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From |
May Boggess <mboggess@stata.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
RE: st: Confidence limits on survival probabilities from stcox |

Date |
01 Feb 2005 10:30:35 -0600 |

On Tuesday, Neville wrote: > > Thanks for Ricardo's idea, but there are two problems: one that the > estimates obtained are not the same as those that stcurve plots (perhaps the > fact that my covariates are categorical variables with more than 2 levels I > may have used the adjustfor option in the wrong way - I put in the dummy > variables, except the baseline ones - so I stand to be corrected on this > one) and two, that one only gets a listing at the time points in the dataset > and not at all the time points. > > ... I can't reproduce the values in the output file > cox1.dta using the sts list command - I've tried using both the by and > adjustfor commands. Assuming one can reproduce the values, how does one > overcome point two above? Let me answer Neville's original question before getting onto the points raised here: there is no command for calculating confidence intervals around the survival curve from a Cox proportional hazard model with covariates. Therneau and Grambsch "Modeling Survival Data" describe some methods for calculating standard errors (page 268) but are less than enthusiastic about the value of some of the confidence intervals obtained. Neville's first question today is how to get the same graph from -sts, adjust()- and -stcurve- following -stcox-. The thing to keep in mind is that -sts- evaluates at all covariates set to zero, whereas -stcurve- evaluates at the mean of the covariates. So to see them produce the same answer, we need to subtract the mean from each covariate so that the means are zero. Here is an example. First the Cox model: clear sysuse cancer stset st,f(di) stcox age drug, bases(surv) stcurve, outfile(results, replace) surv use results, clear list duplicates drop sort _t twoway line surv1 _t, connect(stairstep) save results, replace We see that I get the same plot using -twoway- on the saved results as we did from -stcurve-. I dropped duplicate observations since they don't add anything to the graph. Now -sts-: clear sysuse cancer stset st,f(di) sum age replace age=age-r(mean) sum drug replace drug=drug-r(mean) sts graph, adjustfor(age drug) We should see that the graph looks the same as the one we got above. We can compare the actual values of the function by using -sts gen-: sts gen surv2=s, adjustfor(age drug) keep surv2 _t duplicates drop count sort _t twoway line surv2 _t, connect(stairstep) merge using results list Neville's second question is how to get the values of the survival function for time points that are not in the original dataset. If the survival function was calculated after estimation by -predict- (like it is for -streg-) we know what we would do: after the estimation we would put into the dataset the times we are interested in and then use -predict-. But since with -stcox- the survival function is worked at at the time of estimation, this option is not available to us. However, since the survival function is a step function we can deduce the value of the function at anytime we are interested in. In my example above I had S(28)=.0481023 and S(33)=.0108086. So for any time t between 28 and 33, S(t)=.0481023. -- May mboggess@stata.com * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:**st: Teething troubles in using -gen, mod()-***From:*"Clive Nicholas" <Clive.Nicholas@newcastle.ac.uk>

**References**:**RE: st: Confidence limits on survival probabilities from stcox***From:*"CDSC - Verlander, Neville" <Neville.Verlander@hpa.org.uk>

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