------------------------------------------------------------
         1.nonaaornonanona |   .1526829    .073589    -3.90   0.000     .0593656    .3926867
             1.ageforttest |   2.916752   1.356175     2.30   0.021     1.172531    7.255625
                      1.af |   .3494673    .161598    -2.27   0.023     .1411888    .8649931
          1.ttesttargetinr |   2.409212    1.35103     1.57   0.117     .8026778    7.231175
                     _cons |   4.008227   1.200546     4.64   0.000     2.228436    7.209492
--------------------------------------------------------------------------------------------

.

[Tom Hsiung]

. mlogit firsttherapeuticinrreached i.nonaaornonanona i.ageforttest i.af i.ttesttargetinr, rrr b
> ase(0)

Iteration 0:   log likelihood = -97.068543  
Iteration 1:   log likelihood = -85.364098  
Iteration 2:   log likelihood = -84.413247  
Iteration 3:   log likelihood = -84.409295  
Iteration 4:   log likelihood = -84.409294  

Multinomial logistic regression                 Number of obs     =        187
                                                LR chi2(4)        =      25.32
                                                Prob > chi2       =     0.0000
Log likelihood = -84.409294                     Pseudo R2         =     0.1304

-----------------------------------------------------------------------------------
firsttherapeuti~d |        RRR   Std. Err.      z    P>|z|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
0                 |  (base outcome)
------------------+----------------------------------------------------------------
1                 |
1.nonaaornonanona |   .1526829    .073589    -3.90   0.000     .0593656    .3926867
    1.ageforttest |   2.916752   1.356175     2.30   0.021     1.172531    7.255625
             1.af |   .3494673    .161598    -2.27   0.023     .1411888    .8649931
 1.ttesttargetinr |   2.409212    1.35103     1.57   0.117     .8026778    7.231175
            _cons |   4.008227   1.200546     4.64   0.000     2.228436    7.209492
-----------------------------------------------------------------------------------

.

[Tom Hsiung]

Finally, I got to understand that, by logistic regress, to compute a confidence interval of relative risk ratio is not possible. However, fortunately, logistic regress could output a sample risk for each subgroup and its confidence interval. Also, by logistic regress itself, the absolute risk difference could also be gotten by Stata build-in syntax.

Thanks