Are there any general guidelines for conducting explanatory (rather than predictive) logistic regression analysis when both the outcome variable and the predictor variable of interest are rare events?
I will be conducting a pooled regression analysis of around 50,000 general population survey responses, in order to understand the role of variable $x$ in increasing the frequency of $y=1$. $x=1$ in around 2.5% of responses, and $y=1$ in around 8% of cases.
So even under the null hypothesis of no association, we'd expect around 100 cases where $x=1 \wedge y=1$. From previous studies of treatment seeking convenience populations, we'd expect the odds ratio of $y=1$ given that $x=1$ to be in the range of 1.5 - 10.0. So the number of cases where$x=1 \wedge y=1$ is likely to be around the 150 - 1000 mark (I don't have access to these data yet).
I have previously been told that logistic regression does not perform well when the outcome variable is unbalanced. I have been told by a respected statistician that in this situation I should combine all of the cases where $y=1$ with a subsample of the cases where $y=0$ in order to balance the data set. However, Frank Harrell and others suggest that once the data has been collected, it would be a mistake to discard it except for computational reasons.
In this case, both the outcome variable and the predictor variable of interest are unbalanced. Are there any guidelines for analysis under these conditions?
Please note that I am not interested in mathematical proofs about biased estimators or the like. Rather, I am interested in guidelines for applied researchers about how to deal with real-world datasets like this.