Re: What does convergence/covariance show?

Chuanpu, Thanks for bringing my attention to your excellent simulation study of the problems associated with predicting doses from model based analyses. In your study the highest effect for which doses was predicted was 50% of Emax so I would not expect any real difference between choosing a linear or Emax model to make that kind of prediction. Also the study designs were essentially setup for interpolation. I would also expect that an empirical model should be able to interpolate equally well as a more mechanistic model (provided the empirical model is not too bizarre). I wrote earlier: > The usual purpose of the model is to predict the effect over a range of concentrations. If you choose a linear model because your subjective impression is that the model is "overparameterised" due to large standard errors then you can be certain that any extrapolation will overpredict the size of the effect. If you choose an Emax model you may still have a biased prediction but it will be a better prediction than one from a linear model. In the interpolation range of predictions the Emax model will still do better. I cannot see how it can do worse than the linear model (assuming the model passes other tests of plausibility and the VPC looks OK). Referring to this assertion you said in another email: > Our previously mentioned simulations showed exactly the opposite in > certain situations - i.e., when the power is low. The Emax model > predicted worse because of instability, even though it was the "true" > > model. I had some difficulty identifying where this is described in your paper. Would you please guide me to the page(s) where this can be found? It is however not surprising that if the design is very poor then any model is going to be poor at making predictions. So until I understand your paper better I think I will stick with my original assertion that an Emax model is better than a linear model when one is intends to use it for extrapolation and will be equivalent to empirical models for interpolation. Chuanpu H, Yingwen D. Estimating the predictive quality of dose-response after model selection. Stat Med. 2007;26(16):3114-39. Hu, Chuanpu [CNTUS] wrote: > We have conducted simulations to show that an over-parameterized model, > even if "true" and "significant," could give worse predictions (ref > below). The simulations were conducted perhaps more like in the context > of interpolations. What happens in extrapolation will be very much > depend on the specific situation. However this suggests that the > empirical model may deserve to be given more consideration. > > Reference: Hu C, Dong Y., Estimating the predictive quality of > dose-response after model selection. Statistics in Medicine 2007; > 26:3114-3139. > > Chuanpu > > ~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~* > Chuanpu Hu, Ph.D. > > Director, Pharmacometrics Pharmacokinetics C-3-3 > > Biotechnology, Immunology & Oncology (B.I.O.) > Johnson and Johnson > > 200 Great Valley Parkway Malvern, PA 19355 Tel: 610-651-7423 Fax: (610) 993-7801 E-mail: [email protected] ~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~*~* -- Nick Holford, Professor Clinical Pharmacology Dept Pharmacology & Clinical Pharmacology University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand [email protected] tel:+64(9)923-6730 fax:+64(9)373-7090 mobile: +64 21 46 23 53 http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford