Regular survival analysis versus competing risk analysis

[MIchael Jefferson]

Hi,

I have a question regarding my analysis setup for research on the exit-route for strategies adopted by private equity firms.
However, I wonder if my approach is correct. In the first code below, I separate all the different types of exit using dummy variables, meaning if Trade Sale=1, the rest is zero, and thereby censored, in my sample there are also strategies that have not exited yet.
This is done for multiple types of exit.

In the second, regression, code below, I use the competing risk approach for, for example, Financial Buyout versus Trade Sale. But then I wonder, isn't the first setup the same as the competing risks approach, only that in the second code I specify the competing event being a specific type of exit? I mean, in the first setup, all non-Trade Sale exits are competing events right?

Trade Sale as event, other types of exit are considered censored

stset E_Date, failure(TradeSale==1) id(Strategy_Number) enter(time P_Date) origin(time P_Date)

streg i.ComplexityOfStrategy i.Amount_of_addons Rushed2 i.Distance_Class Rushed_Strategy IVA IQA GDPA Hofstede i.Management_Participation ib(frequent).Entrytype Syndication PE_Experience PF_Experience PE_Experience_Total PF_Experience_Total logPFassets i.HOT_IPO i.HOT_MNA i.CountryGroup i.Exitgroup i.IndustryFE, dist(loglogistic)

     failure _d:  TradeSale == 1
   analysis time _t:  (E_Date-origin)
             origin:  time P_Date
  enter on or after:  time P_Date
                 id:  Strategy_Number

Fitting constant-only model:

Iteration 0:   log likelihood = -643.35433  (not concave)
Iteration 1:   log likelihood = -449.93009  
Iteration 2:   log likelihood = -413.70954  
Iteration 3:   log likelihood = -403.08911  
Iteration 4:   log likelihood = -403.05292  
Iteration 5:   log likelihood = -403.05291  

Fitting full model:

Iteration 0:   log likelihood = -403.05291  (not concave)
Iteration 1:   log likelihood = -287.19392  
Iteration 2:   log likelihood = -219.16267  
Iteration 3:   log likelihood =  -199.7606  
Iteration 4:   log likelihood = -195.86607  (backed up)
Iteration 5:   log likelihood = -190.08325  
Iteration 6:   log likelihood = -189.91269  
Iteration 7:   log likelihood =  -189.9027  
Iteration 8:   log likelihood = -189.90061  
Iteration 9:   log likelihood = -189.90017  
Iteration 10:  log likelihood = -189.90007  
Iteration 11:  log likelihood = -189.90005  
Iteration 12:  log likelihood = -189.90004  

Loglogistic AFT regression

No. of subjects =          917                  Number of obs    =         917
No. of failures =          148
Time at risk    =      2162758
                                                LR chi2(59)      =      426.31
Log likelihood  =   -189.90004                  Prob > chi2      =      0.0000

Trade Sale versus Financial Buyout


Competing risk command:

stset E_Date, failure(TradeSale==1) id(Strategy_Number) enter(time P_Date) origin(time P_Date)
format _origin %td

stcrreg i.ComplexityOfStrategy i.Amount_of_addons Rushed2 i.Distance_Class Rushed_Strategy IVA IQA GDPA Hofstede i.Management_Participation ib(frequent).Entrytype Syndication PE_Experience PF_Experience PE_Experience_Total PF_Experience_Total logPFassets i.HOT_IPO i.HOT_MNA i.CountryGroup i.Exitgroup i.IndustryFE, compete(FinancialBuyout==1) offset(TradeSale)

Result:

 failure _d:  TradeSale == 1
   analysis time _t:  (E_Date-origin)
             origin:  time P_Date
  enter on or after:  time P_Date
                 id:  Strategy_Number

Iteration 0:   log pseudolikelihood = -723.45338  
Iteration 1:   log pseudolikelihood = -686.10508  
Iteration 2:   log pseudolikelihood = -681.40952  
Iteration 3:   log pseudolikelihood =   -681.324  
Iteration 4:   log pseudolikelihood = -681.32395  

Competing-risks regression                       No. of obs       =        917
                                                 No. of subjects  =        917
Failure event  : TradeSale == 1                  No. failed       =        148
Competing event: Financia~t == 1                 No. competing    =        128
                                                 No. censored     =        641

                                                 Wald chi2(59)    =    2149.29
Log pseudolikelihood = -681.32395                Prob > chi2      =     0.0000

The reason for my hesitation is because of the paper by B. Hammer (2016) 'Do buy and Build Strategies Increase Illiquidity of Private Equity Investments?' which is accessible freely online.
In his paper he states:

Therefore, I test for sensitivity of my results to various alternative exit routes in an AFT competing risks framework. This framework is conceptually similar to the baseline AFT regressions presented in Section 3.1 but estimates covariate effects on holding periods for different competing exit routes. To do so, the competing risks regression does not only treat non-exited buyouts as right censored but also exited buyouts with exit channels other than the one under consideration. For example, for exits through Initial Public Offering (IPO), it treats all non-exited and all non-IPO exited buyouts as being right censored. Similar to the baseline AFT regression, I utilize a logistic distribution to parameterize the error term.

If I understand his text correctly, I already performed a 'competing risk regression' without the command, by only allowing the desired type of exit being the event, and the other types of exit treated as censored.

So my real question is:
Should I consider for the first part of my research all types of exit as non-censored (and thus as an event), and in an other part I should use the competing risk event regression for, for example, Financial Buyout versus, together, the other types of exit? Meaning the analysis I have done, with the first code, is not allowed for, since I should use a competing risk regressions for separating the types of exit.

I hope someone can elaborate the difference in my approach, thanks in advance.

Kind regards,

Michael