From: "Sale, Mark" <ms93267@glaxowellcome.com>

Subject: Model building algorithm

Date: Fri, 21 Apr 2000 13:19:10 -0400

Dear users,

I have a model building question:

I have data that I known are two compartment. Using the usual model building algorithm of starting with the simplest model, I ran a one compartment (advan2) model. It minimized successfully, and even ran a covariance step. So, I tried a two compartment next (advan4), without etas on the two additional parameters (K23 and K32). The improvement in the obj was only 3 points. So, I would reject that model as not being better than the one compartment. Instead, since I believed this was a two compartment model I ran the advan4 with etas on both K23 and K32. Now the obj was 60 points better, and I'm happy, ready to move on. My question is, when one adds structural features to a model (by structural here I mean additional compartments, lag time etc, not covariates), would the traditional algorithm suggest they be added with or without etas? My first assumption was that they should be added without etas, because:

1. In the NONMEM short course material, the algorithm (lecture 17) says to build the structural model first, then the statistical,

2. In the same chapter, the material refers to adding features, with etas on all parameters of minimal model

3. I understand the formal hypothesis testing is not possible when adding etas.

4. All reference about model building state that one should added features one at a time, testing each. This implies to me that I should at the THETAs first, test that, then the ETAs at some later point. However, all the usual reference are primarily addressing covariate model building.

However, had I done this, I would have been misled. Comments?

Mark

From: "Bachman, William" <bachmanw@globomax.com>

Subject: RE: Model building algorithm

Date: Fri, 21 Apr 2000 14:13:13 -0400

Mark

My personal experience has been similar to yours. Despite all that we have been taught, I have had better results using models with etas on all the structural parameters, carrying them through the modeling process and then removing those etas which are shown in a final stage not to be supported by the data. Basically building a "full model" followed by "model reduction". Probably considered blasphemous by those with more of a statistical bent, but, it works for me.

William J. Bachman, Ph.D.

GloboMax LLC

Senior Scientist

7250 Parkway Drive, Suite 430

Hanover, MD 21076

Voice (410) 782-2212

FAX (410) 712-0737

bachmanw@globomax.com

From: "Bachman, William" <bachmanw@globomax.com>

Subject: RE: Model building algorithm

Date: Fri, 21 Apr 2000 15:29:21 -0400

I'd like to add a few comments to my previous statement regarding the addition of etas in a model. (Give me enough rope, so to speak ...)

The objective function should not be the only criteria for model acceptability. In fact, in some cases the magnitude of the drop in objective function can be deceptive. One also needs to be concerned with the size of the variances estimated (as well as the array of diagnostic plots, etc.) In the extremes, if the variances go to zero, the data does not support those etas. If the variances are huge, they are driving the model and the parameter they are associated may not be supported by the data. On the other, I have seen instances where the variances appeared huge using the FO method, but, were more modest when the FOCE method was applied, so it appears that those etas should be part of the model.

William J. Bachman, Ph.D.

GloboMax LLC

Senior Scientist

7250 Parkway Drive, Suite 430

Hanover, MD 21076

Voice (410) 782-2212

FAX (410) 712-0737

bachmanw@globomax.com

From: "Sale, Mark" <ms93267@glaxowellcome.com>

Subject: RE: Model building algorithm

Date: Fri, 21 Apr 2000 15:46:25 -0400

Bill,

You're right of course, but this forms a criteria for including an eta, but doesn't address whether the eta should have been added with the theta or after the theta. My additional comments include a reference to an excellent paper by Jose Pinheiro and Doug Bates (Model Building for Non linear Mixed Effects Models - sorry I don't have the rest of the reference, I just have a hard copy in my files). They suggest (as you do) "Starting with a model where all of the parameters have associated random effects and then removing unnecessary terms is probably the best strategy".

They recommend then examining the eigenvalues of the (full) variance-covariance and/or the coefficient of variation matrix (a normalized) variance/covariance matrix) to find those etas that seem to be inconsequential.

Mark

Date: Fri, 21 Apr 2000 13:18:07 -0700

From: LSheiner <lewis@c255.ucsf.edu>

Subject: Re: Model building algorithm

All-

I don't think there is an official "statistical" opinion on this - indeed, the idea of starting with the biggest possible model and then pruning it is probably more consistent with statistical "theory" than building up from a small model. The problem with the backward-elimination-only strategy is usually practical: running into rounding errors, etc.

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.

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).

I can't guarantee that this will help Mark's problem ... perhaps he can tell us whether, if he uses this structure for eta, NONMEM can "see" the biexponentiality of his data better ...

L.

_/ _/ _/_/ _/_/_/ _/_/_/ 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)

Date: Mon, 24 Apr 2000 15:38:05 -0400 (EDT)

From: "Ferrin Harrison 301-827-3213 FAX 301-480-2825" <HARRISONF@cder.fda.gov>

Subject: Model Building Algorithm

Some good messages have been posted on this thread.

Starting from the maximal model and working down, or simply running every conceivable model are allowed. In the linear model with fixed effects format, forward selection and backward elimination should generally give the best model without recourse to running all possible regressions.

The nonlinear random effects format is more complex. I would suggest trying the maximal (all possible parameters included) model before going to other methods of model selection, if only to see whether you have enough data for the model to run.

An aspect encountered was a kind of interpolation problem which I would expect to be more frequent in the nonlinear random effects format, i.e. forward selection and backward elimination can give different answers, even when nesting of the models is preserved.

If the maximal model doesn't run, then adding theta-eta pairs to forward select before reducing would be another interpretation of not working on the etas till the thetas are done; every theta gets an eta till all the thetas are chosen.

The CDER Biometric scientific workstations haven't had a speed upgrade since Peck's last big purchase in 1993, so accepting the 10-20 fold increase in CPU time to use FOCE for model selection would be a problem for me. It would take too many months of CPU time to run through the models when reasonably complex, which would be a problem under the PDUFA/FDAMA review time clocks. If you have the CPU time, I'd certainly favor modeling from FOCE from the start, rather than switching to FOCE for a little validation or precise estimation at the end.

So while a statistician may be disturbed and apprehensive to find you working on a more difficult model selection problem than linear fixed effects, this statistician certainly would not call it blasphemous.

Date: Tue, 25 Apr 2000 07:57:01 +1200

From: Nick Holford <n.holford@auckland.ac.nz>

Subject: Re: Model building algorithm

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 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) ?

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.

--

Nick Holford, Dept Pharmacology & Clinical Pharmacology

University of Auckland, Private Bag 92019, Auckland, New Zealand

email:n.holford@auckland.ac.nz tel:+64(9)373-7599x6730 fax:373-7556

http://www.phm.auckland.ac.nz/Staff/NHolford/nholford.htm

Date: Mon, 24 Apr 2000 13:54:44 -0700

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)

From: "Piotrovskij, Vladimir [JanBe]" <VPIOTROV@janbe.jnj.com>

Subject: RE: Model building algorithm

Date: Tue, 25 Apr 2000 11:59:46 +0200

Mark,

If you choose between two or more canditate structural models, look first at the plots of individual weighted residuals versus time (or sqrt(time) if the range of time is wide and models have two or more exponential terms). The best model produces residuals that show no pattern. The minimum objective function value or AIC are less important, especially if you have many observations per individual. The models you test should have random effects for every structural parameter. The form of $OMEGA matrix is not important. It is sufficient to use just a simple diagonal form: you can optimize $OMEGA after selecting an appropriate structural model. It is even not essential to get the convergence: only the posthoc step is really needed.

You mentioned the article by Jose Pinheiro and Doug Bates. It is available electronically from the following URL:

http://nlme.stat.wisc.edu/Model_Building.ps

Best regards,

Vladimir

----------------------------------------------------------------------

Vladimir Piotrovsky, Ph.D.

Janssen Research Foundation

Clinical Pharmacokinetics (ext. 5463)

B-2340 Beerse

Belgium

Email: vpiotrov@janbe.jnj.com

From: James <J.G.Wright@ncl.ac.uk>

Subject: Re: Model building algorithm

Date: Tue, 25 Apr 2000 13:37:13 +0100

Dear Model builders,

The statistical model defines how the differences between the predictions and observations should be "priced". In this context, interindividual ETA's allow us to pay less for persistent differences between individuals, in terms of the parameters to which they are applied. The problem with backward elimination approaches is that we may end up starting from an overparameterized model and may not be able to make reliable decisions about the components we remove. Although the general textbook advice is to take a stepwise approach to modelling, I too have personal experience of situations were this would be misleading. It was interesting that in Mark's original example, the parameterisation to which the random effects were applied affected the eventual decision. This isn't surprising as random effects on say rate constants or their product with volumes allow for the interindividual ETA to discount serial correlations in different ways. And if we allow off-diagonal elements, this gets even more complicated. Although for example CL and V are almost invariably correlated in practise, I am personally reluctant to introduce a parameter that can enforce such a correlation before attempting to explain noise with (fixed) covariate effects. Incidentally, I was under the impression that asymptotically we can test the change in objective function against a chi-squared distribution to assess STATISTICAL significance. However, this is probably irrelevant as part of model building, which I do not believe should be a sequential decision making process (which ignores interactions between model components and multiple testing issues). And I worry about applying asymptotic tests to a non-infinite sample.

Returning to the original point, I add thetas and then etas usually and objective function drops reassure me a little. This approach could fail if the fixed effect alone did not seem to explain noise, which could easily happen, if for example there was a lot of interindividual noise and especially of the residual error model can slide itself around to downweight the points in the "distribution" phase, and probably for many other reasons which I cannot even conceive of (I'm guessing at situations where there is a small mean difference between the misspecified null model and the more complex alternative but a lot of variability which can be discounted). Or perhaps there a samples in the "distribution" phase in only a subset of individuals. Whilst generally, I would say "Don't let hypothesis testing procedures boss you around", if they don't back you up, you need to be able to justify your position by explaining why. A good way to do this would be to say there were banana-shaped residual patterns for example, although this does not necessarily mean we can characterise the more complex model (and hence continue reliably with that model) although we suspect it is more appropriate. If we honestly believe our objective function is missing something, then maybe we should be double-checking how it has been constructed on the null model- for example is the residual model appropriate? ELS is notorious for its vulnerabibility to misspecification of variance functions, and in this situation objective function changes may not be trustworthy. And even if we believe they are chi-squared distributed (I personally think they have higher variance) and used a five percent alpha, we would make the wrong decision 5% of the time (colloquially speaking). And who knows what effect this owuld have on subsequent tests...thinking about this gives me nightmares. Hopefully, there are clues in other aspects of the model - residuals, estimates, and how they have changed - becuase the objective function alone is a very blunt tool.

James Wright

From: "Sale, Mark" <ms93267@glaxowellcome.com>

Subject: RE: Model building algorithm

Date: Tue, 25 Apr 2000 09:32:01 -0400

Bill, James, Lewis, Nick et al.

This discussion has been very valuable, I am grateful for it. However, I still have a question at hand. I'm actually revising our method sheet for population pk at Glaxo right now. We, for better or worse (probably for better) live in a regulated (read SOP driven) environment. We are expected to justify every decision we make in building these models. I'm sure that "The plots looked better this way" is a perfectly good scientific justification, and my experience suggest that the FDA is very scientific in these discussions. However, we (the royal we) do need to write a method sheet with at least recommendations for a starting point. It is my view that full backwards elimination is impractical. Assume we have a 2 compartment model, with 4 key parameters, ALAG, S2, K and Ka, ignoring k23 and k32. Assume we have the bare minimum of 4 covariates to test (Age, race, weight and gender). This is 16 effects, add in the 5 or 6 typical parameters (ALAG, S2, K, KA, K23 and K32), each with and without ETA's, as well as a full covariance matrix, and I'm quite confident that this model will not converge successfully. In reality, we have many more covariates to examine (2 to 4 measures of liver function, renal function, treatment, center, concomitant medications, concurrent diseases etc, etc) Of course, a more rational approach to selection of which covariates to test on each parameter could be used either based on biology or graphics. So, I think that forward addition, with guidance from the well described graphical methods, is the only practical solution, probably followed by backward elimination with the near final model. This is our current practice. However, my question remains about whether (in forward addition) etas should be used on the parameters. Note that this does not apply only to "structural" parameters (as in my original example, K23 and K32), but can apply to the model of a covariate to a parameter, e.g.

TVWTF = EXP(THETA(1)*WT)) ; TYPICAL VALUE WEIGHT EFFECT

WTF = TVWTF*EXP(ETA(1)) ; TRUE VALUE WEIGHT EFFECT

TVS2 = THETA(2)*WTF ; MODEL FOR VOLUME AS A FUNCTION OF WEIGHT

S2 = TVS1*EXP(ETA(2))

That is, weight may effect volume differently for different people. (Arnold Schwartneggers weight effect, or cirrhosis with ascites weight effect vs the weight effect for the rest of us, adipose tissue). The extreme might be that the drug is distributed to muscle but not fat, and so Arnie has a higher volume (as well as volume/kg), the ascitic has a lower volume in spite of a higher weight, and the rest of us have no relationship of volume to weight. We clearly need an eta to pick up this effect. The classic description of forward addition is to add a single effect and test that. My question is, what is the chances of being misled by complex interactions between fixed and random effects, or more than one fixed effect. I now have one clear example that it can happen. Are there suggestions to avoid it? I think that backward elimination is probably a better algorithm, but is nearly always impractical. At the moment, I'm leaning toward testing both with and with etas before ruling out that effect, with the addition of only the theta being the "purest", but the addition of etas as well being more realistic.

Mark

From: LSheiner <lewis@c255.ucsf.edu>

Subject: Re: Model building algorithm

Date: Tue, 25 Apr 2000 09:24:06 -0700

Two remarks:

1. Unless I did my algebra wrong (which is usual, indeed, often inevitable), and assuming you meant S2 = TVS2*EXP(ETA(2)), your series of equations reduces to log(S2) = a + b*wt + eta1 +eta2 with a and b unknown constants.

If so, then var(eta1) and var(eta2) are not identifiable (unless one or both appear somewhere else in the model not was their sum).

2. More to the point, I agree that we need at least some common practices for building models, and I also agree that saturated models for random effects get quickly out of hand. Her are some thoughts on what the "solution" should look like:

2.1. While we tend to seek the "best" among some set of models that we implicitly consider, we almost surely do not find it, unless our initial set is very small. In any event, the value of a model is not determined by whether it is best in its class, however (who is to say the class contains a model that is "good enough"?) but by its faithfulness to the real world it models, or more practically, by its performance. I think we will have more success seeking agreement on procedures for evaluating models, rather than ones for building them. My current favorites are predictive distributions of interesting marginal statistics, but much work remains to be done.

2.2 I continue to think that it does matter whether the "working" OMEGA used for model building is diagonal or not. That is why I use a full OMEGA when I use the "scale in X and Y" inter-indvidual variability model while building a regression model. We have seen some very peculiar behavior when off-diagonal OMEGA terms are excluded, including the choice of a wrong regression model. See, for example:

J Pharmacokinetic Biopharm 1994 Apr;22(2):165-77

Interaction between structural, statistical, and covariate models in population pharmacokinetic analysis. Wade JR, Beal SL, Sambol NC. Department of Pharmacy, University of California, San Francisco 94143-0446.

The influence of the choice of pharmacokinetic model on subsequent determination of covariate relationships in population pharmacokinetic analysis was studied using both simulated and real data sets. Simulations and data analysis were both performed with the program NONMEM. Data were simulated using a two-compartment model, but at late sample times, so that preferential selection of the two-compartment model should have been impossible. A simple categorical covariate acting on clearance was included. Initially, on the basis of a difference in the objective function values, the two-compartment model was selected over the one-compartment model. Only when the complexity of the one-compartment model was increased in terms of the covariate and statistical models was the difference in objective function values of the two structural models negligible. For two real data sets, with which the two-compartment model was not selected preferentially, more complex covariate relationships were supported with the one-compartment model than with the two-compartment model. Thus, the choice of structural model can be affected as much by the covariate model as can the choice of covariate model be affected by the structural model; the two choices are interestingly intertwined. A suggestion on how to proceed when building population pharmacokinetic models is given.

LBS.

_/ _/ _/_/ _/_/_/ _/_/_/ 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)

From: "Sale, Mark" <ms93267@glaxowellcome.com>

Subject: RE: Model building algorithm

Date: Tue, 25 Apr 2000 13:57:46 -0400

Lewis,

Onward,

I did have an error in my equations, TVS1 should be TVS2, as you pointed out. To make it simple, let's use only additive etas, and a linear relationship between wt and vol then

TVWTS = THETA(1) ; TYPICAL VALUE OF V/WT SLOPE

WTSL= TVWTS + ETA(1) ; TRUE VALUE OF V/WT SLOPE

TVS2 = THETA(2) + WT*WTSL ; TYPICAL VALUE OF S2

S2 = TVS2 + ETA(2) ; TRUE VALUE OF S2

then

S2 = THETA(2)+WT*(THETA(1)+ETA(1)) + ETA(2)

and eta(1) and eta(2) are identifiable, at least not formally unidentifiable. I think that the equations from the previous email reduce similarly, on a log scale.

I agree with your point we need not obsess (too much) about finding the best model, and I'm sure we can all agree that the objective function is not the sole criteria on which to base the model building process. However, we assume that we are looking only find the "best" model, but the "correct" model (in order to do unbiased hypothesis testing). Presumably, no model is better than the correct model, so the correct model must be the best. That, I believe is the reason for seeking the best model. Regardless, we delude ourselves that hypothesis testing is ever appropriate.

Your point about the performance is well taken. I particularly like your sentence but by its faithfulness to the real world it models.

I'll use that next time I discuss with Mike Hale and Keith Muir the relative merits of empiric vs biologically based models. Clinically, we are interested in making some reasonably accurate prediction - about the real world, and often extrapolating those predictions to some other data set.

Mark

From: "Piotrovskij, Vladimir [JanBe]" <VPIOTROV@janbe.jnj.com>

Subject: RE: Model building algorithm

Date: Fri, 28 Apr 2000 09:16:12 +0200

Dear NONMEM users,

I received questions from two members of the list regarding my last posting, so I feel it necessary to make it clear for the entire list.

My original posting was:

>If you choose between two or more canditate structural models, look first at

>the plots of individual weighted residuals versus time (or sqrt(time) if the

>range of time is wide and models have two or more exponential terms). The

>best model produces residuals that show no pattern. The minimum objective

>function value or AIC are less important, especially if you have many

>observations per individual. The models you test should have random effects

>for every structural parameter. The form of $OMEGA matrix is not important.

>It is sufficient to use just a simple diagonal form: you can optimize $OMEGA

>after selecting an appropriate structural model. It is even not essential to

>get the convergence: only the posthoc step is really needed.

It is only applicable if you have many measurement per individual (rich data). The optimal structural model should fit individual data reasonably well, and the best way to evaluate the goodness of individual fit is visual examination of IRES (or IWRES to be exact) versus time and IPRED. If you have only sparse data, this approach will not work, of course.

However, I think, having no rich data you cannot identify the right (realistic) structural model unless the sparse data are collected using an optimal, well-balanced sampling schedule which is most oftenly not the case. Suppose you know the drug has the two-exponential disposition, but you have sparse data and can fit only the one-compartment model? Will you trust parameter estimates then?

Best regards,

Vladimir

----------------------------------------------------------------------

Vladimir Piotrovsky, Ph.D.

Janssen Research Foundation

Clinical Pharmacokinetics (ext. 5463)

B-2340 Beerse

Belgium

Email: vpiotrov@janbe.jnj.com