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Re: modeling binary observations

From: Nick Holford <n.holford>
Date: Fri, 12 Sep 2008 22:39:08 -0400


Without you giving us any further details of the process you are
describing I can only offer some general idea of how you might approach
this. Given that you think that a binary outcome is dependent on the
cumulation of something I am assuming the cumulation is with respect to

This leads to the idea of using a hazard function to describe the
underlying disease process and a modulation of the hazard to reflect the
drug action. The hazard can be integrated (i.e. cumulated) over time in
order to predict the probability of not having had the event upto a
certain point in time (the survivor function).

A specific example of this kind of process might be the build up of
platelets to form a thrombus. The stickiness of each platelet can be
thought of as the hazard. An underlying disease may make the platelets
stickier than usual and thus increases the probability of a thrombotic
event. A drug might decrease stickiness and thus decrease hazard which
in turn would decrease the probability of the event. The clinically
observed outcome would be the time of observation until an event
occurred e.g. a pulmonary embolus.

You could look at
for some background material on this idea.

There are other kinds of cumulative processes that you might want to
describe but with a continuous endpoint for clinical outcome rather than
a binary event. In that case you should consider the non-linear
relationship between conc and effect leading to a cumulative effect. The
cumulative effect (AUC of effect) will not be proportional to the dose
while the simple use of AUC of the concentration will be proportional to
dose (assuming 1st order PK).

See the example of frusemide action and cumulative diuretic effect in


Zhang, Yi [CNTUS] wrote:
> Dear All :
> I'd like to get your opinion on this: when modeling an event (0/1)
> that is caused by an cumulative effect, 1. would cumulative AUC be a
> better predictor than concentration, since CAUC can better capture the
> accumulative process? 2. If CAUC is used, is there good ways to
> implement mechanistic/semi-mechanistic models rather than empirical
> approaches for binary data?
> 3. Can the model results from CAUC be extrapolated to other trial
> designs, why or why not?
> Your input is appreciated. Thanks.
> Yi Zhang
> Centocor

Nick Holford, Dept Pharmacology & Clinical Pharmacology
University of Auckland, 85 Park Rd, Private Bag 92019, Auckland, New Zealand
Received on Fri Sep 12 2008 - 22:39:08 EDT

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