Variance Inflation Factors (or other collinearity measures) with Survival Analysis

[Rahul Muthalaly]

Hi All,

I am performing a survival analysis on a group of patients with a few measures derived from imaging to see if those measures predict outcomes.

I am concerned that many of these measures may be collinear and thus, do not want to include them in the same cox proportional hazards model. I have previously used the variance inflation factor (VIF) as a rough guide of collinearity. Is it possible to measure VIF or an equivalent collinearity parameter in cox PH regression?

Am I best off just seeing if the variables are correlated using a scatter plot? Do you have any pointers regarding whether it is appropriate to include two potentially collinear variables in a multivariate model?

Cheers!

[Carlo Lazzaro]

Rahul:
extreme multicollinearity is dealt by Stata automatically.
Quasi-extreme multicollinearity after -stcox- can be investigated via -estat vce, corr-:

. use "http://www.stata-press.com/data/r14/drugtr.dta", clear
(Patient Survival in Drug Trial)

. stcox i.drug age

         failure _d:  died
   analysis time _t:  studytime

Iteration 0:   log likelihood = -99.911448
Iteration 1:   log likelihood = -83.551879
Iteration 2:   log likelihood = -83.324009
Iteration 3:   log likelihood = -83.323546
Refining estimates:
Iteration 0:   log likelihood = -83.323546

Cox regression -- Breslow method for ties

No. of subjects =           48                  Number of obs    =          48
No. of failures =           31
Time at risk    =          744
                                                LR chi2(2)       =       33.18
Log likelihood  =   -83.323546                  Prob > chi2      =      0.0000

------------------------------------------------------------------------------
          _t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
      1.drug |   .1048772   .0477017    -4.96   0.000     .0430057    .2557622
         age |   1.120325   .0417711     3.05   0.002     1.041375     1.20526
------------------------------------------------------------------------------


. estat vce, corr

Correlation matrix of coefficients of cox model

             |        1.         
        e(V) |     drug       age
-------------+--------------------
      1.drug |   1.0000          
         age |  -0.2281    1.0000

.

[Rahul Muthalaly]

Hi Carlo,

Thanks for the informative answer. In interpreting the correlation coefficients for the variables in that model does it come down to a personal threshold for identifying variables as collinear? Eg, I set a threshold of .80 above which I become concerned for collinearity?

Alternatively, is there a consensus for when collinearity is likely to be a problem?

[Carlo Lazzaro]

Rahul:
not to my knowledge, at least.
Personally, 0.75 triggers a warning chime.

[Richard Williams]

I don't think there is any simple answer to that question. If you drop variables, you run the risk of omitted variable bias. If the sample is large, multicollinearit may cause more problems than when it is small. See the following, esp. p. 4, for a discussion of multicollineaity and what to do about it.

http://www3.nd.edu/~rwilliam/stats2/l11.pdf