Covariate is collinear with time variable in CPHM

[Tom Menard]

Hello,

when running my CPHM, I get missing standard errors for one particular covariate. The covariate describes the generation in control of a company, and is built by dividing the age of the company by 25.
The companies I am looking at are all left truncated, given that they were theoretically at risk of experiencing the event since the founding. To account for that, I used the age as the survival time - now age (time variable) and generation are obviously heavily correlated.

How do I deal with that? Is there any other way then excluding this covariate?

Here is an example of my data and the -stset- I used:

* Example generated by -dataex-. To install: ssc install dataex
clear
input str17 bvd_id float(exit age origin gen_control) int(_t _t0)
"DE11797" 0  8 0 1  .  .
"DE11797" 0  9 0 1  9  8
"DE11797" 0 10 0 1 10  9
"DE11797" 0 11 0 1 11 10
"DE11797" 0 12 0 1 12 11
"DE11797" 0 13 0 1 13 12
"DE11797" 0 14 0 1 14 13
"DE11797" 0 15 0 1 15 14
"DE11797" 0 16 0 1 16 15
"DE11797" 0 17 0 1 17 16
"DE14088" 0 58 0 3  .  .
"DE14088" 0 59 0 3 59 58
"DE14088" 0 60 0 3 60 59
"DE14088" 0 61 0 3 61 60
"DE14088" 0 62 0 3 62 61
"DE14088" 0 63 0 3 63 62
"DE14088" 0 64 0 3 64 63
"DE14088" 0 65 0 3 65 64
"DE14088" 0 66 0 3 66 65
"DE14088" 0 67 0 3 67 66
end

stset age, id(bvd_id) failure(exit==1) enter(age) origin(origin)

I appreciate any help.

[Steve Samuels]

Your question will probably answer itself if you try to include the collinear variable in an stcox statement.

[Steve Samuels]

To answer your question directly: you'll have to exclude the collinear variable. Here's what will happen if it's in the Cox model, assuming that the model converges.

. sysuse auto, clear
(1978 Automobile Data)

. stset mpg , fail(foreign)
                                 
. gen new = mpg/2

. stcox gear new

         failure _d:  foreign
   analysis time _t:  mpg

[iteration table omitted]]

Cox regression -- Breslow method for ties

No. of subjects =           74                  Number of obs    =          74
No. of failures =           22
Time at risk    =         1576
                                                LR chi2(0)       =       80.69
Log likelihood  =   -22.814938                  Prob > chi2      =           .

------------------------------------------------------------------------------
          _t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
  gear_ratio |   28.62453          .        .       .            .           .
         new |   .0066014          .        .       .            .           .
------------------------------------------------------------------------------