I have a very small sample size n=8 in which I have the estimated survival date of each individual and 5 behavioural traits which I would like to correlate with their survival. Can I run an regression model with bootstrap? Is it possivel to run a cox regression?

Is there any analysis that will make sense with this data? Even if I select one of the variable that I hypothesize as most strong for the model or run a PCA? Or shall I throw this data away as it will be useless for any kind of analysis...

It depends. What is the context - why or what for do you perform the analysis?
What is you study about, and what are your research questions? How did you
gather your data?

I think a basic issue, which tends to get ignored in a lot of analysis since it is not a formal statistical requirement is whether you can generalize to anything with just 8 cases. This deals with external not internal validity.

Well my rebuttal would be sure you could do bivariate survival analysis, just make sure you slap those confidence intervals on the estimates and plots!!!

Well my rebuttal would be sure you could do bivariate survival analysis, just make sure you slap those confidence intervals on the estimates and plots!!!

So if you have a population of say ten million you think you can generalize to it with 8 cases I know a lot of pollsters who would be really happy to know that.

If you cannot convince someone not to do something with small sample, tell 'em to slap CI's on it (e.g., HR: 1.1 [95% CI: 0.1, 677.0) should be convincing enough.

I am not sure that addresses generalization to the population (external not internal validity). Or are you saying with a small sample size the CI will be so large relative to the effect size that no one will do it