COX Proportional Hazard Model with Time DependentCovariate

Jeff, Thanks for highlighting the time to event analysis terminology issue. I think nmusers need to pay particular attention to a major difference between two classes of methods. 1. The Cox proportional hazards model is a semiparametric method that is used to describe the difference between treatments. It assumes the underlying hazard for both treatments is the same. 2. Parametric methods (e.g. using the Weibull distribution) try to describe the undelying hazard for each treatment and do not require the assumption that the underlying hazard is the same. The semiparametric method is somewhat similar to doing a bioequivalence analysis with NCA. It can tell you about the difference between the two formulations under the assumption that the clearance is the same but it doesnt tell you the underlying PK parameters (clearance, volume, absorption rate constant etc) and cannot make predictions of the time course of concentration. The parametric time to event method describes the full hazard function but is dependent on assuming a particular model -- just like assuming a specific compartmental model and input function in compartmental PK. As nmusers will appreciate, one can learn and understand much more from a compartmental model than one can from doing a bioequivalence analysis. The parametric approach does not require the restrictive assumption that the underlying hazard is the same for both treatments (which is analogous to having to assume clearance is the same for a bioequivalence analysis). So it depends what you want -- if you just want to collect P values then use the semiparametric method. But if you want to understand the biology of the disease and the effects of drug treatments you need to seriously consider the parametric method. Nick [EMAIL PROTECTED] wrote: > > Liang - There are some examples of NONMEM code in the following link. I have > used this in the past as a good starting point for specifying time-dependent > hazard models. > > http://anesthesia.stanford.edu/pkpd/NONMEM%20Repository/ > > A note on nomenclature, I always felt a bit confused about these models till > I realized the level of ambiguity in the literature. The following words are > often used in an apparent mosaic fashion to describe different analyses that > are actually quite similar. > Survival analysis > Failure analysis > Event modeling > Hazard regression > Cox proportional hazards model > Cox model > Proportional hazards model. > Weibull (...or insert your favorite function here...) proportional hazards > model > Parametric proportional hazards models > Semi-parametric proportional hazards models > Cox regression > Poisson regression, etc... > > For more check out: http://en.wikipedia.org/wiki/Proportional_hazards_models > > Regards, Jeff > > > "Nick Holford" <[EMAIL PROTECTED]> >
> Sent by: [EMAIL PROTECTED] > > œj¬72Z·ÌG{»%Ù·—ÿ± -- Nick Holford, Dept Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand email:[EMAIL PROTECTED] tel:+64(9)373-7599x86730 fax:373-7556 http://www.health.auckland.ac.nz/pharmacology/staff/nholford/

Nick, I would argue that parametric survival models are dependent on the "structural model" (Weibull, Exponential, Gompertz etc.) that you choose for the hazard function and so suffer the same issues as standard PK model building where the choice of covariates, error structures etc. depend on the correct choice of hazard model. The choice of model is still an assumption... On the other hand my understanding of Proportional Hazards models is that we don't necessarily care what the parametric form of the hazard is. We assume that the hazards changes proportionately with changes in the covariates (hence the name). Treatment, dose or exposure variable could be a covariate and although it is usually added in a linear form it doesn't have to. In many cases the form or "shape" of the hazard function itself is a bit of a "nuisance variable" and what we want to know is the influencing factors on survival rates. In this case the proportional hazards model does just fine. I'm hoping that your last paragraph was written at least partly tongue-in-cheek... I would argue that if the range of parametric hazard models you may have tried do not capture features in your data then you may want to examine proportional hazards models. There's a fairly huge statistical literature on these topics (and I have to confess I'm not an expert by any means!). A good reference book is by D. Collett: "Modelling Survival Data in Medical Research", Chapman & Hall / CRC Press. 2003. http://www.amazon.co.uk/Modelling-Survival-Medical-Research-Statistical/ dp/1584883251/ref=pd_bowtega_3/026-9223339-1525240?ie=UTF8&s=books&qid=1 183564051&sr=1-3 Mike