# Interpret odds ratios of ordinal independent variable in logistic regression

I have a set of data where I would like to do logistic regression modeling the odds of a binary outcome variable (Therapy), with Stage as an ordinal explanatory variable (0,1,2,3,4). I am using SAS. The output I have been given is this:

Odds Ratio Estimates and Wald Confidence Intervals
Odds Ratio  Estimate    95% Confidence Limits
Stage 1 vs 0    0.873   0.547   1.394
Stage 2 vs 0    2.434   0.895   6.620
Stage 3 vs 0    0.915   0.431   1.941
Stage 4 vs 0    0.356   0.132   0.961
Stage 2 vs 1    2.788   0.980   7.935
Stage 3 vs 1    1.048   0.465   2.360
Stage 4 vs 1    0.408   0.144   1.156
Stage 3 vs 2    0.376   0.113   1.249
Stage 4 vs 2    0.146   0.038   0.567
Stage 4 vs 3    0.389   0.117   1.288


If I am reporting Stage as an ordinal variable, then is it correct that I create a table like this:

Stage 1 vs 0    0.873   0.547   1.394
Stage 2 vs 1    2.788   0.98    7.935
Stage 3 vs 2    0.376   0.113   1.249
Stage 4 vs 3    0.389   0.117   1.288


Or, should I report it like this:

Stage 1 vs 0    0.873   0.547   1.394
Stage 2 vs 0    2.434   0.895   6.62
Stage 3 vs 0    0.915   0.431   1.941
Stage 4 vs 0    0.356   0.132   0.961


The variable in question, Stage, is a measure of severity of structural variation in an eye that is diagnosed based on set criteria. The differences between 1,2,3, and 4 are different, and 0 is the absence of this structural variation.

For reference, the following is my SAS code.

PROC LOGISTIC data=new;
class EyeID Therapy (ref ="0") Stage (param = ordinal) Gender (ref="M") Ethnicity (ref="C")/ param = ref;
model Therapy = Stage Gender age A1c Ethnicity;
oddsratio Stage;
run;


You could use either table. The choice depends on the question you want to use the odds ratios to answer.

Stage 1 vs 0    0.873   0.547   1.394
Stage 2 vs 1    2.788   0.98    7.935
Stage 3 vs 2    0.376   0.113   1.249
Stage 4 vs 3    0.389   0.117   1.288


What are the odds of therapy in Stage I severity compared to no structural variation (zero)? What are the odds of therapy in Stage II severity versus Stage I severity?...so on and so forth. These would answer the questions such as - are the differences in odds with each subsequent category similar, or are Stage 4 and Stage 3 both more likely to get therapy and therefore the difference (OR) is not substantial?

Single Referent Category

Stage 1 vs 0    0.873   0.547   1.394
Stage 2 vs 0    2.434   0.895   6.62
Stage 3 vs 0    0.915   0.431   1.941
Stage 4 vs 0    0.356   0.132   0.961


With single reference category we often choose the lowest or highest extreme. You might see a threshold effect here and choose to dichotomize or make a recommendation that "all patients with Stage X and above get therapy" etc.

Interesting with your results is that they show a similar pattern, where something is going on with Stage 2 being much more likely to receive therapy than Stage 0 or Stage 1 (adjacent analysis) per the point estimate. Statistically, however, your confidence intervals are large and all cross the null value of 1.0 so you may be lacking power here.