interpretation of correlation matrix of regression coefficients in Cox regression?

Question

I am using SPSS to perform Cox regression. After finding all the significant covariates, there is a table called correlation matrix of regression coefficients.

My question is what kind of information can I interpret from this table? If I see high correlations between the regression coefficients of two covariates, for example it is 0.99 between the regression coefficients of PCPT and LTCPT in the table below.

Does it mean that I need to be more careful with the results? I have checked the similarity among all the variables. According to the similarity matrix, there is no high correlation between PCPT and LTCPT though.

Correlation Matrix of Regression Coefficients:

              ACT    ATP      ALT   LTCPT   MALTCPT OIWSF_YEAR
 ATP         .109                   
 ALT        -.126   .044                
 LTCPT       .055   .008    -.240           
 MALTCPT     .031   .025     .052   .169        
 OIWSF_YEAR  .058   .062    -.079   .166    .062    
 PCPT        .044  -.072    -.252   .990    .053    .156

Answer 1

High correlations between coefficient estimates indicate a nearly singular fisher information matrix, which indicates near non-identifiability of your model. A common source of non-identifiability is when you have complete separation (e.g. everyone with a particular covariate combination does, or does not survive; this is most common with categorical predictors) or you have a covariate that is (nearly) a linear combination of the others. In this case, it looks like PCPT and LTCPT are probably highly correlated.

Answer 2

Regarding the correlation coefficients of the regression coefficients, they will be useful for simulation, but their original use stems from the original covariance matrix, where the square root of the diagonal elements forms the standard errors of regression coefficients used to calculate the t-test for each coefficient, i.e, $t_j=\beta_j/s.e.(\beta_j)$.