[Clyde Schechter]

Sorry, I messed that up. Yes, it's true that the estimation is done on log hazard ratios. But in my calculations, I forgot to replace that 1.0106 by its logarithm, 0.01054. So, at rus = 1 and time = 1, hr = exp(0.01054*1*1) = 1.0106. At time = 2, hr = exp(0.01054*1*2) = 7.55.

For male, where the "hr" shown is 0.995, note that log(0.995) = -.005, which is negative. So for a male at time 1, we get hr = exp(-.005*1*1) = .995, and at time 2 we get hr(=exp-.005*1*2) = 0.990. At time 3 it will be exp(-.005*1*3) = .985, and so on. So, with a reported hr less than 1 we see that over time the actual hazard ratio decreases (as I imagine you expected.)

Really sorry for that error in presentation.

[chris lal]

Hi again. Picking back up on the same paper. I estimate a CPH and get the following results:

          _t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
private_school |   1.084918   .0131008     6.75   0.000     1.059542    1.110901
 parent_degree |   1.036325   .0085779     4.31   0.000     1.019648    1.053274
               |
   ucas_points |
            2  |   1.046038   .0149801     3.14   0.002     1.017086    1.075815
            3  |   1.098231   .0161512     6.37   0.000     1.067027    1.130347
            4  |   1.206048   .0195503    11.56   0.000     1.168332    1.244981
            5  |   1.256637    .023299    12.32   0.000     1.211792    1.303142
               |
   institution |
            2  |    1.33643   .0151982    25.50   0.000     1.306971    1.366552
            3  |   1.498578   .0162562    37.29   0.000     1.467053    1.530781
               |
      stem_deg |   1.368801   .0117528    36.56   0.000     1.345959    1.392031
   good_degree |   1.984004   .0289519    46.95   0.000     1.928064    2.041568
          male |   1.090991    .009065    10.48   0.000     1.073368    1.108904
         white |   .9940768   .0097113    -0.61   0.543     .9752241    1.013294

I ran

estat phtest

which identified variables that violate the proportional hazards assumption.

I re-estimated the model using the

tvc

option for variables that violated the ph assumption.

I get the following output

------------------------------------------------------------------------------
            _t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
---------------+----------------------------------------------------------------
main           |
 parent_degree |   1.069952   .0087547     8.26   0.000      1.05293    1.087249
   good_degree |   2.033264   .0295145    48.89   0.000     1.976232    2.091942
      stem_deg |   1.440901    .012121    43.42   0.000     1.417339    1.464854
---------------+----------------------------------------------------------------
tvc            |
   ucas_points |
            2  |   1.003136   .0024505     1.28   0.200     .9983443     1.00795
            3  |   1.005227   .0025247     2.08   0.038     1.000291    1.010188
            4  |   1.018113   .0027929     6.54   0.000     1.012653    1.023601
            5  |   1.022258   .0032001     7.03   0.000     1.016005     1.02855
               |
private_school |   1.012391   .0020176     6.18   0.000     1.008444    1.016353
               |
   institution |
            2  |   1.042142   .0020272    21.22   0.000     1.038177    1.046123
            3  |   1.064581   .0019526    34.12   0.000     1.060761    1.068415
               |
          male |   .9957625   .0013836    -3.06   0.002     .9930543    .9984781
         white |   .9960991   .0016262    -2.39   0.017      .992917    .9992915

My question is about a variables such as male and white. Male is greater than 1 in the original estimates, but less than 1 when estimated using the tvc option. Is there a generic way from to explain that switch? Is it simply the case that as Male violates the ph assumption in the first model, that the estimate for the variable is simply discarded/meaningless, and that the only relevant value is that of the second model, where it is correctly estimated using the tvc option. Does the same premise apply to White, which also violated the ph assumption in the original, but was insignificant, before becoming significant in the second set of estimates. Is the insignificance of the estimate in the first set of estimates again simply ignored, as it violated the ph assumption.?