notes cox's proportional hazards model

notes cox's proportional hazards model - Eco 572: Research...

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Eco 572: Research methods in Demography Cox's Proportional Hazards Model We continue our analysis of the cancer relapse data used for Kaplan-Meier. This is the dataset used as an example in Cox's original paper: Cox, D.R. (1972) Regression Models and Life tables, (with discussion) Journal of the Royal Statistical Society, 34: 187--220. (This is a slightly revised and shorter version of a handout used in my survival analysis short course.) The first task is to read and stset the data: . infile group weeks relapse using /// > http://data.princeton.edu/eco572/datasets/gehan.dat (42 observations read) . stset weeks, failure(relapse) failure event: obs. time interval: (0, weeks] exit on or before: failure ------------------------------------------------------------------------------ 42 total obs. 0 exclusions ------------------------------------------------------------------------------ 42 obs. remaining, representing 30 failures in single record/single failure data 541 total analysis time at risk, at risk from t = 0 earliest observed entry t = 0 last observed exit t = 35 Relative Risk To fit a Cox model we use the stcox with all the defaults: . gen treated = group == 2 . stcox treated failure _d: relapse analysis time _t: weeks Iteration 0: log likelihood = -93.98505 Iteration 1: log likelihood = -86.385606 Iteration 2: log likelihood = -86.379623 Iteration 3: log likelihood = -86.379622 Refining estimates: Iteration 0: log likelihood = -86.379622 Cox regression -- Breslow method for ties No. of subjects = 42 Number of obs = 42 No. of failures = 30 Time at risk = 541 LR chi2(1) = 15.21 Log likelihood = -86.379622 Prob > chi2 = 0.0001 ------------------------------------------------------------------------------ _t | Haz. Ratio Std. Err. z P>|z| [95% Conf. Interval] http://data.princeton.edu/eco572/CoxModel.html (1 of 6) [2/12/2008 10:35:12 AM]
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Eco 572: Research methods in Demography -------------+---------------------------------------------------------------- treated | .2210887 .0905501 -3.68 0.000 .0990706 .4933877 ------------------------------------------------------------------------------ Stata reports hazard ratios (exponentiated coefficients) by default. Here we see that treatment reduces the risk of relapse by 78% at any duration. To obtain the coefficients you can use the nohr option, or with just one type . di _b[treated] -1.5091914 Treatment of Ties Stata has several ways of handling ties. Cox's original proposal is called exactp for exact partial likelihood. An alternative is exactm for the exact marginal likelihood. Both are computationally intensive. A good approximation is
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This note was uploaded on 02/12/2008 for the course ECON 572 taught by Professor Rodriguez during the Spring '06 term at Princeton.

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notes cox's proportional hazards model - Eco 572: Research...

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