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From |
Sara Muller <s.muller@cphc.keele.ac.uk> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: RE: st: C-statistic with -gologit2- |

Date |
Thu, 08 Oct 2009 08:41:39 +0100 |

Best wishes, Sara Newson, Roger B wrote:

Yes, you would have to calculate separate c-statistics with -mlogit-, as you describe. And these would have to be restricted to the 2 groups being compared, in order to make sense. In the case of mlogit, you could also calculate multiple c-statistics, one for each partition of the outcome values. Alternatively, you could presumably define one stratum for each partition of the outcome variable, expand each subject into a cluster of observations (1 observation per subject per partition), define X for each subject-partition as a binary indicator of that subject's membership of the higher group in that partition, define Y for each subject-partition as the linear predictor for that subject of membership of the upper group in that partition, and define the summary c-statistic as the Harrell's c of Y with respect to X, stratified by partition. As in: somersd X Y, cluster(subject) wstrata(partition) transf(c) tdist where -subject- is the subject ID for each subject-partition, -partition- is the partition variable for each subject-partition, and Y and Y are as defined above. The c-statistic would then summarize the general ability of the linear predictors (as stored in Y) to predict the membership of upper groups of partitions (as stored in X), restricted to comparisons involving the same linear predictor for the same partition. I hope this helps. Best wishes Roger Roger B Newson BSc MSc DPhil Lecturer in Medical Statistics Respiratory Epidemiology and Public Health Group National Heart and Lung Institute Imperial College London Royal Brompton Campus Room 33, Emmanuel Kaye Building 1B Manresa Road London SW3 6LR UNITED KINGDOM Tel: +44 (0)20 7352 8121 ext 3381 Fax: +44 (0)20 7351 8322Email: r.newson@imperial.ac.ukWeb page: http://www.imperial.ac.uk/nhli/r.newson/Departmental Web page: http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/ Opinions expressed are those of the author, not of the institution. -----Original Message----- From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Richard Williams Sent: 07 October 2009 20:59 To: statalist@hsphsun2.harvard.edu; 'statalist@hsphsun2.harvard.edu' Subject: Re: st: RE: st: C-statistic with -gologit2- At 01:30 PM 10/7/2009, Newson, Roger B wrote:In the case of ordinal regression, instead of using the predictedprobability, you should use the linear predictor, computed using-predict- with the -xb- option. This linear predictor is an ordinalpredictor of the outcome. It then makes sense to use thec-statistic, although the confidence intervals should only be takenseriously if calculated (using out-of-sample prediction) in adifferent dataset from the dataset in which the ordinal model was fitted.Thanks Roger. This won't work with gologit2, because there aremultiple equations and hence multiple XBs. gologit2 is like mlogitin that respect.In the case of mlogit, there are multiple linear predictors,interpreted as the log odds ratios (per X-unit) of the variousnon-baseline outcomes compared to the baseline outcome. In thatcase, the c-statistic for the linear predictor for each non-baselineoutcome only makes sense if restricted to observations with eitherthat non-baseline outcome or the baseline outcome.So, does that mean you would compute separate C statistics only usinggroups 1 and 2, then 1 and 3, then 1 and 4 (assuming group 1 is thebaseline and there are 4 groups).gologit2 doesn't quite fit into this scheme either. gologit2 is likea series of binary logistic regressions with differentdichotomizations of the original ordinal variable. First, it isgroup 1 versus groups 2, 3, 4; then groups 1 and 2 versus groups 3and 4; then groups 1, 2 and 3 versus 4. If proportional odds holdseach dichotomization produces the same coefficients except for theintercepts. I am not sure how the C statistic fits in with such ascheme; perhaps, in the above you would have 3 different C statistics?------------------------------------------- Richard Williams, Notre Dame Dept of Sociology OFFICE: (574)631-6668, (574)631-6463 HOME: (574)289-5227 EMAIL: Richard.A.Williams.5@ND.Edu WWW: http://www.nd.edu/~rwilliam * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

-- Sara Muller Research Associate: Biostatistics Arthritis Research Campaign National Primary Care Centre Primary Care Sciences Keele University Staffordshire, ST5 5BG Tel: +44 (0) 1782 734853 Fax: +44 (0) 1782 733911 Email: s.muller@cphc.keele.ac.uk * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**st: C-statistic with -gologit2-***From:*s.muller@cphc.keele.ac.uk

**Re: st: C-statistic with -gologit2-***From:*Jeph Herrin <junk@spandrel.net>

**Re: st: C-statistic with -gologit2-***From:*Richard Williams <Richard.A.Williams.5@ND.edu>

**st: RE: st: C-statistic with -gologit2-***From:*"Newson, Roger B" <r.newson@imperial.ac.uk>

**Re: st: RE: st: C-statistic with -gologit2-***From:*Richard Williams <Richard.A.Williams.5@ND.edu>

**RE: st: RE: st: C-statistic with -gologit2-***From:*"Newson, Roger B" <r.newson@imperial.ac.uk>

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