[Mithila shrestja]

Thank you All,
When I used

poisson glioma_cases ibn.dg_y ibn.AgeGroup, irr noconstant

It gave me output as:
poisson glioma_cases ibn.dg_y ibn.AgeGroup, irr noconstant
note: 18.AgeGroup omitted because of collinearity

Iteration 0: log likelihood = -4712.7613
Iteration 1: log likelihood = -3879.0241
Iteration 2: log likelihood = -3872.1993
Iteration 3: log likelihood = -3872.1943
Iteration 4: log likelihood = -3872.1943

Poisson regression Number of obs = 1584
Wald chi2(61) = 50379.35
Log likelihood = -3872.1943 Prob > chi2 = 0.0000

------------------------------------------------------------------------------
glioma_cases | IRR Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dg_y |
1970 | .386133 .0599448 -6.13 0.000 .2848348 .5234567
1971 | .3693446 .057729 -6.37 0.000 .2718867 .5017363

IRR is calculated for all years (not shown above) 1970-2013. Non of the year is omitted.

Then I made another analysis:

poisson glioma_cases i.dg_y i.AgeGroup i.sex, ir

poisson glioma_cases i.dg_y i.AgeGroup i.sex, ir

Iteration 0: log likelihood = -3845.3136
Iteration 1: log likelihood = -3835.2889
Iteration 2: log likelihood = -3835.1744
Iteration 3: log likelihood = -3835.1744

Poisson regression Number of obs = 1584
LR chi2(61) = 4564.99
Prob > chi2 = 0.0000
Log likelihood = -3835.1744 Pseudo R2 = 0.3731

------------------------------------------------------------------------------
glioma_cases | IRR Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dg_y |
1971 | .9565217 .1164529 -0.37 0.715 .7534671 1.214298
1972 | 1.065217 .126259 0.53 0.594 .8443962 1.343786


And finally,

margins dg_y, predict(ir)

margins dg_y, predict(ir)

Predictive margins Number of obs = 1584
Model VCE : OIM

Expression : Predicted incidence rate, predict(ir)

------------------------------------------------------------------------------
| Delta-method
| Margin Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
dg_y |
1970 | 3.833333 .326315 11.75 0.000 3.193768 4.472899
1971 | 3.666667 .3191424 11.49 0.000 3.041159 4.292174

It matches with the IRR in the above table.

I am not still getting how I could interpret margins as predicted incidence rates(per what???)

[Clyde Schechter]

It matches with the IRR in the above table.

No, it doesn't. Nor should it.

In the output you got from
poisson glioma_cases ibn.dg_y ibn.AgeGroup, irr noconstant the incidence rate ratios for each year are the incidence rates conditional on AgeGroup = the age-group that was dropped from the model to provide a reference category, in this case AgeGroup = 18. Moreover, sex does not appear in that model, so the results are marginal with respect to sex.

In the output from the analysis using -poisson- followed by -margins-, you are getting incidence rates that are adjusted for the distributions of Age Group and sex. These are completely different constructs from the above, and any resemblance between their numeric results is coincidental.

The units of the predicted incidence rates depend on how your data is structured. Assuming that each observation in your data set reflects the number of cases of glioma diagnosed in a particular age group and sex in a given year with some fixed number of members of people sampled for each such grouping. Let's say, for example, that each observation represents 10,000 people. Then the units for the incidence rates are cases per 10,000 person-years. If each observation represents 100,000 people, then it's cases per 100,000 person-years. And so on.

Now, if in fact each age group-sex-year combination has a different size population underlying it (which would be more typical of epidemiologic data), then your modeling is incomplete and the results are uninterpretable. In that case, you need to add a variable to your data set showing for each observation the number of people who were observed, and add that variable's name as an -exposure()- option in your -poisson- command.

[Richard Williams]

I'll just add that Clyde has better eyes than me or is less lazy at deciphering things. Put ALL the code and output between code tags, not just the command. It is really hard to read the output otherwise, and by the time something has gotten to post 17 I (unlike Clyde!) am not willing to put in the effort.

[Maarten Buis]

This is a rare occation where Clyde made a mistake: In #12 you get the incidence rates when adding the irr option not the incidence rate ratios because he left out the constant and used the ibn. prefix.

This only applies to year, as that is the variable that was completely added. Age had a reference category (as year already captured the constant, so a reference category was required for age)

I know it is somewhat confusing that something labeled incidence rate ratios is actual an incidence rate (or ratio of incidence ratios for interaction terms). For a long time this was the reason that Stata refused to give the constant whenever you asked for some irr, or or or rrr: that coefficient is not an incidence rate ratio, odds ratio or relative risk ratio, but a incidence rate, odds, or relative risk. I think it is right that the constant is now reported, but it does require that the user know the difference in meaning between these parameters.

[Mithila shrestja]

Thank you all for your comments and suggestions.

In # 16; I meant to say the predicted count of 1971 is (3.666667/3.833333)=0.956521 higher than the year 1970.I mean this matches with the table showing IRR as below:

poisson glioma_cases i.dg_y i.AgeGroup i.sex, irr

Iteration 0:   log likelihood = -3845.3136  
Iteration 1:   log likelihood = -3835.2889  
Iteration 2:   log likelihood = -3835.1744  
Iteration 3:   log likelihood = -3835.1744  

Poisson regression                                Number of obs   =       1584
                                                  LR chi2(61)     =    4564.99
                                                  Prob > chi2     =     0.0000
Log likelihood = -3835.1744                       Pseudo R2       =     0.3731

------------------------------------------------------------------------------
glioma_cases |        IRR   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        dg_y |
       1971  |   .9565217   .1164529    -0.37   0.715     .7534671    1.214298
       1972  |   1.065217    .126259     0.53   0.594     .8443962    1.343786

I am receiving different options to calculate age/sex adjusted incidence rates. I have tried both, the results are not same, so its dragging me in the pool of confusions.

First, I tried with

 poisson glioma_cases i.dg_y i.AgeGroup i.sex, exposure (pop) irr

Iteration 0:   log likelihood = -3616.7325  
Iteration 1:   log likelihood = -3596.5893  
Iteration 2:   log likelihood = -3596.4588  
Iteration 3:   log likelihood = -3596.4588  

Poisson regression                                Number of obs   =       1584
                                                  LR chi2(61)     =    4290.15
                                                  Prob > chi2     =     0.0000
Log likelihood = -3596.4588                       Pseudo R2       =     0.3736

------------------------------------------------------------------------------
glioma_cases |        IRR   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        dg_y |
       1971  |   .9458415   .1151529    -0.46   0.647     .7450537    1.200741
       1972  |   1.041913   .1234982     0.35   0.729     .8259203    1.314391

followed by margins:

margins dg_y, predict(ir)

Predictive margins                                Number of obs   =       1584
Model VCE    : OIM

Expression   : Predicted incidence rate, predict(ir)

------------------------------------------------------------------------------
             |            Delta-method
             |     Margin   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        dg_y |
       1970  |   .0000358   3.05e-06    11.71   0.000     .0000298    .0000418
       1971  |   .0000338   2.95e-06    11.46   0.000     .0000281    .0000396

Then,again

poisson glioma_cases ibn.dg_y ibn.AgeGroup ibn.sex, exposure(pop) irr nocons
note: 18.AgeGroup omitted because of collinearity
note: 2.sex omitted because of collinearity

Iteration 0:   log likelihood = -4365.3937  
Iteration 1:   log likelihood =  -3602.199  
Iteration 2:   log likelihood = -3596.4625  
Iteration 3:   log likelihood = -3596.4588  
Iteration 4:   log likelihood = -3596.4588  

Poisson regression                                Number of obs   =       1584
                                                  Wald chi2(62)   = 1005483.13
Log likelihood = -3596.4588                       Prob > chi2     =     0.0000

------------------------------------------------------------------------------
glioma_cases |        IRR   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        dg_y |
       1970  |   .0000182   2.85e-06   -69.78   0.000     .0000134    .0000248
       1971  |   .0000172   2.71e-06   -69.67   0.000     .0000127    .0000235

The incidence rates are not same. Please suggest me which one is correct way.

Thank you.

[Clyde Schechter]

It's not a question of which is "correct." They are different incidence rates. In the first instance (poisson glioma_case i.dgy..., followed by margins) you are getting yearly incidence rates that are adjusted for age-group and sex. In the second instance (poisson glioma_cases ibn.dg_y...), you are getting yearly incidence rates conditional on AgeGroup = 18 and sex = 2 (i.e. age-sex specific).

So both are "correct" for particular purposes. It depends on which one you want/need.

[Clyde Schechter]

@Maarten, #16. You are, of course, correct.

[Mithila shrestja]

Thank you so much Clyde. It helped me a lot.

[Mithila shrestja]

Now, I have age/sex adjusted incidence rates for all years (1970-2013).
How could I get overall age adjusted incidence rates, not for individual years.

[Clyde Schechter]

Rerun the -poisson- regresion, omitting the year variable. Then rerun margins (also without mentioning the year variable). (Note, if you want age-adjusted, and not age-sex adjusted, then also omit the sex variable.)