From P.M.C.Wright@ncl.ac.uk Tue Nov 21 02:04:47 1995

I wish to devise a useful method for modeling the indcidence of adverse effects based on an underlying PK model. The adverse effects will usualy be dichotomous (i.e. either they do happen or they dont) and may not necessarily occur with a direct temporal relationship with any particualar drug concentration.

Do any users have any suggestions based on their previous experience

Peter Wright
Tel: 0191 222 6982
Department of Anaesthesia
Fax: 0191 222 8988=20
University of Newastle upon Tyne
Beeper: 01893 917710

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From pascal Tue Nov 21 11:32:31 1995

One usual way to modelize a dichotomous variable is through the classical logistic model that transforms any function taking its values in the interval [-INF, +INF] into a probability function taking its values in [0, 1]. Other transformations are possible, as the probit one.

Let Y be the dependant variable, with Yij=1 adverse effect, Yij=0 NO adverse effect measured at jth time for ith patient; X be a set of covariates that may or may not include the concentration. The logistic model for the probability of Yij given Xij is:

p(Yij=1 | Xij) = exp(g(Yij | Xij)) / [1+exp(g(Yij | Xij))]
p(Yij=0 | Xij) = 1 - p(Yij=1 | Xij)

Where g the logit takes its values in the interval [-INF, +INF] and can be defined as:

g(Yij=1|Xij) = f(X,theta) + eta{i} + eps{i,j}

with f any linear or non-linear function (e.g. a PK, or PK-PD model model) of covariates; theta the parameters of the function f; eta{i} a random vector representing shift from population model and eps{i,j} the random intra-individual variability.

A nice example of implementation of such a model is given by Lewis Sheiner and can be found in the NONMEM repository subdirectory NONMEM.DIR/LOGIST.DIR, maintained by Steve Shafer and Jaap Mandema at Stanford. This can be reached using the ftp anonymous:

pkpd.icon.palo-alto.med.va.gov

This site can also be consulted using a WWW browser at:

http://pkpd.icon.palo-alto.med.va.gov/

However this does not preclude the question of Peter's data: this type of model needs a lot of data in order to estimate the parameters, since each dichotomous observation carries very little information. This means lot of patients and/or lots of observations/patients.

Pascal Girard

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