Can I interpret IRR as prevalence ratio?

[Zhianni Yang]

Hula, I'd like to know whether irr can be interpreted as prevalence? I'd like to estimate the prevalence tb mdr cases and using poisson mdr, irr it yields 0.7368. I know this is wrong but how should I obtain the prevalence estimation using poisson regression?

Thanks

[Andrea Discacciati]

Assuming that mdr is a binary (0/1) variable, then yes: 0.7368 is the sample prevalence (proportion of 1's) and an estimate of the population's prevalence.

Note that if you're interested only in the point estimate, you don't need a regression model (like Poisson): you can just compute the sample proportion (-help tabulate-).
At the same time, even if not strictly necessary, any (generalised linear) regression model will do: eg, linear, logistic, log-binomial... (see output below).
Different story if you are interested in obtaining a valid 95% confidence interval too.

. webuse lbw
(Hosmer & Lemeshow data)

.
. // prevalence of low = 1
. tabulate low

Birthweight |
     <2500g |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |        130       68.78       68.78
          1 |         59       31.22      100.00
------------+-----------------------------------
      Total |        189      100.00

.
. regress low, noheader
------------------------------------------------------------------------------
         low | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   .3121693   .0337954     9.24   0.000     .2455025    .3788361
------------------------------------------------------------------------------

. poisson low, irr nolog

Poisson regression                                     Number of obs =     189
                                                       LR chi2(0)    =   -0.00
                                                       Prob > chi2   =       .
Log likelihood = -127.68836                            Pseudo R2     = -0.0000

------------------------------------------------------------------------------
         low |  Inc. rate   Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   .3121693    .040641    -8.94   0.000     .2418651    .4029092
------------------------------------------------------------------------------

. logit low, nolog

Logistic regression                                    Number of obs =     189
                                                       LR chi2(0)    =   -0.00
                                                       Prob > chi2   =       .
Log likelihood = -117.336                              Pseudo R2     = -0.0000

------------------------------------------------------------------------------
         low | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   -.789997    .156976    -5.03   0.000    -1.097664   -.4823297
------------------------------------------------------------------------------

. di invlogit(_b[_cons])
.31216931

. binreg low, rr nolog

Generalized linear models                         Number of obs   =        189
Optimization     : MQL Fisher scoring             Residual df     =        188
                   (IRLS EIM)                     Scale parameter =          1
Deviance         =  234.6719962                   (1/df) Deviance =   1.248255
Pearson          =  188.9999975                   (1/df) Pearson  =   1.005319

Variance function: V(u) = u*(1-u)                 [Bernoulli]
Link function    : g(u) = ln(u)                   [Log]

                                                  BIC             =  -750.7764

------------------------------------------------------------------------------
             |                 EIM
         low |       Risk   std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |   .3121693   .0337058   -10.78   0.000     .2526292     .385742
------------------------------------------------------------------------------

.
end of do-file

[Zhianni Yang]

Hi, thank you for answering. I forgot to mention that mdr is a variable which consists of three response= 0 (no resistance), 1 (resistant to 1 drug), and 2 (to 2 drug). How am I supposed to interpret this, or would it be better to categorize them all into 2 different cattegories (0=no resistant) (1=resistant)?

[Andrea Discacciati]

would it be better to categorize them all into 2 different cattegories (0=no resistant) (1=resistant)?

It's impossible for us to tell what the "best" thing to do is. It depends on your research question, which we don't know anything about.

That said, if mdr is a numeric variable that takes on values 0/1/2, the exponentiated coefficient (constant) from your Poisson model cannot be interpreted as a sample proportion (to be clear: it's *not* equal to the sample proportion of "1 or 2's" or to the sample proportion of "2's", for example). You can check it yourself with the -tabulate- command (see a toy example below).
0.736... is equal to the sample mean of the mdr variable, which is a meaningless quantity in this case.

. clear

.
. set seed 44

. set obs 100
Number of observations (_N) was 0, now 100.

. gen y = rbinomial(1, 0.2) + rbinomial(1, 0.2)

.
. // Sample proportions
. tabulate y

          y |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |         57       57.00       57.00
          1 |         40       40.00       97.00
          2 |          3        3.00      100.00
------------+-----------------------------------
      Total |        100      100.00

.
. // NOT sample proportion! 0.46 is equal to the (sample) mean of y
. poisson y, irr nolog

Poisson regression                                      Number of obs =    100
                                                        LR chi2(0)    =   0.00
                                                        Prob > chi2   =      .
Log likelihood = -83.799766                             Pseudo R2     = 0.0000

------------------------------------------------------------------------------
           y |  Inc. rate   Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
       _cons |        .46   .0678233    -5.27   0.000     .3445522    .6141305
------------------------------------------------------------------------------

. summarize y

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
           y |        100         .46    .5581354          0          2

.
end of do-file