Kalpan Meier Curve

[Anuradha Saikia]

Hello everyone.
I am working on Cox regression using a panel dataset. My observation is 4029 with 255 firms. The following is a part of dataset what I used
input float C_ID int Time double Informality byte Failure double ROA
1 18 1.02 0 9.68
1 19 -.42 0 11.37
1 20 .39 0 15.66
1 21 .24 0 16.66
1 22 .04 0 11.86
1 23 .02 0 11.99
1 24 .01 0 12.97
1 25 -.05 0 6.92
1 26 .02 0 3.83
1 27 -.34 0 2.99
1 28 .35 0 7.06
1 29 .23 0 12.99
1 30 .01 0 12.13
1 31 .07 0 14.15
1 32 -.02 0 12.61
1 33 .09 0 8.05
1 34 -.03 0 5.02
2 56 -.22 0 6.43
2 57 -.42 0 6.72
2 58 .39 0 7.2
2 59 .24 0 8.74
2 60 .04 0 9.47
2 61 .02 0 5.86
2 62 .01 0 .95
2 63 -.05 0 2.15
2 64 .02 0 1.47
2 65 -.34 0 1.93
2 66 .35 0 2.29
2 67 .23 0 3.54
2 68 .01 0 3.89
2 69 .07 0 4.37
2 70 -.02 0 6.31
2 71 .09 0 3.79
2 72 -.03 0 3.04
3 6 -.36 0 73.54
3 7 -.34 0 23.98
3 8 .39 0 20.96
3 9 .25 0 16.02
3 10 .05 0 36.97
3 11 -.02 0 22.29
3 12 .04 0 14.62
3 13 0 0 12.84
3 14 -.07 0 14.62
3 15 -.49 0 27.82
3 16 .7 0 73.17
3 17 .3 0 27.63
3 18 -.04 0 49.05
3 19 .02 0 21.81
3 20 .08 0 44.49
3 21 .13 0 23.93
3 22 -.04 0 30.87
4 9 .01 0 35.63
4 10 -.29 0 6.57
4 11 .21 0 11.42
4 12 .22 0 15.86
4 13 .01 0 15.36
4 14 -.01 0 23.5
4 15 -.02 0 5.01
4 16 -.02 0 5.61
4 17 .02 0 8.91
4 18 -.4 0 10.87
4 19 .37 0 6.54
4 20 .25 0 4.58
4 21 -.01 0 5.19
4 22 .02 0 23.51
4 23 -.01 0 35.08
4 24 .03 0 34.43
4 25 -.04 0 35.42
5 61 .04 0 13.53
5 62 -.39 0 6.81
5 63 .33 0 4.36
5 64 .24 0 4.39
5 65 .01 0 3.3
5 66 -.01 0 3.47
5 67 -.02 0 3.43
5 68 0 0 5.78
5 69 0 0 5.92
5 70 -.49 0 5.35
5 71 .58 0 6.41
5 72 .26 0 6.6
5 73 0 0 13.14
5 74 0 0 18
5 75 .01 0 316.4
5 76 .05 0 351.51
5 77 -.03 0 365.06
6 9 -.02 0 15.57
6 10 -.39 0 15.68
6 11 .33 0 4.44
6 12 .24 0 6.06
6 13 .01 0 6.98
6 14 -.01 0 6.8
6 15 -.02 0 8.44
6 16 0 0 9.67
6 17 0 0 9.75
6 18 -.49 0 5.94
6 19 .58 0 4.29
6 20 .26 0 8.9
6 21 0 0 14.47
6 22 0 0 12.38
6 23 .01 0 2.08
the main independent variable is informality; failure is the event for firm liquidation, and time is the time to liquidation. ROA is firm profit. Here failure event coded as 1 is not visible and it comes later. I tried to plot the Kalpan Meier curves after Cox regression. But the graph does not look appropriate. Kindly help. Also, there are two groups based on firm resource diversification. Please help me understand what is wrong with the graph and why. It will be very helpful as this is my thesis work.

[Carlo Lazzaro]

Anuradha:
I'm under the impression that the two KM curve do overlap before drifting apart from, say, 65 onwards.
Why thyy do behave this way, I do not know, and your excerpt (with no Failure=1) does not help, unfortunately.

. sum F

    Variable |        Obs        Mean    Std. dev.       Min        Max
-------------+---------------------------------------------------------
     Failure |        100           0           0          0          0

[Anuradha Saikia]

Thank you Carlo Lazzaro . I do not know myself too, but my number of firms undergoing failure as in coded as failure=1, is only 20. Could a small sample of failure firms be the cause ?

[Carlo Lazzaro]

Anuradha:
yes, it might be.
What does the logrank test tell you?

[Paul Dickman]

I tried to plot the Kaplan Meier curves after Cox regression. But the graph does not look appropriate. Please help me understand what is wrong with the graph and why.

What is it that you think is "not appropriate" or "wrong"? Without more information we can only guess. Carlo, I believe, guessed that you didn't expect survival to be so high and it seems that this is simply due to the number of failures being relatively small.

Or is the problem that you wanted to plot curves based on the fitted Cox model and therefore expected them to follow a similar pattern due to the proportional hazards assumption? Here's an example (from the online help) of plotting curves based on a fitted Cox model:

webuse drugtr
stcox age drug
stcurve, survival at1(drug=0) at2(drug=1)

You will see that the default graph title (at least in version 18) is "Cox proportional hazards regression". The title in your graph is what one gets by default with:

sts graph, by(drug)

These are empirical curves and have nothing to do with the Cox regression model you fitted. You'll get the same curves without fitting a Cox model.

Please, explain why you think the curve you got is wrong (i.e., how does it differ from what you expected) and also show the code you used.

[Anuradha Saikia]

Thank you Paul Dickman. I am posting the code of the cox regression which is used on my panel data .

 stcox Informality  POLRISK HHI SIZE RD ESG SG Sub_Diversification, vce(robust)

Here informality is my main independent variable . The output is what I got as below

         failure _d:  Failure
   analysis time _t:  Time

Iteration 0:   log pseudolikelihood = -140.81549
Iteration 1:   log pseudolikelihood = -132.50115
Iteration 2:   log pseudolikelihood = -132.03338
Iteration 3:   log pseudolikelihood = -132.02234
Iteration 4:   log pseudolikelihood = -132.02234
Refining estimates:
Iteration 0:   log pseudolikelihood = -132.02234

Cox regression -- Breslow method for ties

No. of subjects      =        4,023             Number of obs    =       4,023
No. of failures      =           20
Time at risk         =        99038
                                                Wald chi2(8)     =       41.64
Log pseudolikelihood =   -132.02234             Prob > chi2      =      0.0000

-------------------------------------------------------------------------------------
                    |               Robust
                 _t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
--------------------+----------------------------------------------------------------
        Informality |   .3067587   .1551332    -2.34   0.019     .1138491    .8265409
            POLRISK |   1.61e+07   1.45e+08     1.84   0.066     .3240018    7.97e+14
                HHI |    1.23364   .5463154     0.47   0.635     .5178869    2.938608
               SIZE |   .9017934   .0406553    -2.29   0.022     .8255295    .9851028
                 RD |   1.085062   .0376696     2.35   0.019     1.013687    1.161463
                ESG |   1.042232   .0173778     2.48   0.013     1.008723    1.076855
                 SG |   .8022922   .6836328    -0.26   0.796     .1510164     4.26227
Sub_Diversification |   .5433092   .3179976    -1.04   0.297     .1725205    1.711013
-------------------------------------------------------------------------------------

.

THEN I used the following code for Kaplan Maeier failure curve

  sts graph, failure

.

[Anuradha Saikia]

I get the following Kaplan Maeir curve which I am not able to interpret.

[Paul Dickman]

The "failure curve" is one minus survival. It shows the estimated probability of failure as a function of time. There are relatively few failures (only 20) in your data so the the probabilities are low.

Note that the curve is completely independent of the Cox model. You would get the same curve without ever fitting a Cox model.

[Anuradha Saikia]

Okay Paul Dickman . I understand the concern is with my less failure firms .