> > coxph does not use any information that are in the dataset between event > > times (or "death times") , since computation only occurs at event times. > This is the consequence of the use of partial likelihood in the Cox model. >[...] >You need to make more assumptions, such as a >smooth baseline hazard, and you can always use parametric models and a >full likelihood (but you may have to program them yourself). > Brian D. Ripley
If I'm not wrong, another alternative might be to use explicitely a Poisson model (following Dickman et al., who propose another method of fitting a model close to Cox's model. Reference at the end.). So my question is on R syntax (sorry if it is a naive question): does the following do the job I think it does (full likelihood - using full dataset - for a model close to Cox's) ? summary(glm(formula = status ~ x1+x2+offset(log((stop-start)/365.25 )), family = poisson(link = log), na.action =na.omit, control = list(epsilon = 0.001, maxit = 50, trace = F),data=Xstep2)) Dickman et al. recommand the offset ln(yj) where yj is person-time at risk for the observation. start and stop are days in my dataset. About two thirds of my observations are one-year long. status= 1 for event, 0 for censored observations. The ten "coef" estimated with coxph are nearly the same as the ten "estimate" with glm, the p-values are close. (The covariate for which it is not the case is a covariate which changes very quickly, and thus may be badly measured with partial likelihood, with computation only at death time). I think the baseline hazard is constant here. Dickman et al. use link ln(muj ?d*j ) where d*j is the known baseline hazard for observation/at time j. They say: "d*j is the expected number of deaths (due to causes other than the cancer of interest and estimated from general population mortality rates") [...] Fitting the model requires software which supports the estimation of generalized linear models with the so-called user-defined link functions. Most general purpose statistical software packages support this feature, including SAS (from version 6.10), Stata (from version 7), S-plus, R and GLIM.""). First, I do not know how to specify such a link function in R. Second, if I can specify such alink, I could use (in place of d*j), the smooth baseline estimated after doing a Cox regression. But I don't know how to fit (for instance) a piecewise constant baseline hazard with a Poison glm, except trying all possible models (within a given class) with a for( ) loop and taking the highest loglikelihood. Thank you a lot for any help. Mayeul KAUFFMANN Univ. Pierre Mendes France Grenoble - France Reference: Dickman;Sloggett, Hills, Hakulinen, "Regression models for relative survival", Statist. Med. 2004; 23:51-64 (DOI: 10.1002/sim.1597) available at http://www.pauldickman.com/publications/regression_models_for_relative_survival.pdf they say: The underlying model is an additive hazards model where the total hazard is written as the sum of the known baseline hazard and the excess hazard associated with a diagnosis of cancer. "We assume that the number of deaths, dj , for observation j can be described by a Poisson distribution, dj follows Poisson(muj) where muj =lambdaj.yj and yj is person-time at risk for the observation. The observations can represent either [...] individual patients or subject bands (as in Section 3)." fiting the model requires software which supports ----- Original Message ----- From: "Prof Brian Ripley" <[EMAIL PROTECTED]> To: "Mayeul KAUFFMANN" <[EMAIL PROTECTED]> Cc: <[EMAIL PROTECTED]> Sent: Friday, August 13, 2004 8:40 AM Subject: Re: [R] How to use the whole dataset (including between events) in Cox model (time-varying covariates) ? ______________________________________________ [EMAIL PROTECTED] mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
