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From |
"Anders Alexandersson" <andersalex@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Help please re Ocratio |

Date |
Wed, 31 Oct 2007 11:15:29 -0400 |

Jon Heron (ALSPAC) <Jon.Heron@bristol.ac.uk> would like an extra bit of clarification about the continuation ratio model: > It sounds like, if I want to fit an ocratio model and then examine the > individual pairs of effects I either fit two logistics > > 1 [=1] versus 2 & 3[=0] > 2 [=1] versus 3 [=0] > > and compare with an ocratio on an outcome ordered 1,2,3 > > > or fit two logits > > 1 [=0] versus 2 & 3[=1] > 2 [=0] versus 3 [=1] > > and compare with an ocratio with outcome ordered the other way i.e. > 3,2,1 > > > If this is the case, and a quick experiment with Stata suggests it is, > and since the continuation ratio model is not reversible (unlike > proportional odds), how do I decide which one to do? > > I guess the former I think that the answer depends on what you want to compare. Bender and Benner (2000, 681) suggest that a "forward" continuation ratio model (your option 1) seems useful if the response Y represents "survival times". For example, you want to compare short survival times versus high survival times. In contrast, a "backward" (or reverse) continuation ratio model (your option 2) seems useful if Y represents "disease status". For example, you want to compare bad disease vs mild disease. Bender and Benner illustrate the backward continuation ratio model. It is also important to distinguish between "stopping" and "continuation" continuation ratio models. I find the terminology in the documentation for R's function vgam() by Yee helpful, see http://www.stat.auckland.ac.nz/~yee/VGAM/. I try to summarize the four models here: continuation ratio Probability, j = 1,2 -------------------- -------------------- a. forward stopping P[Y=j|Y>=j] b. reverse stopping P[Y=j+1|Y<=j+1] c. forward continuation P[Y>j|Y>=j] = a with reversed signs d. reverse continuation P[Y<j+1|Y<=j+1] = b with reversed signs It seems to me that logistic regression and Rory Wolfe's -ocratio- estimates (a). Logistic regression assumes equal slopes on original data, or unequal slopes on expanded data. In comparison, -ocratio- assumes equal slopes only but you can test this assumption, and the sign of the slope is opposite but that is easy to handle. It seems that Maarten Buis's -seqlogit- estimates (c). How to estimate version (b) or (d) of the continuation ratio model in Stata, or how to extend the continuation ratio model(s) as a mixed-model? For mixed-model version, the literature (e.g, Grilli 2005) suggests the use of logistic regression on expanded data, but I have not had a chance to try this nor have I found an example to replicate. Any suggestions? References ---------- Bender, R., Benner, A. 2000. Calculating ordinal regression models in SAS and S-Plus. Biometrical Journal 42(6): 677-699. Grilli, L. 2005. The random-effects proportional hazards model with grouped survival data: a comparison between the grouped continuous and continuation ratio versions. Journal of the Royal Statistical Society, Series A. 168(1): 83-94 Anders Alexandersson andersalex@gmail.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/

**References**:**st: Help please re Ocratio***From:*"Jon Heron (ALSPAC)" <Jon.Heron@bristol.ac.uk>

**Re: st: Help please re Ocratio***From:*"Anders Alexandersson" <andersalex@gmail.com>

**Re: st: Help please re Ocratio***From:*"Jon Heron (ALSPAC)" <Jon.Heron@bristol.ac.uk>

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