LEADING ARTICLE
`
`Clin Pharmacokinet 2002; 41 (1): 1-6
`0312-5963/02/0001-0001/$25.00/0
`
`© Adis International Limited. All rights reserved.
`
`Using Pharmacokinetic-
`Pharmacodynamic Relationships to
`Predict the Effect of Poor Compliance
`Jean-Pierre Boissel and Patrice Nony
`Department of Clinical Pharmacology, Claude Bernard University and Teaching Hospital,
`Lyon, France
`
`Abstract
`
`Since it is difficult to improve patient compliance to drug prescriptions, an
`alternative is to select a drug with less consequences for poor compliance, that
`is, a drug that has the capacity of ‘forgiveness’. Forgiveness is the property of a
`drug which, when compared with another medicine with different pharmaco-
`kinetics and/or concentration-effect relationships, blunts the consequences of
`missing one or two doses in a row, or has a greater variability in the timing of
`intake. Simulations show that drugs with a concentration-effect relationship
`modelled with an effect compartment, for example a delayed response, have
`more forgiveness. A marker of forgiveness would be of some help for doctors
`deciding which drug to prescribe to patients who are poor compliers.
`
`1. Poor Compliance with Drug Therapy
`
`Compliance with therapy is defined as the de-
`gree of coincidence between a person’s behaviour
`and the prescription instructions given by their
`physician.[1] It has been observed for centuries that
`compliance with doctors’ prescriptions is not al-
`ways perfect, whatever the markers for compliance
`used. The interest in compliance stems from the
`fundamentals of pharmacology: that there is for all
`drugs a dose-effect relationship, related to a con-
`centration-effect relationship at the site of action,
`which is mediated through the interaction of drug
`with receptor. Thus, if less than the prescribed dosage
`is taken, the effect will be less than expected, and if
`more is taken, the effect will be greater and delete-
`rious effects may occur.
`The shape of the dose-effect relationship explains
`the varying effect of taking less (or more) than the
`prescribed dose, as illustrated in figure 1. Missing
`
`20% of the prescribed dose when the expected ef-
`fect is at or near the plateau will change little in the
`treatment efficacy (A), whereas one or two pills
`missed at the maximum slope of the dose-effect
`curve could halve the effect (B).
`The idea of a continuous, increasing, relationship
`between dose and effect is quite old, much older
`even than the discovery of receptors, and is the
`basis of drug discovery, development and practice.
`The existence of this relationship has been con-
`firmed by the progress in pharmacokinetics and
`pharmacodynamics since the beginning of the last
`century, as explained in all textbooks of pharmaco-
`therapy. However, for most drugs and their expected
`clinical effects we do not know precisely the shape
`of the relationship shown in figure 1, which remains,
`in these cases, mostly speculative. Nevertheless,
`this relationship is the rationale for the current be-
`lief that poor compliance could alter the effective-
`
` EXHIBIT NO. 1027 Page 1
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`
`Boissel & Nony
`
`Simple statistics can summarise a patient’s com-
`pliance history, although none incorporate all the
`features of compliance. Different markers may be
`calculated: the percentage of days with accurate
`dose intake (or compliance rate), the percentage of
`prescribed doses taken, the percentage of drug hol-
`idays (days without drug intake), the time variabil-
`ity in drug intake, the percentage of too short or too
`long administration intervals, the median and quar-
`tiles of administration intervals.
`The diversity of the pattern of poor compliance
`and the difficulty in improving compliance through
`changes in patients’ behaviour have led to more
`focus on the drug itself. Not all drugs have the same
`relationship between dose and concentration, and
`concentration and effect, respectively. The idea
`that the consequences of noncompliance vary with
`the particular drug has initiated research aimed at
`characterising which drugs are more demanding
`than others in terms of compliance. This has led to
`the concept of ‘forgiveness’. For instance, drugs
`with a very narrow therapeutic index (for example
`antiarrhythmic agents) would be preferred with for-
`giveness, i.e. with the capacity that missing (or re-
`peating) one or a few doses will not be of conse-
`quence for the expected efficacy (or safety). Finally,
`a difficulty in exploring the potential consequences
`of less than optimal compliance is our inability to
`link the pharmacological effect of a drug with its
`efficacy on a clinical outcome. Although many
`models are potentially appropriate, there is, in most
`cases, very little evidence available to select the
`best one.[3]
`
`2. Capacity for Forgiveness
`
`A drug for which a dose can be missed without
`having too much effect on the expected benefit and
`safety of the prescription is said to have the prop-
`erty of forgiveness. The notion of treatment for-
`giveness has been defined by Urquhart[4] as the
`property of a drug, given as a repeated treatment,
`to forgive the omission of one dose, or several
`doses in a row, without a loss of efficacy. Some
`intuitive examples come to mind: (i) drugs that are
`stored somewhere in the body in a releasable
`
`A
`
`B
`
`Dose
`
`100
`90
`80
`70
`
`60
`50
`40
`30
`
`20
`10
`0
`
`Percentage of plateau response (Emax)
`
`2
`
`Fig. 1. Relationship between dose and effect, expressed as a
`percentage of the maximal response.
`
`ness of a prescription. As such, the dose-effect
`relationship, whether precisely known or pure
`guesswork, remains the underlying compulsory as-
`sumption of any research on the consequences of
`less than optimal compliance behaviour. In parallel
`to the expected pharmacological effects and clin-
`ical efficacy, a similar reasoning can be made for
`concentration-dependent adverse effects: their in-
`cidence increases with dose or concentration, and
`the same relationship as that shown in figure 1 is
`assumed, and sometimes empirically observed.[2]
`One challenge in studying varying compliance,
`from whatever perspective, including its conse-
`quences for the expected efficacy, is that no single
`feature can express it. First, there is no single cat-
`egory of noncompliers, but a spectrum of variable
`compliance with, roughly, five patients in about six
`who do not comply satisfactorily and one patient
`in about six complying poorly, taking less than
`40% of prescribed doses with long and widely vari-
`able administration intervals.[1] Secondly, several
`patterns of less than full compliance can be defined:
`(i) delay in the beginning and/or the termination of
`treatment; (ii) intake of nonprescribed drugs; (iii)
`omission of one or several doses; (iv) errors in the
`size of the dose to be taken; and (v) inappropriate
`and irregular timing in administration. Thus, instead
`of noncompliance, it seems more appropriate to
`speak of poor compliance.
`
`© Adis International Limited. All rights reserved.
`
`Clin Pharmacokinet 2002; 41 (1)
`
` EXHIBIT NO. 1027 Page 2
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`Predicting the Effect of Poor Compliance
`
`3
`
`form;[5] (ii) drugs with a very long elimination
`half-life, so the steady-state blood concentration
`does not change very much when a dose is missed;[5]
`(iii) drugs with an indirect effect model, i.e. a delayed
`effect compared with blood concentration; and (iv)
`drug regimens at the plateau of the dose-effect
`curve (see figure 1). The last situation depends on
`the prescription, whereas the former depend on the
`drug itself and its interactions with the body. These
`cases are considered in this article. They should be
`investigated with proper approaches in order to
`confirm the anticipated forgiveness and to provide
`a formal framework for identifying drugs with this
`capacity. We will limit the derivation to efficacy,
`although a similar approach can be applied to con-
`centration-dependent adverse effects. Following
`the last remarks of the previous section, we will
`assume that a sustained pharmacological effect,
`
`with a given average value, is required for the ex-
`pected clinical efficacy.
`
`3. Labelling for Compliance
`
`Knowledge of the consequences of poor com-
`pliance for a particular drug belongs to the general
`framework of prescription information, as does
`other information in the drug data sheet. Such
`knowledge is useful for doctors to manage compli-
`ance and to allow them to put emphasis on drugs
`with low forgiveness. Recommended dosage re-
`gimens are chosen for all drugs from extensive
`clinical experience during phase II and III trials.
`Although it is likely that compliance is better in
`clinical trials, this has never been documented, and
`the safety and therapeutic implications of poor
`compliance are rarely explored during clinical tri-
`als. Thus, dosage recommendations reflect a set-
`
`Drug A
`
`k12
`
`1
`
`Effect
`
`2
`
`k20
`
`Drug B
`
`k12
`
`1
`
`Effect
`
`2
`
`k20
`
`k12 = 1.385; k20 = 0.389; V1 = 1; V2 = 5;
`F = 0.65; D = 100; half-life = 1.78
`
`k12 = 1.385; k20 = 0.99; V1 = 1; V2 = 5;
`F = 0.65; D = 200; half-life = 0.7
`
`Drug C
`
`Drug D
`
`3
`
`k32
`
`k23
`
`2
`
`k20
`
`k12
`
`1
`
`Effect
`
`k12
`
`1
`
`2
`
`k20
`
`k2e
`
`Effect
`
`ke0
`
`k12 = 1.385; k20 = 0.389; k23 = 0.1;
`k32 = 0.06; V1 = 1; V2 = 5; V3 = 8.33;
`F = 0.65; D = 100; half-life = 14.9
`
`k12 = 1.385; k20 = 0.389; k2e = 0.001;
`ke0 = 0.1325; V1 = 1; V2 = 5; Ve = 0.03774;
`F = 0.65; D = 100; half-life = 1.78
`
`Fig. 2. Four drugs, A, B, C and D, with different pharmacokinetic-pharmacodynamic models (see figures 3 and 4). For drugs A, B
`and C there is a direct relationship between the concentration in the central compartment 2 and effect: E(t) = 2 • C2(t). For drug D,
`the effect compartment causes an indirect pharmacokinetic-pharmacodynamic relationship: E(t) = Ce(t). 1 = absorption compartment;
`2 = central compartment; 3 = peripheral compartment; e = effect compartment; Cx(t) = concentration in compartment x at time t; D
`= dose; E(t) = effect at time t; F = bioavailability; kxy = intercompartmental transfer rate constant; kx0 = elimination rate constant from
`compartment x; Vx = volume of compartment x (all expressed in arbitrary units).
`
`© Adis International Limited. All rights reserved.
`
`Clin Pharmacokinet 2002; 41 (1)
`
` EXHIBIT NO. 1027 Page 3
`
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`
`

`
`Boissel & Nony
`
`used here to prove that forgiveness occurs in par-
`ticular pharmacokinetic and pharmacodynamic sit-
`uations. It involves a computer simulation starting
`from the mathematical models used to describe the
`kinetics of an in vivo pharmacological response.
`Usually, the models considered involve a pharmaco-
`kinetic model, a pharmacodynamic response model
`with a pharmacodynamic effect summary. This in-
`termediate pharmacodynamic effect can also be re-
`lated to a clinical effect using physiological models
`or statistical models (such as logistic regression,
`for example).
`The results of these simulations allow us to pre-
`dict therapeutic failure or rebound effects on clin-
`ical outcomes, when the model linking the pharma-
`cological and clinical effect is known or can be
`guessed, or only on the expected pharmacological
`effect when it cannot, during recurrent drug holi-
`days (i.e. two to three or more sequential days with-
`out drug administration), variability in administra-
`tion intervals or variability in pharmacokinetic
`properties, assuming the superposition principle
`applies. For a given drug, knowledge of its phar-
`macokinetic-pharmacodynamic relationship is re-
`quired to identify its capacity for forgiveness. In
`addition, we will illustrate the relationship between
`the pharmacokinetic-pharmacodynamic character-
`istics of a drug and its capacity for forgiveness.
`
`5. Examples
`
`We compared the time dependence of the phar-
`macological effect of four drugs with different
`pharmacokinetic and pharmacodynamic proper-
`ties. The main features of their pharmacokinetic
`and pharmacodynamic models are shown in figure
`2. Drugs A, B and C differ by their pharmacokinetic
`features: B has an elimination half-life half that of
`A, and C is stored in a peripheral compartment that
`will blunt variations of the concentration of the
`drug in the central compartment. Drug D differs
`from all others by its indirect relationship between
`concentration in the central compartment and effect,
`modelled by an effect compartment.[7,8] Drugs A,
`B and C have a direct pharmacokinetic-pharmaco-
`
`Drug A
`Drug B
`Drug C
`Regular administration interval
`Irregular administration interval
`
`4
`
`35
`
`30
`
`25
`
`20
`
`15
`
`10
`
`5
`
`Effect
`
`120
`
`140
`130
`Time (arbitrary unit)
`
`150
`
`Fig. 3. Examples of the impact of pharmacokinetics on forgive-
`ness. Drug B has a half-life half that of drug A; drug C has a
`peripheral compartment and the same half-life as drug A.
`
`ting of drug use that may be different from current
`medical practices.
`It would be a great help for a prescriber to know
`whether he/she could authorise or should restrict
`variability in the time interval between two consec-
`utive administrations and the dosage errors which
`should not be exceeded for each drug. In the inter-
`ests of both accuracy and full disclosure, drug la-
`belling should include some information on the
`consequences of the major patterns of noncompli-
`ance. In addition to meeting the ethical standard of
`full disclosure, labelling that includes such infor-
`mation would also provide a rational basis for ef-
`forts to improve patient compliance, the outcome
`of treatment and the quality of ambulatory care. In
`this perspective, the concept of forgiveness looks
`promising.
`
`4. Prediction of the Effect of Poor
`Compliance and Forgiveness
`
`The only approach that can be used to predict
`the effect of poor compliance for different drug-
`specific pharmacokinetic-pharmacodynamic relation-
`ships is in silico studies.[6] This approach will be
`
`© Adis International Limited. All rights reserved.
`
`Clin Pharmacokinet 2002; 41 (1)
`
` EXHIBIT NO. 1027 Page 4
`
` AMNEAL
`
`

`
`Predicting the Effect of Poor Compliance
`
`5
`
`dynamic relationship, i.e. their site of effect is the
`central compartment.
`The pharmacological effect over time is ob-
`tained by computation (figure 3 and figure 4). The
`comparison started after steady state (more than 10
`half-lives) has been reached through regular drug
`administration, i.e. full compliance. Poor compli-
`ance is simulated by irregular administration inter-
`vals. We did not use simulation to account for vari-
`ability of model parameters, which should be done
`if one has to compare real drugs.
`
`variation of the effect due to irregular drug intake
`intervals. Thus, drugs with indirect concentration-
`effect relationships have a better capacity for for-
`giveness as compared with those with direct con-
`centration-effect relationships, since the peak
`effects are lower (less adverse effects) and trough
`effects are higher (more sustained clinical efficacy).
`Furthermore, the ‘smoothing’ effect of the indirect
`relationship appears to be greater than that result-
`ing from increased half-life or a peripheral com-
`partment (compare figures 3 and 4).
`
`5.1 Pharmacokinetic Forgiveness
`
`6. Conclusion
`
`Intuitively, poor compliance with a short half-
`life drug will induce lower trough concentrations
`when the administration interval is increased, and
`higher peak concentrations when the administration
`interval is decreased. If the drug has a direct effect
`model, this will lead to a less sustained pharmaco-
`logical effect and a higher rate of concentration-
`dependent adverse effects at peak drug concentra-
`tions. The above computations and simulation
`support these intuitive thoughts, and added that,
`more generally (everything else being equal), drugs
`with an indirect effect have a more sustained phar-
`macological effect.
`The major conclusion from the above derivation
`is that drugs may differ greatly in terms of capacity
`for forgiveness, depending on their pharmacokinetic
`and pharmacodynamic properties, i.e. their spe-
`cific chemistry, metabolism and mechanism of ac-
`tion. Therefore, ideally, physicians should be able
`to select the proper drug, for instance in narrow
`therapeutic range situations and/or for patients
`who are more likely not to comply with the pre-
`scribed regimen, on its capacity for forgiveness.
`However, in order to achieve that in practice, pre-
`scribers should have access to appropriate indica-
`tor(s) of forgiveness.
`
`Acknowledgements
`
`This work was supported by APRET (Agence Pour la
`Recherche et l’Evaluation Thérapeutique), the Luennec
`Medical School and Lyon Teaching Hospital.
`
`In figure 3, the comparison between drugs A, B
`and C suggests that a longer half-life and a periph-
`eral compartment are better for forgiveness, since
`the variation of the effect is much greater with drug
`B.
`
`5.2 Pharmacodynamic Forgiveness
`
`In figure 4, the improvement of forgiveness
`with an indirect concentration-effect relationship
`is striking. The effect compartment smooths the
`
`Regular administration intervals
`Irregular administration intervals
`
`Drug A
`
`Drug D
`
`25
`
`20
`
`15
`
`10
`
`5
`
`Effect
`
`120
`
`125
`
`140
`135
`130
`Time (arbitrary units)
`
`145
`
`150
`
`Fig. 4. Examples of the impact of concentration-effect relation
`on forgiveness. The unshaded area under the concentration-
`time curve shows drug A with a direct concentration-effect rela-
`tions hip [E(t) = C2(t)] and the shaded area under the
`concentration-time curve shows drug D with an indirect concen-
`tration-effect relationship [E(t) = Ce(t)]. C2(t) = concentration in
`central compartment at time t; Ce(t) = concentration in effect
`compartment at time t; E(t) = effect at time t.
`
`© Adis International Limited. All rights reserved.
`
`Clin Pharmacokinet 2002; 41 (1)
`
` EXHIBIT NO. 1027 Page 5
`
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`
`

`
`6
`
`Boissel & Nony
`
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`
`Correspondence and offprints: Jean-Pierre Boissel, Depart-
`ment of Clinical Pharmacology, Claude Bernard University
`and Teaching Hospital, Lyon, France.
`E-mail: jpb@upcl.univ-lyon1.fr
`
`© Adis International Limited. All rights reserved.
`
`Clin Pharmacokinet 2002; 41 (1)
`
` EXHIBIT NO. 1027 Page 6
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` AMNEAL