- On 24 Dec 1998 at 17:31:31, Roger_Jelliffe (jelliffe.-a-.hsc.usc.edu) sent the message

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Dear Colleagues:

I don't understand all this discussion of how to weight the data,

whether

it is better to weight by 1/y^2 or by doing the log transformation, for

example. Why not skip all thiese assumptions and simply calibrate the assay

over its working range, and then fit the relationship between the

concentration and the SD with a polynomial so one can have a good estimate

of the SD with which each single level is measured, so one can then fit

according to the Fisher information of each concentration, namely the

reciprocal of the variance of each data point? The problem is that the

coefficient of variation is hardly ever constant, and the SD needs to be

known over its entire working range.

If one uses the log transformation, for example, a concentation of 10

units has only 1/100 the weight (Fisher info) of a concentration of 1 unit,

and only 1/10,000 the weight of a concentration of 0.1 units. Is this

realistic? I don't think so. I really don't understand all this discussion

about a point that can be easily answered simply by calibrating each assay,

by determining its error pattern over its working range. This point is

discussed more fully in Therapeutic Drug Monitoring 15: 380-393, 1993.

Of course there are other errors than just the assay. There are those

associated with errors in preparing and giving each dose, and in recording

the times when the doses were given, and with recording the times when the

serum samples were drawn. What sense does it make to assume that all of

these these are also part of the measurement noise, and then to use the log

transformation or 1/y^2 as the description of them? Most of them are

actually part of the process noise, not the measurement noise. But whatever

is done, why not start by knowing what the assay errors actually are?

Sincerely,

Roger Jelliffe - On 28 Dec 1998 at 16:26:56, Mats Karlsson (mats.karlsson.-a-.biof.uu.se) sent the message

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Dear collegues,

Roger_Jelliffe (by way of David_Bourne) wrote:

>

> PharmPK - Discussions about Pharmacokinetics

> Pharmacodynamics and related topics

>

> Dear Colleagues:

>

> I don't understand all this discussion of how to weight the data,

> whether

> it is better to weight by 1/y^2 or by doing the log transformation, for

> example.

That discussion deals with the shape of the distribution of errors as

opposed

to the magnitude, which is discussed below. (Although I have just

joined this

list and not followed the preceding discussion and therefore may have

misinterpreted

the topic of the discussion).

> Why not skip all thiese assumptions and simply calibrate the assay

> over its working range, and then fit the relationship between the

> concentration and the SD with a polynomial so one can have a good estimate

> of the SD with which each single level is measured, so one can then fit

> according to the Fisher information of each concentration, namely the

> reciprocal of the variance of each data point? The problem is that the

> coefficient of variation is hardly ever constant, and the SD needs to be

> known over its entire working range.

>

> If one uses the log transformation, for example, a concentation of 10

> units has only 1/100 the weight (Fisher info) of a concentration of 1 unit,

> and only 1/10,000 the weight of a concentration of 0.1 units. Is this

> realistic? I don't think so. I really don't understand all this discussion

> about a point that can be easily answered simply by calibrating each assay,

> by determining its error pattern over its working range. This point is

> discussed more fully in Therapeutic Drug Monitoring 15: 380-393, 1993.

>

> Of course there are other errors than just the assay. There are those

> associated with errors in preparing and giving each dose, and in recording

> the times when the doses were given, and with recording the times when the

> serum samples were drawn. What sense does it make to assume that all of

> these these are also part of the measurement noise, and then to use the log

> transformation or 1/y^2 as the description of them? Most of them are

> actually part of the process noise, not the measurement noise. But whatever

> is done, why not start by knowing what the assay errors actually are?

>

> Sincerely,

>

> Roger Jelliffe

>

As I understand the suggestion, one should

1. Approximate the assay error magnitude by a polynomial

2. Fit a PK model to the data using two models for residual error, one

for assay

error (fixed from step 1) and one for process noise (to be estimated).

Some comments on such a scheme.

- The term "process noise", I assume is used to indicate that other

factors than

the underlying drug concentration may influence the error magnitude.

This is an

important point that has been made before (e.g. J Pharmacokinet

Biopharm 23:651-672, 1995;

J Pharmacokinet Biopharm 26:207-246, 1998).

- I missed one important source of errors from the list and that is

model misspecification.

Our models will always only be approximations and this is particularly

obvious in most analyses of

models/data incorporating oral absorption. Our residual error model

must reflect this.

- The original question of the shape of error distribution is not

addressed by the above scheme.

- To do step 1, i.e. approximating the assay error by a function, is not

trivial

and involves assumptions and model selection of its own. Since assay

variability in step 2,

is to be fixed (i.e. taken to be known without error) maybe also such a

procedure demand more assay data

than normally is collected. A polynomial is used for approximation and

as polynomials may behave

badly in ranges without data, and thus also the spacing of assay

standards may need to be different

from what is otherwise chosen.

- The above scheme has the advantage that, we will not obtain estimates

of the total

residual error below the assay error. However, in my experience, that

is not a problem and indeed,

in the vast majority of population PK analyses, assay error is only a

minor component of the total

residual error. The residual error is usually very well determined (in

population analyses) and

the part of the model for which prior information is of the least

value. In population analyses,

I therefore fail to see any advantage of having one component of the

residual error fixed to

a previous estimate. Since it is usually difficult to obtain

information on the residual error

model and magnitude in individual PK analyses, the above scheme may well

in such analyses be of value.

Best regards,

Mats Karlsson

Div. of Pharmacokinetics and Biopharmaceutics

Uppsala University

Sweden

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