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Re: st: Cox Competing Risks Model (Cox CRM)

From   Steven Samuels <>
Subject   Re: st: Cox Competing Risks Model (Cox CRM)
Date   Wed, 27 Jul 2011 23:30:53 -0400

If you use the stratified version of the Lum/McNeil model, as I suggested, then the log-likelihood of the combined model will be the total of the separate log-likelihoods. Notice the coefficients of the third are those in the first two.  


sysuse auto, clear

eststo clear
stset mpg
eststo M1: qui  stcox turn length if foreign==0, nohr
eststo M2: qui  stcox turn length if foreign==1, nohr
eststo M3: qui stcox c.turn#ibn.foreign c.length#ibn.foreign, nohr strata(foreign)
estadd scalar Log_Likelihood =e(ll): M1 M2 M3
estout M1 M2 M3,  cells(b se) stats(Log_Likelihood)

di    -131.9868  +  -42.78481   

esttab M1 M2 M3,  title(Separate & Combined Models) label nonumbers mtitles("Domestic" "Foreign" "Combined") stats(Log_Likelihood)

On Jul 27, 2011, at 8:46 AM, Stefan Göke wrote:

Dear statalisters,

I am aware that a competing risks can be implemented e.g. via a separate Cox models or via augmenting the data before applying a Cox model. 

Reading “He et al. (2010) A Competing Risks Analysis of Corporate Survival in Financial Management” and “Dickerson et al. (2003) Is attack the best form of defence? A competing risks analysis of acquisition activity in the UK in Cambridge Journal of Economics”, I am curious to know whether somebody on the list knows how to implement those models in Stata. In fact, the authors present results for three competing risk types where each covariate has a separate coefficient per risk type. However, LL, Chi2 are only presented once, implying that it is only one model the authors estimate. The only way I know to do this is via three separate models that would have one LL, Chi2 etc. each.

Here is an excerpt of table 4 p. 1713 from He et al (2010) to illustrate my question. Their three risk types are bankruptcy, M&A, privatized. –LL is only reported once.

Cox CRM Model Without Heterogeneity	
	Bankruptcy	M&A	Privatized	
Profitability	−3.0515∗∗∗	1.1989	4.9439∗∗∗	
Growth	−0.9699	0.3095∗∗	0.3105∗∗∗	
Size	0.5173∗∗∗	0.194	0.5300∗∗∗	
Turnover (market)	−0.0051	−0.0011∗∗	−0.0019∗∗	
Turnover (stock)	−0.2964	0.0361∗∗∗	0.0042	
Stock performance	−24.74∗∗∗	12.14∗∗	−5.928	
FCF	0.3675	10.9	15.02∗∗∗	
Tax	31.58∗	26.49	−5.8077	
q-ratio	0.1767∗∗∗	0.1231	−0.4449∗∗∗	
Leverage	−0.1151	−1.3721	−1.3365∗	
Investment	−0.3223	−1.4312	0.0621	
- ln L 458.44				

Many thanks for your consideration


Stefan Göke
Ph.D. Candidate
Department of Management
University Paderborn

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