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

Dear all

I am evaluating a surgical risk factor in a small retrospective study (N=20, 6 events). The potential risk factor is a continuous variable measured during the operation. I am fully aware of the limitations of such a small sample size, but I’ve applied several robust methods to address potential bias and instability. I would like to know if these findings hold some clinical/statistical weight, or if they should be dismissed as “nonsense.”

Methods & Results:

• Univariable Firth’s Penalized Regression: OR 1.259 (95% CI: 1.028–1.759), p=0.02.

• BCa Bootstrap (1,000 resamples): 95% CI for OR was 1.008–1.810 (does not cross 1.0).

• Internal Validation of the model: Apparent AUC was 0.7738. Using bootstrap-based optimism correction, the mean optimism was only 0.0016 (Bias-corrected AUC: 0.7722).

The Question: Does the fact that the signal survived both Firth’s penalization and BCa-bootstrap correction provide some compelling evidence for a pilot study? Or is it still statistically non-sensical to draw any conclusions from such a small dataset?

I’d appreciate your critical and candid views.