Proc Surveylogistic Link=Glogit: Are the "Odds Ratio Estimates" actually Relative Risk Ratios (RRRs)

[YYK273]

Hi SAS Community,

I am currently running a multinomial logistic regression analysis using PROC SURVEYLOGISTIC with LINK=GLOGIT. The dependent variable (group) has 4 categories (1, 2, 3, 4), with category 4 as the reference group. All covariates are categorical except for age, which is continuous. Below is my SAS code and log:

proc surveylogistic data=mydata;
    class group(ref='4') RArace(ref=first) ragender(ref=last) 
          RAEDUC4(ref=last) HwATOTBcd(ref=last) RWSTROKE(ref=first) 
          RWDIABE(ref=first) RWHEARTE(ref=first) RWHIBPE(ref=first) 
          BMIcd(ref='2.18.5-24.9') flag_mixall_COH(ref=first) / param=ref;
    model group = flag_mixall_COH BLRAGEY RArace ragender RAEDUC4 HwATOTBcd 
                   RWSTROKE RWDIABE RWHEARTE RWHIBPE BMIcd / link=glogit df=infinity;
    weight RWTCRNH0_SD;
    cluster RAEHSAMP;
    strata RAESTRAT;
run;

NOTE: PROC SURVEYLOGISTIC is fitting the generalized logitmodel. The logits modeled contrast each response categoryagainst the reference category (GROUP=4).NOTE: Convergence criterion (GCONV=1E-8) satisfied.NOTE: Only one cluster in a stratum. The estimate of variancewill omit this stratum.NOTE: Only one cluster in a stratum. The estimate of variancewill omit this stratum.NOTE: Only one cluster in a stratum. The estimate of variancewill omit this stratum.NOTE: PROCEDURE SURVEYLOGISTIC used (Total process time):real time 0.61 seconds

Questions:

1. Does the code look correct for my analysis, given that group is nominal and I am accounting for survey design (weights, clusters, and strata)?

2. In the output, SAS provides a table titled "Odds Ratio Estimates." However, according to the SAS documentation, the generalized logit model for nominal outcomes is expressed as:
   

3. Based on this formula, if I exponentiate the Maximum Likelihood Estimates, the resulting values should be Relative Risk Ratios (RRRs), not Odds Ratios (ORs), correct?

4. Could the "Odds Ratio Estimates" table in the SAS output be actually represent RRRs since I used LINK=GLOGIT? If not, how can I compute RRRs?

5. Any other advice or clarifications about my code or understanding of the output?
   
   Thank you so much for your help! I want to ensure I am interpreting the results correctly and that my analysis setup is appropriate.

[SAS_Rob · Accepted solution]

Based on the description you gave, the code appears to be correct.

The reported odds ratios are actually odds ratios.  When you use the default effects coding for the CLASS variables then the OR are no longer calculated as Exp(Beta).  The LOGISTIC documentation has some further details on this:

SAS Help Center: Odds Ratio Estimation

As far as calculating the relative risk is concerned you should be able to use the approach detailed in this usage note.  The only difference would obviously be that you would use SURVEYLOGISTIC instead of LOGISTIC.  Using the STORE statement in SURVEYLOGISTIC should be sufficient for getting the MACRO all that it needs.

57798 - Estimating relative risks in a multinomial response model

[YYK273]

Thank you so much! Very helpful!