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From |
jpitblado@stata.com (Jeff Pitblado, StataCorp LP) |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: stcox output: p-value and CI don't agree |

Date |
Wed, 08 Aug 2007 16:09:22 -0500 |

Michael McCulloch <mm@pinest.org> posted a question regarding a perceived contradiction between a p-value and 95% CI from -bootstrap- of results from the -stcox- command. Michael, Philip Ryan <philip.ryan@adelaide.edu.au>, and Richard Williams <Richard.A.Williams.5@ND.edu> discussed the issue over several emails. Before I offer my thoughts on this discussion, I note that there is nothing wrong with -bootstrap- or -stcox-. The perceived contradiction was due to the incorrect assumption that -bootstrap- was reporting a p-value for the test of a hazard ratio against one. The p-values in the tables reported by Stata's estimation commands, including -bootstrap-, are always for tests against zero. -stcox- reports exponentiated coefficients (hazard ratios) by default, but the reported tests are of the null hypotheses that the true underlying coefficients are zero. The default (hazard ratio) confidence intervals (CIs) for -stcox- are obtained by exponentiating the limits of the CIs for the underlying coefficient. Now I'll summarize the thread and add a few of my own comments. Michael was using the -bootstrap- prefix with the following user-written program: program boot_hr, rclass stcox drug indeplist, local foreach var of varlist `X' { return scalar `var' = exp(_b[`var']) } end This program assumes the dataset is properly -stset- and the user-written -indeplist- program has been installed (see -ssc describe indeplist-). Michael shows an example of how he is using -bootstrap- and the above program: . sysuse cancer . stset studytime, failure(died) . set seed 12358 . bootstrap drug=r(drug), reps(100) : boot_hr The above can be done without using -boot_hr-, here's how . bootstrap drug=exp(_b[drug]), reps(100) seed(12358) : stcox drug Michael later pointed out his reason for using -boot_hr-. He needs -bootstrap- to ignore the fact that -iweight-s were -stset-. Thus Michael is using -boot_hr- to prevent -bootstrap- from figuring out that weights are being used by the estimation command. This assumes that resampling the observations and performing estimation using the weights associated with the resampled observations is appropriate. While this is reasonable for -aweight-s and arguably reasonable for -pweight-s, I would strongly discourage anyone from trying this with -fweight-s (instead consider expanding the data and dropping the weights). Michael indicated that his weights were the inverse probability of exposure, something one might consider as -iweight-s as Michael did The -force- option of -bootstrap- accomplishes the above, but I must strongly warn that it is the user's responsibility to verify that resampling observations and using the weights associated with the resampled observations is appropriate. When bootstrapping the coefficients -e(b)- from an estimation command, -bootstrap- is able to properly label the reported values in its table. -bootstrap- uses the estimation command to report its results when it can. Thus something like . bootstrap, reps(100) seed(12358) : stcox drug will report hazard ratios, because -stcox- is being used to report the results. However using -exp_list- or a user-written program that cannot replay results, as in . bootstrap drug=r(drug), reps(100) : boot_hr implies that -bootstrap- must report its own results and labels the bootstrapped point estimates using the standard 'Coef.' column header. I believe this is what ultimately contributed to the confusion. --Jeff jpitblado@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**:**Re: st: stcox output: p-value and CI don't agree***From:*Michael McCulloch <mm@pinest.org>

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