Sample hazard ratio and cumulative hazard - discrete time competing risks survival analysis

[Chris Rooney]

I was reading this paper (link: http://www.ecares.org/index2.php?opt...=152&Itemid=20) as I am doing something very similar. Now doing some reading, I realise I have to use a multinomial logit model, which is not a problem. However, I am wondering how they obtain their sample hazard functions (e.g. p.12 or p.13) and cumulative hazards (e.g. p.17 or p.18) [apart from manually calculating them of course]. Obviously, we don't have access to the data, but I'm wondering if any of you have any idea of how one would go about estimating the sample and cumulative hazard in a discrete time, competing risks survival analysis setting.

All the guides for Stata are geared towards continuous time data, and from the guides I have read on the multinomial logit for competing risks survival analysis, they don't talk about the sample hazard or cumulative hazard at all. I know with the mlogit command, you can specify the 'relative risk ratio' option, but is that the same as a hazard ratio?

[Steve Samuels]

You will need a good understanding both event history and multinomial logit models to do this analysis. A good start for learning how to set up data for discrete event history is Lesson 6 of of Stephen Jenkins's fine web page "Survival analysis with Stata" (http://www.iser.essex.ac.uk/survival-analysis) Especially important is the data set up, which will also apply to to your problem. Stephen's page includes a link to his draft book manuscript "Survival Analysis", which describes discrete even models from a more conceptual point of view.

The paper you cite (Ortiz and Dehon, 2011) quotes another paper (Scott and Kennedy, 2005) for their method. If you send me a private message with your email address, I will send you a copy of the Scott and Kennedy paper. Scott and Kennedy used Stata for their analysis, but the posted link in their paper no longer works. There is a chance that Ortiz and Dehon also used Stata. To jump start your analysis, I suggest that you request Stata code from both sets of authors. If you have complex survey data, note that Stata now has the svy: mlogit command to replace svymlog, which Scott and Kennedy used.

To answer your question: the Relative Risk Ratio is a ratio of hazard ratios, as defined by the authors. Also, note that the hazard ratio as defined by the authors is not the same as the hazard ratio used in proportional hazards model, The former is a ratio of hazards (probabiities) for two different outcomes at a single time, with covariate values held constant; the latter is the ratio of hazards at a single time for one outcome for two different values of a covariate. Confusing? Yes!


References.
ORTIZ, Elena ARIAS, and Catherine Dehon. 2011. The Roads to Success: Analyzing Dropout and Degree Completion at University.

Scott, Marc A, and Benjamin B Kennedy. 2005. Pitfalls in pathways: Some perspectives on competing risks event history analysis in education research. Journal of Educational and Behavioral Statistics 30, no. 4: 413-442.