I have a dataset where the outcome is binary. 95% yes, 5% no. For whatever reason I decided to fit a fully adjusted model with other covariates like race, age, education and other demographics related variables. One variable that I had to include was “time’”. This is when participants responded to the outcome. The interesting thing about this is that the O.R , odds ratio for time is 1.34. One unit of time is 1 year. In theory the model suggests at 34% increase in Yes , each year. My question is , what does this OR of 34% increase every year mean when the outcome is already at 95% to begin with. I have 4 years worth of data in my study.
(as a pre p.s., I would suspect/query whether the handling of time is appropriate in this modelling setting, or if using some survival analysis or similar analysis that handles time from baseline differently is better. But can’t comment further on that from the details and that is a separate issue. I will answer the more general question here since it applies to any odds ratio with a common outcome.)
The issue is that the odds ratio is modelling the change in the odds for a one-unit change in the predictor (regardless of whether that predictor is time, or some other numerical measurement).
Your current interpretation of the OR is as though it were a relative risk, which only holds when the outcome is rare (both for unexposed and exposed settings).
In this context of a very-common outcome like this, an OR of 1.34 (for a one-unit change; the same would apply if this was the OR for a binary indicator) is a very small absolute difference in risk.
In this case, and ignoring adjustment (see below), with an “unexposed” probability of 0.95 and an OR of 1.34 for “exposed” (or a one-unit change in exposure), the “exposed” group probability would be 0.962.
Adjustment complicates things somewhat for conceptualisation, but can be ignored for the general point here that the absolute difference is small in this example.