I'm working a retrospective / prospective cohort study on a very rare disease (5 patients a year presenting in my institution). I have a sample of 30 patients that I was able to gather over several years with all available data.

I measured parameter A in my patients and noticed it significantly affects survival. There is also established international prognostic scoring system that significantly affects survival in my sample of patients (let's call this score parameter B). There is high correlation between these two parameters (p<0,001, r2=0,37). When I perform Cox regression analysis, I get significatnt overall model fit (p=0,025), but both parameter A and parameter B can't predict survival independently of each other in my small sample (p=0,098 and p=0,621 respectively). I believe it is due to high degree of correlation and they actually represent the same thing - disease activity.

When I include third measured parameter in a regression model (let's call it parameter C that is shown to affect survival of patients in previosuly published papers, but doesn't affect survival in my small sample (univariantly p>0,05)), my multivariate model on 30 patients returns significant effect of both parameter A (0,01) and parameter C (p=0,033) - parameter B (p=0,82) that is so far recognized prognosic score can't predict survival independently in a model including parameters A and C.

Is this legitimate analysis (since I have small nuber of patients and I included parameter insignificant in univariate analysis)?

Thank you in advance

P.S. - all parameters are numerical variables, I checked significance of univariate effect by including each one separately witohut others in Cox regression model.