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Re: CrcL or Cr in pediatric model

From: Leonid Gibiansky <LGibiansky>
Date: Tue, 13 Jan 2009 17:49:54 -0500

Jakob,

The model that I mentioned is not additive; it is multiplicative:

Parameter= MeanValue*Effect1(WT)*Effect2(RF)

but the effect of RF is expressed as a linear function of RF
Effect2(RF) = 1 + THETA()*RF

Leonid


--------------------------------------
Leonid Gibiansky, Ph.D.
President, QuantPharm LLC
web: www.quantpharm.com
e-mail: LGibiansky at quantpharm.com
tel: (301) 767 5566




Ribbing, Jakob wrote:
> Leonid,
>
> I notice that you are now also suggesting an additive model (even if you
> call 1+THETA empirical) so I guess that we agree this parameterisation
> is acceptable? The way you and Nick would normalize RF in principle
> turns this into an additive model but parameterized in a way that is
> more stable (i.e. less correlation between the estimates of population
> parameters).
>
> I can agree with you (and Nick) that it is appealing to use some kind of
> standardized or normalized renal function. My initial suggestion was a
> simple parameterisation that would avoid counting WT twice (from Peters
> original question). As you point out, if CRCL can be exactly determined
> by
> WT the model would be over parameterized with high correlation between
> the estimates (and CRCL would not contain any additional information).
> Even if that is not the case with Peters data (OFV drops when adding
> CRCL) we can assume that de-correlating the covariates makes the model
> more stable. If my simple model would not converge or if I decide to
> keep RF in the model (apriori or after testing it), I would change to a
> normalized RF.
>
> Jeff, testing for the interaction can be a way of evaluating whether you
> got the final model right (not anything you do before you included all
> the covariates you think are important). I would pay more attention to
> if the interaction seems important than the p-value. As you point out,
> you can achieve the same using simulations (or standard gof plots), but
> you need to stratify on BOTH WT and RF (at the same time). If you have
> sufficient data, the above assessments may help you identify model
> deficiencies like what you mention for CRCL. This in turn, makes one
> consider using alternative models or renal markers or ways of
> calculating RF. I think you find possible corrections of CRCL in Nicks
> references given earlier in this thread.
>
> Thanks
>
> Jakob
>
> -----Original Message-----
> From: owner-nmusers
> On Behalf Of Leonid Gibiansky
> Sent: 13 January 2009 20:37
> To: Nick Holford
> Cc: nmusers
> Subject: Re: [NMusers] CrcL or Cr in pediatric model
>
> Nick,
>
> Just to set the record straight:
> I did NOT proposed model (1):
> TVCL=THETA(1)*(WT/70)^(3/4) + THETA(2)*(WT/70)^(3/4)
> Rather I mentioned that this is not an appropriate model.
>
> Model 2 is indeed empirical. Instead of BSA you can use WT^(3/4) or any
> other normalization:
> TVCL=THETA(1)*(WT/70)^(3/4) * RF^GAMMA
>
> RF is the renal function.
>
> GAMMA is the fudge factor. You can set it to one or replace RF^GAMMA by
> other empirical function of RF, e.g., 1+THETA()*RF. The point is that
> renal impairment may influence not only renal clearance itself but also
> a lot of other body functions (metabolism, in particular). Linear
> dependence (that you mentioned) may or may not be sufficient to account
> for these changes.
>
> Use of categorical covariates, indeed, sacrifices some information but
> it can be used to detect whether it makes sense to use more
> detailed/mechanistic models: if categorical description does not show
> any renal impairment effect, it makes no sense to use more complicated
> models, and it makes sense to explain dependence of CL on CRCL by WT,
> AGE or other available covariates.
>
> Best
> Leonid
>
> --------------------------------------
> Leonid Gibiansky, Ph.D.
> President, QuantPharm LLC
> web: www.quantpharm.com
> e-mail: LGibiansky at quantpharm.com
> tel: (301) 767 5566
>
>
>
>
> Nick Holford wrote:
>> Leonid,
>>
>> You propose two models
>>
>> Model 1: TVCL=THETA(1)*(WT/70)^(3/4) + THETA(2)*(WT/70)^(3/4)
>> Model 2: TVCL=THETA(1)*(WT/70)^(3/4) * (CRCL/BSA)^GAMMA
>>
>> As you say, Model 1 clearly is not identifiable to distinguish
> THETA(1)
>> and THETA(2). An identifiable model would be:
>>
>> Model 3: TVCL=(THETA(1) + RF*THETA(2)) * (WT/70)^(3/4)
>>
>> Here RF is the renal function. Note I use renal function as a relative
>
>> measure of the function of the kidney which is the way it is typically
>
>> used in clinical practice e.g. one says 'this patient has normal renal
>
>> function' or 'this patient has poor renal function'. In previous
>> publications (eg. see Mould 2002, Matthews 2004, Anderson 2007) I have
>
>> used the RF factor to identify the relationship between a biomarker
> such
>> as CLcr and the renal component of clearance. Note that RF is size
>> independent. Size is applied, independently, to both the non-renal
>> (THETA(1)) and the renal clearance (THETA(2)) through theory based
>> allometric scaling.
>>
>> Model 3 is mechanism based and can be used to test mechanistic
>> hypotheses e.g. is renal clearance linearly related to RF? and
> extended
>> e.g. is there a drug interaction on non-renal clearance with a known
>> metabolism inhibitor which is not expected tochange renal elimination?
>>
>> Model 2 is quite empirical. It uses BSA for scaling althought this is
>> known to have a poor theoretical foundation and is worse than theory
>> based allometry using WT^3/4 when these models are tested using GFR in
>
>> relation to size (Rhodin 2008). The gamma parameter has no physical
>> intepretation. The model cannot distinguish the effect of a metabolic
>> inhibitor on non-renal clearance. I cannot see any point in using this
>
>> model unless you are just a statistician interested in generating P
> values.
>> The interesting challenge is how to define RF. In adults (Mould 2002,
>> Matthews 2004) this has been done relative to a 'normal' standard
>> CLcrSTD of 6 L/h/70kg. Individual CLcr was predicted using Cockcroft &
>
>> Gault (Mould 2002) or with a very similar but mechanistically enhanced
>
>> model in Matthews (2004). The individual CLcr prediction was based on
>> age, sex and serum creatinine but the prediction was standardised to
> 70
>> kg. The RF was then calculated from CLcr/CLcrSTD.
>>
>> In children it is possible to predict Clcr using height and the
> Schwartz
>> formulae which were empirically derived for different age groups and
>> unfortunately scaled to a BSA of 1.73M^2. Very frequently one has
> only
>> got weight so it makes the Schwartz method more difficult to use. It
> is
>> possible to predict BSA from weight alone in children (1935) then use
>> the DuBois & DuBois formula with weight to determine an appropriate
>> height. In this way one can use just weight alone to predict CLcr
>> (uncorrupted by BSA) in different age groups of children. Other
> methods
>> have been proposed e.g. Leger (2002), Cole (2004) but these have been
>> developed in older children and the Cole method can predict negative
>> values (see Anderson 2008).
>>
>> The method for predicting RF in children is to use the GFR prediction
>> model (Rhodin 2008) to obtain a 'normal' GFR based on maturation and
>> size. Then predict individual CLcr using a model to predict creatinine
>
>> production rate (CPR) and dividing by the measured serum creatinine
>> (Scr). ie. CLcr=CPR/Scr. The RF is then calculated similarly to adults
>
>> from CLcr/GFR. In adults CLcr is quite close to GFR but in young
>> children the CLcr is typically higher than GFR by 15% or more
>> (Hellerstein 1992). Because there are no good standards for Clcr in
>> children and because GFR is a biomarker more closely related to the
>> function of the kidney overall the 'normal' GFR is preferable to a
>> 'normal' CLcr.
>>
>> I am currently working on an extension to the model proposed in
> Anderson
>> (2007) which uses vancomycin clearance and GFR observations to deduce
>> how CLcr can be predicted from maturation and size from very premature
>
>> neonates to young adults. This new CLcr method has shown itself
> capable
>> of identifying RF variation in neonates which substantially reduces
>> between subject variability in neonatal vancomycin clearance (18%
>> compared with 28%) (work in progress).
>>
>> Leonid asked these questions in an earlier response to Peter. I have
>> added some comments:
>>
>>> 1. I usually normalize CRCL by WT^(3/4) or by (1.73 m^2 BSA) to
> get
>>> rid of WT - CRCL dependence. If you need to use it in pediatric
>>> population, normalization could be different but the idea to
> normalize
>>> CRCL by something that is "normal CRCL for a given WT" should be
> valid.
>> BSA is a bad idea. It is provably worse than WT^3/4 (Rhodin 2008) and
> is
>> persists through tradition and a mistaken allometric theory developed
>> over 100 years ago (See Anderson 2008).
>> Normalization to "normal CRCL for a given WT" is a good idea and in a
>> more complex form is what I have described above (WT alone is not good
>
>> enough for neonates -- post-menstrual age must be included too).
>>> 2. In the pediatric population used for the analysis, are there
> any
>>> reasons to suspect that kids have impaired renal function ? If not, I
>
>>> would hesitate to use CRCL as a covariate.
>> In general I agree with you that in most cases there is no need to
>> suspect renal function impairment in children. Indeed the big problem
>> has been how to know if renal function impairment existed. Impairment
>> implies that the non-impaired normal value is known. The work of
> Rhodin
>> (2008) finally provides a method predicting normal GFR but it was a
>> necessary assumption of that analysis that all the GFR measurements
> were
>> made in children without renal disease.
>>> 3. Often, categorical description of renal impairment allows to
>>> decrease or remove the WT-CRCL correlation
>> Categorical descriptions are necessarily less informative. You just
>> throw away information by putting people into boxes. It is a way of
>> hiding the problem not solving it.
>>
>>
>> So in conclusion I encourage people working in this area to use
>> mechanism based models to understand how renal function influences
>> pharmacokinetics and at the very least compare the predictions of an
>> empirical model (e.g. Model 2) with a mechanism based model (e.g.
> Model
>> 3) so that you can understand what you are missing.
>>
>> Nick
>>
>> Anderson, B. J., K. Allegaert, et al. (2007). "Vancomycin
>> pharmacokinetics in preterm neonates and the prediction of adult
>> clearance." Br J Clin Pharmacol 63(1): 75-84.
>>
>> Anderson, B. J. and N. H. Holford (2008). "Mechanism-based concepts of
>
>> size and maturity in pharmacokinetics." Annu Rev Pharmacol Toxicol 48:
>
>> 303-32.
>>
>> Boyd, E. (1935). The growth of the surface area of the human body.
>> Minneapolis, University of Minnesota Press.
>>
>> Cole, M., L. Price, et al. (2004). "Estimation of glomerular
> filtration
>> rate in paediatric cancer patients using 51CR-EDTA population
>> pharmacokinetics." Br J Cancer 90(1): 60-4.
>>
>> DuBois, D. and E. F. DuBois (1916). "A formula to estimate the
>> approximate surface area if height and weight be known." Archives of
>> Internal Medicine 17: 863-871.
>>
>> Hellerstein, S., U. Alon, et al. (1992). "Creatinine for estimation of
>
>> glomerular filtration rate." Pediatric Nephrology 6: 507-511.
>>
>> Leger, F., F. Bouissou, et al. (2002). "Estimation of glomerular
>> filtration rate in children." Pediatr Nephrol 17(11): 903-7.
>>
>> Matthews, I., C. Kirkpatrick, et al. (2004). "Quantitative
> justification
>> for target concentration intervention - Parameter variability and
>> predictive performance using population pharmacokinetic models for
>> aminoglycosides."
>>
>> Mould, D. R., N. H. Holford, et al. (2002). "Population
> pharmacokinetic
>> and adverse event analysis of topotecan in patients with solid
> tumors."
>> Clinical Pharmacology & Therapeutics. 71(5): 334-48.
>> British Journal of Clinical Pharmacology 58(1): 8-19.
>>
>> Rhodin, M. M., B. J. Anderson, et al. (2008). "Human renal function
>> maturation: a quantitative description using weight and postmenstrual
>> age." Pediatr Nephrol. Epub. (please contact me if you want a pdf
> copy)
>>
>>
>>
>> Leonid Gibiansky wrote:
>>> Jakob,
>>> Restrictions on the parameter values is not the only (and not the
>>> major) problem with additive parametrization. In this specific case,
>>> CRCL (as clearance) increases proportionally to WT^(3/4) (or similar
>>> power, if you accept that allometric scaling has biological meaning
> or
>>> that the filtration rate is proportional to the kidney size). Then
> you
>>> have
>>>
>>> TVCL=THETA(1)*WT^(3/4)+THETA(2)*WT^(3/4)
>>> (where the second term approximates CRCL dependence on WT).
>>> Clearly, the model is unstable.
>>>
>>> Answering the question:
>>>> why would two persons, with WT 50 and 70 kg
>>>> but otherwise identical (including CRCL and any other covariates,
>>>> except WT), be expected to differ by 36% in CL?
>>> we are back to the problem of correlation. If two persons of
> different
>>> WT have the same CRCL, they should differ by the "health" of their
>>> renal function. I would rater have the model
>>> CL=THETA(1)*(WT/70)^(3/4)*(CRCL/BSA)^GAMMA
>>> Then, if two subjects (50 and 70 kg) have the same CRCL, their CL
> will
>>> be influenced by WT, and by renal function (in this particular
>>> realization, CRCL per body surface area). While the result could be
>>> the same as in
>>> CL ~ CRCL,
>>> we described two separate and important dependencies:
>>> CL ~ WT; and CL ~ renal function
>>> For the patient that you mentioned, they act in the opposite
>>> directions and cancel each other, but it is important to describe
> both
>>> dependencies.
>>>
>>>> Regarding 3 below, is the suggestion to estimate
>>>> independent allometric
>>>> models on CL for each level of renal function?
>>> The suggestion was to define the renal disease as categorical
>>> variable, and then correct CL, for example:
>>> TCL ~ THETA(1) (for healthy)
>>> TCL ~ THETA(2) (for patients with severe renal impairment)
>>>
>>> Thanks
>>> Leonid
>>>
>>> --------------------------------------
>>> Leonid Gibiansky, Ph.D.
>>> President, QuantPharm LLC
>>> web: www.quantpharm.com
>>> e-mail: LGibiansky at quantpharm.com
>>> tel: (301) 767 5566
>>>
>>>
>>>
>>>
>>> Ribbing, Jakob wrote:
>>>> Leonid,
>>>>
>>>> I usually prefer multiplicative parameterisation as well, since it
> is
>>>> easier to set boundaries (which is not necessary for power models,
> but
>>>> for multiplicative-linear models). However, boundaries on the
> additive
>>>> covariate models can still be set indirectly, using EXIT statements
> (not
>>>> as neat as boundaries directly on the THETAS, I admit).
>>>>
>>>> In this case it may possibly be more mechanistic using the additive
>>>> parameterisation: For example if the non-renal CL is mainly liver,
> the
>>>> two blood flows run in parallel and the two elimination processes
> are
>>>> independent (except there may be a correlation between liver
> function
>>>> and renal function related to something other than size). A
>>>> multiplicative parameterisation contains an assumed interaction
> which is
>>>> fixed and in this case may not be appropriate. If the drug is mainly
>>>> eliminated via filtration, why would two persons, with WT 50 and 70
> kg
>>>> but otherwise identical (including CRCL and any other covariates,
> except
>>>> WT), be expected to differ by 36% in CL? This is what you get using
> a
>>>> multiplicative parameterisation. The fixed interaction may also
> drive
>>>> the selection of the functional form (e.g. a power model vs a linear
>>>> model for CRCL on CL). I do not know anything about Peter's specific
>>>> example so this is just theoretical.
>>>>
>>>> Regarding 3 below, is the suggestion to estimate independent
> allometric
>>>> models on CL for each level of renal function?
>>>>
>>>> Thanks
>>>>
>>>> Jakob
>>>>
>>>> -----Original Message-----
>>>> From: owner-nmusers
> [mailto:owner-nmusers
>>>> On Behalf Of Leonid Gibiansky
>>>> Sent: 12 January 2009 23:30
>>>> To: Bonate, Peter
>>>> Cc: nmusers
>>>> Subject: Re: [NMusers] CrcL or Cr in pediatric model
>>>>
>>>> Hi Peter,
>>>>
>>>> If allometric exponent is fixed, collinearity is not an issue from
>>>> the mathematical point of view (convergence, CI on parameter
>>>> estimates, etc.). However, in this case CRCL can end up being
>>>> significant due to additional WT dependence (that could differ from
>>>> allometric) rather than
>>>>
>>>> due to renal function influence (that is not good if you need to
>>>> interpret it as the renal impairment influence on PK).
>>>>
>>>> Few points to consider:
>>>> 1. I usually normalize CRCL by WT^(3/4) or by (1.73 m^2 BSA) to
>>>> get rid of WT - CRCL dependence. If you need to use it in pediatric
>>>> population, normalization could be different but the idea to
>>>> normalize CRCL by something that is "normal CRCL for a given WT"
>>>> should be valid.
>>>> 2. In the pediatric population used for the analysis, are there
>>>> any reasons to suspect that kids have impaired renal function ? If
>>>> not, I would hesitate to use CRCL as a covariate.
>>>> 3. Often, categorical description of renal impairment allows to
>>>> decrease or remove the WT-CRCL correlation
>>>> 4. Expressions to compute CRCL in pediatric population (note that
>
>>>> most of those are normalized by BSA, as suggested in (1)) can be
> found
>>>> here:
>>>> http://www.globalrph.com/specialpop.htm
>>>> http://www.thedrugmonitor.com/clcreqs.html
>>>> 5. Couple of recent papers:
>>>> http://www.clinchem.org/cgi/content/full/49/6/1011
>>>> http://www.ajhp.org/cgi/content/abstract/37/11/1514
>>>>
>>>> Thanks
>>>> Leonid
>>>>
>>>> P.S. I do not think that this is a good idea to use additive
> dependence:
>>>> TVCL=THETA(X)*(WT/70)**0.75+THETA(Y)*CRCL
>>>> --------------------------------------
>>>> Leonid Gibiansky, Ph.D.
>>>> President, QuantPharm LLC
>>>> web: www.quantpharm.com
>>>> e-mail: LGibiansky at quantpharm.com
>>>> tel: (301) 767 5566
>>>>
>>>>
>>>>
>>>>
>>>> Bonate, Peter wrote:
>>>>> I have an interesting question I'd like to get the group's
>>>>> collective opinion on. I am fitting a pediatric and adult pk
>>>>> dataset. I have fixed weight a priori to its allometric exponents
>>>>> in the model. When
>>>> I
>>>>> test serum creatinine and estimated creatinine clearance equation
> as
>>>>> covariates in the model (power function), both are statistically
>>>>> significant. CrCL appears to be a better predictor than serum Cr
> (LRT
>>>> =
>>>>> 22.7 vs 16.7). I have an issue with using CrCL as a predictor in
>>>>> the model since it's estimate is based on weight and weight is
>>>>> already in the model. Also, there might be collinearity issues
> with
>>>>> CrCL and weight in the same model, even though they are both
>>>>> significant. Does
>>>>> anyone have a good argument for using CrCL in the model instead of
>>>> serum Cr?
>>>>> Thanks
>>>>>
>>>>> Pete bonate
>>>>>
>>>>>
>>>>>
>>>>> Peter L. Bonate, PhD, FCP
>>>>> Genzyme Corporation
>>>>> Senior Director
>>>>> Clinical Pharmacology and Pharmacokinetics
>>>>> 4545 Horizon Hill Blvd
>>>>> San Antonio, TX 78229 USA
>>>>> _peter.bonate
>>>>> phone: 210-949-8662
>>>>> fax: 210-949-8219
>>>>> crackberry: 210-315-2713
>>>>>
>>>>> alea jacta est - The die is cast.
>>>>>
>>>>> Julius Caesar
>>>>>
>>>>>
>
Received on Tue Jan 13 2009 - 17:49:54 EST

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