Kreara

Calculation of adjusted odds ratio using Proc logistic

Prepared by Resmi Sukumar

Adjusted odds ratios are the odds of a dichotomous event adjusted for or controlling for other possible variables in the model. For example in a model where the response variable is the presence or absence of a disease, an odds ratio for a binomial exposure variable is an adjusted odds ratio for the levels of all other risk factor included in the model.

Adjusted odds ratio and corresponding 95% confidence interval is obtained by performing logistic regression analysis, this technique is implemented in the SAS® System using PROC LOGISTIC.

Logistic regression analysis provides adjusted odds ratio if adjustors are used as additional predictors, otherwise it provides unadjusted odds ratio.

The general syntax of PROC LOGISTIC is:

PROC LOGISTIC DATA=dsn ;
MODEL depvar = indepvar(s)/options;
RUN;

Example:
Suppose we are interested in conducting a case control study to evaluate the relation among cases and controls between different genotypes. The different gene statuses are ‘abnormal’ and ‘normal’ where normal is considered as referent group. For this purpose we generate a dataset as follows

/*Random data generation*/

data genestat;
do i=1 to 50;
gene=round(1 + (3-1)*uniform(10));
age =round(1+(3-1)*uniform(15));
ethnic=round(1+(3-1)*uniform(14));
status=round(1+(2-1)*uniform(16));
cascon=round(1+(2-1)*uniform(17));
output;
end ;
drop i;
run;

/*formats */
proc format;
value gene 1= 'Gene1' 2= 'Gene2' 3= 'Gene3';
value cascon 1='Case' 2='Control';
value age 1='<18' 2="'18-35'" 3="'">35';
value ethnic 1='Asian' 2='Caucasian' 3='Other';
value status 1='Abnormal' 2='Normal ';

proc sort data=genestat ;
by gene;
format gene gene. cascon cascon. status status. age age. ethnic ethnic.;
run;

Let’s consider a model with variable status, age and ethnic are as predictors.

/*proc logistic for calculating adjusted odds ratio*/
ods trace on;
ods output CLoddsWald=gene_cancer(where=(Effect="status Abnormal vs Normal"));

proc logistic data=genestat;
class status/param=ref ref=last;/* reference parameter ref=last
i.e. ref='Normal'*/
model cascon=status age ethnic / clodds=both;/* clodds =gives WALD confidence Interval for odds ratio*/
by gene ;
run;

ods output close;
ods trace off;

The MODEL statement names the response variable and the explanatory effects, including covariates, main effects, interactions, and nested effects. The CLASS statement names the classification variables to be used in the analysis. The CLASS Statement permits specification of a reference level. By default, the lowest level of the variable placed in the CLASS Statement is treated as the reference category. The BY statement is used to obtain separate analyses on observations in groups defined by the BY variables.

The output table is obtained as

This shows that Gene1 and Gene2 are less likely to have the abnormal genotype status in case than control. Adjusted odds ratio for Gene3 shows that the odds of abnormal genotype occurring in the case group are higher than it occurring in control group.

Let's now consider the model where status is the only predictor.

/*proc logistic for calculating unadjusted odds ratio*/
ods trace on;
ods output CLoddsWald=gene_cancer(where=(Effect="status Abnormal vs Normal"));

proc logistic data=genestat;
class status/param=ref ref=last;/* reference parameter ref=last
i.e. ref='Normal'*/
model cascon=status / clodds=both;/* clodds =gives WALD confidence interval
for odds ratio*/
by gene ;
run;

ods output close;
ods trace off;

The output table is obtained as

This shows that the odds of abnormal genotype occurring in the case group are higher than it occurring in control group for gene 3 while it same for genes 1 and 2.