Odds ratio from logistic regression isn't negative when it should be

Question

I just recently started working with logistic regression, and I'm struggling with the interpretation of the results.

Say I have brain disease (BD) as an outcome and gestational age (GE) as an explanatory variable. The OR is 0.99. I have used R to calculate this:

gl1 <- glm(BD~GE, data, family = "binomial")

How do I know what my reference group is in this case? Does the model pick a reference for me? Individuals with disease is explained by 1, and individuals with no disease are 0. The clinical theory is that individuals with a low GE is more likely to get BD.

But this doesn't make sense to me in this case. Every time I Google this issue, I get: "every increase of GE is associated with 0.99 times the odds of BD". But shouldn't it be opposite? That is, every decrease of GE, is associated with 0.99 time the odds of BD?

Answer 1

It may help to read more about how odds work. A place to start might be: Interpretation of simple predictions to odds ratios in logistic regression.

To answer your specific question, $0.99$ is a negative relationship. Every time you increase gestational age by $1$ unit (week?) the odds of having a brain disease is multiplied by $0.99$. That's less than $1.0$, so the odds are decreasing. To illustrate, let's imagine the odds of brain disease for babies born at $30$ weeks is $1.0$. Now, let's see what happens to the odds of brain disease as babies are born later (less early):

      week  odds(BD)
 [1,]   30 1.0000000
 [2,]   31 0.9900000
 [3,]   32 0.9801000
 [4,]   33 0.9702990
 [5,]   34 0.9605960
 [6,]   35 0.9509900
 [7,]   36 0.9414801
 [8,]   37 0.9320653
 [9,]   38 0.9227447
[10,]   39 0.9135172
[11,]   40 0.9043821

The odds are in fact decreasing.