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From |
"Stephen P. Jenkins" <[email protected]> |

To |
[email protected] |

Subject |
Re: st: st: question about multinomial transition model |

Date |
Tue, 13 May 2003 14:22:43 +0100 (GMT Daylight Time) |

On Tue, 13 May 2003 13:03:20 +0100 [email protected] wrote: > Hi, > The full reference is Diggle & Zeger (1994) Analysis of Longitudinal data. Oxford : Oxford university press. > My model is about competing risk factor model. I have four competing risk factors, let say A, B , C and D and 6 explanatory variables. I want to estimate the transitions from state A at one time to the next time or visit with include the explanatory variables. It mean tried to estimate the rates transition probabilities pr(Yij |Yij-1)plus the effect of explanatory variables (sort of Markov chain regression model for multinomial responses). > > Thank you in advance for the sugessions of software that can fit the above model. > I do not have access to the 1994 book or the second edition. (By Diggle and others, 2002.) However, let me argue that you can probably estimate the model in Stata. Assume you have an /independent/ competing risks (ICR) model. Next decide whether the process generating your survival times (i) occurs in continuous time and exact survival times are available (dates), or (ii) occurs in continuous time but observed survival times are grouped into intervals ('interval censoring'), or (iii) you have an intrinsically discrete time process. (ii) is perhaps the most common situation in the social sciences. In cases (i), (ii), it turns out that the likelihood for the k-state ICR model can be factored into k separate models that can be estimated independently (using destination-specific censoring indicators) using standard single-risk models. For case (i), use -streg-, -stcox-, and so on, in Stata. For case (ii), supposing intervals of equal length (e.g. a 'month' or 'year'), use -cloglog- or -logit- applied to data reorganised so that there is one obs for each interval that each subject is at risk of event occuring. For case (iii), the ICR likelihood does not factor conveniently but can be estimated straightforwardly using a multinomial logit model program (-mlogit- in Stata). The result for case (i) appears in any standard survival analysis text. Result (ii) is not so well-known, but is stated by Narandrenathan & Stewart (Applied Statistics 1993). Both results are informally explained in chapter 8 of the notes available at: http://www.iser.essex.ac.uk/teaching/stephenj/ec968/pdfs/ec968lnotesv2r.pdf The result re (iii) is stated informally by P. Allison (1984), Survival Analysis, Sage. I conjecture that the Diggle/Zeger multinomial model that you referred to longitudinal data as if they were of case (iii). However check also whether case (ii) applies to you. Stephen ---------------------- Professor Stephen P. Jenkins <[email protected]> Institute for Social and Economic Research (ISER) University of Essex, Colchester, CO4 3SQ, UK Tel: +44 (0)1206 873374. Fax: +44 (0)1206 873151. http://www.iser.essex.ac.uk * * 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/

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