ROC analysis - what to do when the base rate is low

I'd be incredibly grateful to anyone who could help me with a ROC analysis problem.
Study background
I'm currently working on my PhD looking at the predictive validity of two risk assessment tools (violence and sexual violence) when implemented in clincal practice. The outcome data are violent incidents (minor and serious), and reconviction. I've used ROC analysis to assess if the tools can accurately differentiate between violent and non-violent individuals. And I've also conducted a survival analysis on those outcome data where the AUC results was statistically significant.
I did a power analysis prior to the study, so can confirm that my sample is big enough (n = 109) to ensure sufficient power to detect statistical differences between violent and non-violent people.

For the violence risk assessment tool, I found only 3 serious incidents. For the sexual violence risk assessment tool, there was only 1 serious incident.

My concern is that both risk assessment tools were only statistically predicitve for serious incidents, i.e. the outcome variable with the least number of events. In fact, for the sexual violence risk assessment tool (where n = 1 serious incident), the AUC on one subscale was 1.0, i.e. perfect. This just does not seem right.
Also, while the survival analysis reflects the pattern of the ROC analysis, and though the overall sample size (n = 109) is sufficient, I don't think I can use this analysis as there are so few serious incidents.

Possible explanations
I understand that ROC analysis does not take account of outliers, so perhaps those with a serious incident were outliers and therefore impact on the statistics. However, I checked if those with a serious incident were different from those without a serious incident, and while I am aware that the sample sizes are different (3 vs 106), the two samples are similar in terms of number of minor incidents.

I also understand that while a difference in scores may be statistically significant on the ROC curve, this does not mean that it is clinically relevant. So any interpretation of these results needs to be done with caution.

The main point is that ROC analysis is supposed to be independent of the number of events, so theoretically this should not impact on my results, but it just does not seem right. I have searched the literature but have not come across any research paper reporting ROC results on a small number of events, hence I have no comparison.

I would be very grateful for any advice or guidance. Perhaps, somebody knows of a more appropriate analysis to use?

Thank you, Gaby