Cox proportional hazard model

[Julia Stelz]

Hello everyone,

I am trying to replicate a part of this paper for my master thesis. In the paper, the authors state: "The last two columns of Table 7 report the regression results from a proportional hazard Cox model. We use a sample of 765 successful mergers(..). The dependent variable is the number of days to complete the deal between the announcement date and the effective date."

https://pdf.sciencedirectassets.com/...qb&type=client

I have created a similar dependent variable for my own study which solely consists of days to deal completion. As in the original study, I did not include incomplete or withdrawn mergers.

However, when setting up the Cox model, stata is asking me to define a failure condition. As all of my included deals were completed and therefore belong to the survival condition, I do not get any meaningful results when running the model this way (coefficient is one, no p-value).

My question is now if there is any way of using the Cox model with the described variable. If the authors of the study managed to do it, there must be a way. i just haven't been able to figure out exactly to do it.

Thank you for your help,
Julia

[Carlo Lazzaro]

Julia:
time to complete deal cannot be the dependent variable of a surival regression model (semiparametric, like Cox, or parametric like Weibull and other); the dependedent variable should be an event (failure, although, despite, its seemingly gloomy definition can well be a postive result) such as successful/unsuccesfull mergers, as reported in the caption of Table 7 of the working paper (https://poseidon01.ssrn.com/delivery...118078&EXT=pdf) that preceded the article you mentioned.

[Julia Stelz]

Dear Carlo,

Thank you for your answer. My apologies, but I am not very familiar with the Cox (and similar) model(s) yet, so maybe that is why I don't understand entirely.
In the table 7, in the link you posted it also says: "In columns (7) and (8), we use a non-parametric Cox model to estimate the regressions. The dependent variable is the number of days spent to complete the deal (i.e., the length of days from the announcement date to the effective date)." The author (I emailed her) added to it: "For Cox model, you need to define the length of a time horizon as dependent variable. In our regression, it is the number of days between announcement date and completion date of mergers. Therefore, it won't be possible to include deals that are not completed."

If I now create a dummy DV for successful/unsuccessful mergers, all data points would be for the 'successful' outcome, right? If I were to use this variable, how then would I include the number of days, to show that my IV has an effect on time to deal completion? Like I said, I might be missing a fundamental point here and would be grateful for any suggestions :-)

Thank you,
Julia

[Carlo Lazzaro]

Julia:
as per Author's reply, it seems that they consider that all the merges were successfull.
Hence, in Stata-ish, you should set -failure=1- for the entire sample.
I do hope that the folowing example, that follows a similar approach, can be helpful:

. use http://www.stata-press.com/data/r15/kva
(Generator experiment)

. stset failtime

     failure event:  (assumed to fail at time=failtime)
obs. time interval:  (0, failtime]
 exit on or before:  failure

------------------------------------------------------------------------------
         12  total observations
          0  exclusions
------------------------------------------------------------------------------
         12  observations remaining, representing
         12  failures in single-record/single-failure data
        896  total analysis time at risk and under observation
                                                at risk from t =         0
                                     earliest observed entry t =         0
                                          last observed exit t =       140

. stcox load bearings

         failure _d:  1 (meaning all fail)
   analysis time _t:  failtime

Iteration 0:   log likelihood = -20.274897
Iteration 1:   log likelihood = -10.515114
Iteration 2:   log likelihood = -8.8700259
Iteration 3:   log likelihood = -8.5915211
Iteration 4:   log likelihood = -8.5778991
Iteration 5:   log likelihood =  -8.577853
Refining estimates:
Iteration 0:   log likelihood =  -8.577853

Cox regression -- Breslow method for ties

No. of subjects =           12                  Number of obs    =          12
No. of failures =           12
Time at risk    =          896
                                                LR chi2(2)       =       23.39
Log likelihood  =    -8.577853                  Prob > chi2      =      0.0000

------------------------------------------------------------------------------
          _t | Haz. Ratio   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
        load |    1.52647   .2188172     2.95   0.003     1.152576    2.021653
    bearings |   .0636433   .0746609    -2.35   0.019     .0063855    .6343223
------------------------------------------------------------------------------

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