Re: Model building algorithm

From: LSheiner <lewis@c255.ucsf.edu> Subject: Re: Model building algorithm Date: Mon, 24 Apr 2000 13:54:44 -0700 Nick Holford wrote: > > LSheiner wrote: > > > > I think the injunctions you have heard about building the structural model > > first were not stated as they should have been: the idea is to create the structural > > model in a context of a flexible inter-indivdiuual variance model, so > > Bill's idea of putting etas on everything goes along with that philosophy. > > Indeed, I think we have all seen cases where doing what Bill saqys, but > > limiting OMEGA to be strictly diagonal has led to problems in model building. > > My 2 cents -- a flexible between subject variability (BSV) model means > to me having a full block OMEGA structure so that any parameter which > has BSV is by default assumed to be correlated with any other parameter. > The rationale for this is that NOT including the covariance implies a > specific assumption that the covariance is zero. This assumption might > be reasonable for the covariance between a set of PK parameters and a > set of PD parameters in the same model but I would not think it > reasonable a priori to have a zero covariance within the set of PK > parameters or within the set of PD parameters. > > Note that the same idea applies to within subject variability (WSV). The > commonly known example of WSV uses occasion as a covariate to identify > between occasion variability (BOV) (aka IOV). An OMEGA BLOCK should be > considered the default for parameters with BOV e.g. BOV in a PK model > may often be due to differences in bioavailability which will be > reflected in the covariance between CL/F and V/F. Failure to use an > OMEGA BLOCK for BOV is the same as saying biovailability does not > influence CL/F and V/F (assuming there is not a an explicit OMEGA for F > in the model). I agree -- when I said "limiting OMEGA to be strictly diagonal has led to problems in model building" I thought I was saying taht one was well advised to use a full OMEGA - i.e., with off-diagonal elements non-zero. > > > I generally now-a-days, use a 2 x 2 OMEGA while building my > > regression model, one eta scales Y > > (i.e., Y = F*(1+eta) or F*EXP(eta)) and one eta scales X (usually > > time ... This is implemented as TSCALE = exp(eta), where TSCALE is > > allowed). Effectively, then the generic variability model is > > F = fn(time*exp(eta1))*exp(eta2). > > Can you explain why you would use this rather than the more common model > for variability in Y e.g. > F = fn(time*exp(eta1))*exp(eps1) ? Again, perhaps not clear - I was talking about inter-individual variability - in NONMEM speak, F models the prediction (regression function), and Y models the observation. So to be complete, I was actually suggesting: F = fn(time*exp(eta1))*exp(eta2) Y = Fexp(eps1) + eps2 > > How do you interpret the eta on Time? If you had used an additive model > e.g. TSCALE=eta then I would think of this as reflecting random error in > measurement of time but I have difficulty understanding the subject > specific magnitude. I find it even harder to interpret a proportional > model where the error in time gets bigger the longer one waits. It's not an error, but a source of variation. The eta on time simple rescales the time scale for each indivdiual: things run "slower" for some and "faster" for others - it covers, in a non-parametric way, diffferences between individuals in the "time" dimension, much as the eta multiplying F covers differences among indivduals in the spatial dimension. The time-scaling works for example for inter-species scaling, and corresponds to the idea of normalizing time to species lifetimes so all lifetimes are unity after transformation. -- _/ _/ _/_/ _/_/_/ _/_/_/ Lewis B Sheiner, MD (lewis@c255.ucsf.edu) _/ _/ _/ _/_ _/_/ Professor: Lab. Med., Bioph. Sci., Med. _/ _/ _/ _/ _/ Box 0626, UCSF, SF, CA, 94143-0626 _/_/ _/_/ _/_/_/ _/ 415-476-1965 (v), 415-476-2796 (fax)