Other thread subtopics:

Centering Covariates

Covariate Models Using Weight (Allometric Scaling)

Predefined Models vs. "Context-Sensitive" Emperical Models

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From: "Stephen Duffull" <sduffull@fs1.pa.man.ac.uk>

Subject: Re: Covariate Models Using Weight

Date: Fri, 19 Nov 1999 09:15:41 -0000

There has been considerable discussion about covariate models etc. I perceive that the discussion has slightly wider implications. Are covariates that have a mechanistic flavour better than those that do not (or none at all)?

1) If you have a choice of two covariates (eg creatinine clearance or serum creatinine). eg. If you have a renally cleared drug and you can use either estimated creatinine clearance (eg Cockcroft and Gault or Jelliffe & Jelliffe) as a covariate or some empirical model based on serum creatinine and both models yield the same objective function with the same number of parameters then which do you use? I personally prefer the generality of the creatinine clearance equation. The same is true for Nick's argument - if an allometric scaling factor has been developed that has generality outside of the particular experiment that is being considered currently and still predicts as well as an empirical choice then I personally would prefer using it (even if I could not substantiate the value of the power (3/4) in this particular experiment).

2) If a covariate does not improve the fit of your model do you include it? eg If adding WT^(?) as a covariate for Vd or CL does not alter the objective function significantly - then do you include it as a descriptor? This depends on why you are modelling (eg descriptive or predictive). If "predictive" then it would be difficult not to believe that larger people don't have larger Vd or CL - even if you couldn't show this based on the current experimental design.

I don't think it is bad to include prior beliefs, as long as they have some basis in reality, in the model building exercise and indeed if the process needs to be formalised then a Bayesian solution may be appropriate.

In both examples assumptions in model building need to be transparent to the user.

Just a thought

Steve

=====================

Stephen Duffull

School of Pharmacy

University of Manchester

Manchester, M13 9PL, UK

Ph +44 161 275 2355

Fax +44 161 275 2396

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

Subject: RE: Covariate Models Using Weight

Date: Fri, 19 Nov 1999 12:09:44 +0100

Good point, Steve.

Mechanistic considerations are very useful and can guide model development. Just one example from own practice: a drug is eliminated exclusively via renal route. WT and CLCR are almost equal as predictors for CL. What to prefer? I prefer CLCR to WT since I know the mechanism of elimination. CLCR and WT are highly correlated and that is why the inclusion of WT in CL submodel works as well as CLCR. The problem of correleted predictors! Mechanistic considerations help selecting right predictors.

Vladimir

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Vladimir Piotrovsky, Ph.D.

Janssen Research Foundation

Clinical Pharmacokinetics

B-2340 Beerse

Belgium

Email: vpiotrov@janbe.jnj.com

Date: Fri, 19 Nov 1999 10:09:16 -0600

From: James Gallo <JM_Gallo@fccc.edu>

Subject: Re: Covariate Models Using Weight

I would be hesistant to use CLCR [creatinine clearance] as a covariate for a drug that undergoes appreciable renal excretion, particularly if CRCL is estimated from a standard formula. These calculated formulas are derived [depending on the particular formula, Cockcroft-Gault, etc...] from, if my memory is correct, a relatively small populations of subjects. Moreover, its been shown that other measures [such as 51Cr-EDTA clearance] are better predictors of renal function or glomerular filtration rate than the 'calculated' formulas that suggest CRCL is of lower mechanistic value. These latter methods [51Cr-EDTA, etc..] of estimating renal function are not always readily available, however, I believe [I think someone has published on this as well] estimation of renal function/GFR by serum creatinine plus other covariates is a better predictor than the 'calculated' formulas.

You also raise the issue of correlation [collinearity] amongst covariates. There are a variety of objective criteria that can indicate such a problem that you are probably much more familiar with than myself. Not to deny you artisitc freedom as a modeler, but I would like to think objective criteria can direct your selction of covariates in most cases. At the same time, if I interpret your message correctly, I agree that selection of covariates is problematic even given objective criteria.

jim gallo

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

Subject: RE: Covariate Models Using Weight

Date: Sun, 21 Nov 1999 10:28:24 +0100

1. I would certainly prefer 51Cr-EDTA to CLCR, but the former is rather an exception in clinical practice.

2. I would also prefer measured CLCR to calculated. If we speak about calculated CLCR as a single parameter describing renal function, there is a lot of formulas, all based on relatively small number of subjects. I personally like the formula appeared in NONMEM Users Guide Part V, p.33 (the calculated parameter is called RF which stands for "renal function"):

RF = WT*(1.66-0.011*AGE)/SCR

3. Applying any of the above mentioned formulas (Cockcroft-Gault including) is exactly what you suggest: "estimation of renal function/GFR by serum creatinine plus other covariates".

Vladimir

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Vladimir Piotrovsky, Ph.D.

Janssen Research Foundation

Clinical Pharmacokinetics

B-2340 Beerse

Belgium

Email: vpiotrov@janbe.jnj.com

Date: Sun, 21 Nov 1999 10:22:07 -0600

From: James Gallo <JM_Gallo@fccc.edu>

Subject: Re: Covariate Models Using Weight

Possibly we agree on how renal function can be 'modeled' using covariates, however, application of pre-defined formulas, such as you indicate in points 2 and 3 [ala Cockcroft-Gault, or similar] is not what I meant by "estimation of renal function/GFR by serum creatinine plus other covariates". Such formulas would be derived uniquely for the particular drug and database.

jim gallo

Date: Mon, 22 Nov 1999 15:00:52 +1300

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

Subject: Re: Covariate Models Using Weight

James Gallo wrote:

> Possibly we agree on how renal function can be 'modeled' using covariates,

> however, application of pre-defined formulas, such as you indicate in points

> 2 and 3 [ala Cockcroft-Gault, or similar] is not what I meant by "estimation

> of renal function/GFR by serum creatinine plus other covariates". Such

> formulas would be derived uniquely for the particular drug and database.

I doubt if the above is very practical because it is highly unlikely that there exists in the database the essential item used by C&G and other predictive formulae i.e. the creatinine production rate.

These formulae are a combination of two separate models:

1. CLcr = Creatinine Production Rate/ Steady State Serum Creatinine

= CPR/Scr

[I will restrict my remarks to creatinine concentrations which are assumed to be at steady state]

2. CPR = f(age,weight,gender)

[Other covariates might also be included eg. height to predict ideal body weight instead of using total body weight]

Model 1 is a well understand theoretical model that everyone who has ever been learned any pharmacokinetics should be familar with.

Model 2 is an empirical model based on some understanding of covariates that predict muscle mass. It is then assumed that creatinine production is directly proportional to muscle mass.

The C&G formula is based on direct measurement of urinary creatinine excretion rates. Bjornsson (1979) combined the original data from Cockcroft & Gault with further data from 2 other similar observatonal studies of creatinine excretion to obtain a larger data set with 936 females and 219 males. He then used the C&G model and offered the following model and parameters for CLcr prediction (ml/min):

Males CLcr = (143.5 - (1.095*Age) * Wt * 0.07

Females CLCr = (119.5 - (0.915*Age) * Wt * 0.07

where Age is in years and Wt is in kg (0.07 is a magic number to get CLcr in units of ml/min).

I am not aware of a larger and more complete analysis of such a database. I use a model based on these parameters when I wish to predict CLcr. In some 10 years of doing population analyses I do not recall ever seeing a drug company database that offered creatinine excretion rate as a covariate. So I have never had the opportunity to do as Jim Gallo proposes: "Such formulas would be derived uniquely for the particular drug and database".

I much prefer the Bayesian (biology and science based) to the frequentist (empirical, ignore the past) view of these things. Use of the Bjornsson parameters suits my Bayesian leanings because it is based on a reasonable biological+empirical model and a superset of the C&G data.

Returning to Jim Gallo's suggestion. One could be totally empirical and try to do something like this:

CL = CLnonrenal + f(age,weight,gender,SCr)

but this ignores the extensive knowledge on how these covariates are related to creatinine production rate.

Isolating the prediction of CLcr allows one to identify separately how one or more of these covariates e.g. age, might predict CLnonrenal e.g.

CL = CLnonrenal*(1+Fage*(Age-AgeStd)) + CLrenal*(1+Fclcr*(CLcr-CLcrStd))

where CLcr is predicted from (age,weight,gender,SCr) with fixed parameters such as those described by Bjornsson. AgeStd and CLcrStd are the age and creatinine clearance in the standard individual who has CLnonrenal and Clrenal equal to the population estimate and Fage and Fclcr are parameters of empirical covariate models. The covariate model for CLrenal could be made more biological by testing the assumption that CLrenal is 0 when CLcr is 0 with:

CL = CLnonrenal*(1+Fage*(Age-AgeStd)) + CLrenal*CLcr/CLcrStd

I recommend reading the excellent review of the topic of predicting renal function using serum creatinine by Bjornsson. It covers not only the prediction of CLcr assuming steady state, but also prediction of creatinine volume of distribution and prediction of CLcr using non-steady state serum creatinine. He also explicitly discusses the use of lean body mass versus actual body weight and recommends for practical reason to use ideal body weight for obese patients.

Bjornsson TD. Use of serum creatinine concentrations to determine renal function. Clin Pharmacokin 1979; 4:200-222

--

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, 22 Nov 1999 10:58:08 +0100

From: Karin Fattinger <fattinge@kpt.unizh.ch>

Subject: Covariate Models Using Weight

I just would like to add, that there exists a new formula predicting renal function from serum creatinine (and other covariates) developed from 1628 patients with chronic renal disease:

Levey-AS; Bosch-JP; Lewis-JB; Greene-T; Rogers-N; Roth-D, A more accurate method to estimate glomerular filtration rate from serum creatinine: a new prediction equation. Modification of Diet in Renal Disease Study Group, Ann-Intern-Med. 1999 Mar 16; 130(6): 461-70.

Besides serum creatinine concentrations and covariates(Age, gender and race), this formula includes also serum albumin concentrations and serum urea nitrogen concentrations.

Division of Clinical Pharmacology and Toxicology

Date: Mon, 22 Nov 1999 10:01:47 +0000

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

Subject: CrCL, 51-CrEDTA etc.

Dear Nick, Valdimir, James etc.

My personal experience is that the Cockcroft & Gault formula is not very good (at least, in cancer patients, I would not recommend its use). The paper by C&G is vulnerable to criticism from many aspects (4% women, questionable methodology) I am not familiar with the paper by Bjornsson, but if it is from 1979, then we again have to be wary that creatinine assays may have changed a lot since then (and certainly have in my experience). Another problem is that we can't really know the creatinine production, or guarantee that we are in steady-state. We have done some work with surrogate markers and gained a modest improvement over the conventional covariates used (SCr, body size measure, sex, age). If we are trying to generate a surrogate for creatinine production using age, weight and gender, then this may well be population-dependent and before using the Bjornsson formula this would have to be considered careful. Perhaps we can all agree that mechanistic considerations suggest we should reciprocate serum creatinine.

James

PS 51Cr-EDTA clearance and creatinine clearance don't actually measure the same thing. Which we use depends on the drug (and clinical population) - its the drugs clearance that we need a predictor for (not how much creatinine is in their urine).

Date: Mon, 22 Nov 1999 08:45:17 -0600

From: James Gallo <JM_Gallo@fccc.edu>

Subject: Re: Covariate Models Using Weight

Nick,

I feel you also are missing my point about covariate modeling related to renal function or any other mechanism related to drug disposition. For some reason you seem to want to adhere to PRE-DEFINED Formulas to describe CRCL and subsequently drug clearance. Certainly these formulas may be useful, either as Bayesian priors or less rigoursly to suggest functional relationships. Nonetheless, one might question if the population they are derived from [Cockcroft and Gault or Bjornsson] are analogous to the population in which one is using to model. These PRE-DEINED formulas indicate age and weight are accounted for, but what about disease state to name just one other cofounding variable. Papers by Chatelut and Boddy indicate that carboplatin clearance is better predicted by 'unique' formulas rather than 'canned' ones.

Given the problem of developing a population model for DRUG X that undergoes appreciable renal clearance, I believe it is more rational to start from scratch. There should be little bias at this stage. Possibly one may find remnants of the PRE-DEFINED formula in the final formula [so what], but I would be surprised to find a PRE-DEFINED formula as a better predictor that the uniquely-derived formula. I'm sure you are aware that CRCL is presumably being used as a measure of GFR, and many drugs also undergo active tubular secretion and reabsorption so using a PRE-DEFINED formula unduly complicates the modeling by embedding particular variables [age and wt,...] in the estimation of CRCL. These variables may not have the same relationship to other clearance mechanisms.

I don't understand your comments related to size of databases and drug companies,and this is a reason to use these PRE-DEFINED formulas. My guess is that anyone undertaking the development of a population-based PK model assumes that their database is large enough to identify meaningful relationships between covariates and drug clearance or volume of distribution. These relationships will undoubtedly reveal covarites that have a mechanistic basis and those that do not. Let's assume the task was to model a drug that underwent 100% hepatic clearance. One would not have [or want] PRE-DEFINED formulas to relate covariates and clearance, and would start from scratch to identify significant covariate-CL relationships. This is exactly the strategy I would prefer to use for a drug that undergoes renal clearance. Why should you use a PRE-DEFINED formula that makes use of a SURROGATE [creatinine]?

jim gallo

From: "Stephen Duffull" <sduffull@fs1.pa.man.ac.uk>

Subject: Re: Covariate Models Using Weight

Date: Mon, 22 Nov 1999 17:04:44 -0000

James Gallo wrote (in relation to a comment from Nick):

> I feel you also are missing my point about covariate modeling related to

> renal function or any other mechanism related to drug disposition. For

> some reason you seem to want to adhere to PRE-DEFINED Formulas to describe

> CRCL and subsequently drug clearance.

This was my original point. If there is little difference in the fit between two models (one "predefined" and one not) to the same data then incorporating the "predefined" model which has proven generality seems more mechanistic than

developing a "context-sensitive" model empirically (which has unknown generality). The choice of the "predefined" model (or "context-insensitive" model) is then up to the modeller (obviously no one model is going to solve all problems).

Steve

=====================

Stephen Duffull

School of Pharmacy

University of Manchester

Manchester, M13 9PL, UK

Ph +44 161 275 2355

Fax +44 161 275 2396

**********************************************************

Other thread subtopics:

Centering Covariates

Covariate Models Using Weight (Allometric Scaling)

Predefined Models vs. "Context-Sensitive" Emperical Models