modeling binary observations

> 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 > > >

Hello Dr. Zhang, The first reference below discusses some issues and interpretations using CAUC to model binary (0/1) events. In general, CAUC, being non-mechanistic, can have trouble identifying sources of delay, which can have impact on decision-making. Also, CAUC would have difficulty predicting the responses of subjects should they be withdrawn from medication (unless some function were used to un-accumulate the AUC). In the case that we studied, it did provide reasonable predictions of the responses. So one might infer from this that covariate analysis used for certain predictions might not be problematic. The second reference provides a method for constructing semi-mechanistic (?) models. The method is based on the idea of an unobserved (or unobservable) continuous variable. The semi-mechanistic models are built with respect to this 'latent' variable. This method, given sufficient data, should be able to parttion delay between PK (keo) or PD (kin,kout) sources, which could have an impact on decision making and dosing strategies. 1.) Hutmacher, Matthew M., Nestorov, Ivan, Ludden, Tom, Zitnik, Ralph, Banfield, Christopher Modeling the Exposure-Response Relationship of Etanercept in the Treatment of Patients With Chronic Moderate to Severe Plaque Psoriasis J Clin Pharmacol 2007 47: 238-248 2.) Exposure-response modeling using latent variables for the efficacy of a JAK3 inhibitor administered to rheumatoid arthritis patients Matthew M. Hutmacher, Sriram Krishnaswami and Kenneth G. Kowalski Volume 35, Number 2 / April, 2008 Hope these help. Kind regards, Matt

Yi, 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 time. 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 http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford/teaching/pharmacometrics/_docs/modelling_likelihoods_using_NONMEM_VI.pdf 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 http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford/teaching/medsci722/_docs/1_cumulative_effects.pdf Nick 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 n.holford http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford

Yi, 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 time. 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 http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford/teaching/pharmacometrics/_docs/modelling_likelihoods_using_NONMEM_VI.pdf 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 http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford/teaching/medsci722/_docs/1_cumulative_effects.pdf Nick 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 [EMAIL PROTECTED] tel:+64(9)923-6730 fax:+64(9)373-7090 http://www.fmhs.auckland.ac.nz/sms/pharmacology/holford