Cox regression with 6 variables in 30-something patients sample, is it legitimate?


I'm doing some research and I have a sample of 33 patients. I'm testing an association of one new parameter (let's call it X) on survival and comparing it to previous prognostic score calculated from 5 parameters.

- When I compare X with each out of 5 prognostic parameters in a series of bivariate Cox models I get significant result for X in each case (5 comparisons, p<0.01 - Bonferroni corrected).
- When I compare X with prognostic score derived from aforementioned parameters I get significant overall model fit, but insignificant result for both X and the score.
- When I compare X in a common model (X+5 variables) I get significant overall model fit and significant result for X while tested variables get knocked out from the model (forward selection) or get insignificant (enter model). Is this legitimate? I know the rule of thumb for max. number of variables is total N divided by 10. However, I have 5 established variables that I would like to test.

Thank you in advance, Kind regards