Risk factor evaluation in a small surgical sample (N=20, Events=6)

It is mathematically impossible to assess differences when there are 6 events. That’s because you cannot even estimate risk in your situation if there are no predictors, i.e., you can’t even estimate the intercept in a logistic model were all slopes known to be zero. See this. So this is a futile project, unfortunately.

When doing penalization empirically (i.e., when not specifying a prior distribution to a Bayesian model) the sample size required to choose the right penalty can be quite large. It’s a lose-lose situation unfortunately.

The best you can do is to report a Wilson 0.95 confidence interval for the unknown outcome probability assuming homogeneous risk, which is [0.15, 0.52]. The point estimate of 0.3 is not meaningful. To nail down the average risk to 0.15 - 0.52 means we don’t know very much.