Concentration-Effect Analysis of Antihypertensive Drug Responses

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Concentration-Effect Analysis ofAntihypertensive Drug Responses

John L. Reid and Peter A. Meredith

It is now widely recognized that a rigid stepped-care approach to antihypertensive therapy isnot universally appropriate. Individualized treatment may result in good or better bloodpressure control and a simpler regimen without troublesome side effects. Successful develop-ment of such a strategy depends on accurate characterization of a dose-response relation andquantitative assessment of the response in each individual. In the past such relations haveproved to be hard to identify for antihypertensive drugs, often because of inappropriate studydesign during drug development Despite failure of earlier studies to identify drug concentra-tion-antihypertensive response relations, use of concentration-effect modeling, which recog-nizes and characterizes the temporal discrepancy between drug concentration and effect, hasproved more successful. By using such an approach, it has been possible to characterize theconcentration-effect relations after acute and steady-state antihypertensive therapy withprazosin, doxazosin, nifedipine, verapamil, and enalapril. With enalapril and nifedipine, it hasbeen demonstrated that the mathematical parameters of effect derived from the first dose canpredict the response to these drugs after 4-6 weeks of treatment These findings suggest thatthe definition of individual concentration-effect relations may be of value in the rational choiceof antihypertensive drug therapy and optimization of dose and dose frequency. In particular,the approach can provide valuable information on dose-effect relations and should optimizechoice of dose intervals in drug development and practice. (Hypertension 1990;16:12-18)

In the last 40 years, the treatment of hypertensionhas developed dramatically from therapeutic"impotence" in the 1930s and 1940s to the

range of effective drugs available today. Strategies ofdrug use have reflected the classes of drugs availableas well as contemporary views of the pathogenesis ofhypertension. In the 1950s and 1960s, with a limitedchoice available, single drugs were used in what arenow regarded as heroic doses.1 The price was fre-quent and severe side effects, which were, to a largedegree, dose related. The basis of the successful"step care" approach was the use of relatively lowdoses of drugs in rational combination to achieve thedesired effect without intolerable side effects.2 Selec-tion of a diuretic or /3-adrenergic receptor blocker asfirst choice, followed by the two drugs together, andaddition of a vasodilator such as hydralazine was thebasis of a popular triple therapy step care regimen.Alternative vasodilators have been proposed andused for the third step.34

Although it is important not to underestimate thevalue of this pragmatic empirical approach in the1970s and early 1980s, recent developments raise

From the Department of Medicine and Therapeutics, Universityof Glasgow, Glasgow, Scotland.

Address for correspondence: Dr. J.L. Reid, Western Infirmary,Glasgow, Gil 6NT, Scotland.

questions about the usefulness of a rigid stepped careregimen.4-6 The recognition that side effects or asso-ciated diseases commonly limit the applicability ofstandard drugs such as diuretics or /3-blockers,together with the recent introduction of alternativefirst line drugs such as angiotensin converting enzyme(ACE) inhibitors, calcium antagonists, and a-adrenergic receptor blockers, has led the JointNational Committee in the United States7 and theInternational Society of Hypertension/World HealthOrganization Mild Hypertension Liaison Committee8

to propose a broader based and more flexible strat-egy. A new therapeutic approach is emerging basedon an individualized choice of therapy.6910 Ideally,this would involve an initial selection from four orfive alternative first-line drugs based on clinical anddemographic information about the individualpatient, a rapid assessment after the first dose thatthe patient is likely to have a satisfactory response,and finally the selection of the optimum dosage forlong-term treatment. This strategy is appealing as itreflects optimal clinical practice,9 but a major prob-lem is identifying which drugs are individually suitedto which patients. Simple demographic factors suchas age have not proved as useful in individuals1112 assome early reports claimed.13 Similarly, biochemicalmarkers such as plasma renin activity1415 have not

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Reid and Meredith Antihypertensive Drug Response 13

proved reliable or discriminating predictors ofresponse in mild-to-moderate essential hypertensiveindividuals on a normal (Western) salt intake.1617

It is important to recognize that in practice the"response" to an antihypertensive drug is a quanti-tative variable and not a simple categorical "yes/no"answer. There is a consistent placebo corrected"response rate" of 40% to 50% to a wide range ofdrugs given as monotherapy.918-19 The rate observeddepends on the patient group studied and the defi-nition of response used. Addition of a second drugfrom a different class usually increases the responserate to 70% and 80%. It is our impression fromseveral similar studies that there is a considerableoverlap in "responders" to monotherapy with drugsof different pharmacological classes; however, othersdisagree9-18 and this aspect warrants a formal trial.All would acknowledge that new, well-controlledstudies in this area are indicated. Response to treat-ment is not easy to assess even with a measurable endpoint like blood pressure. The choice of dose andfrequency of administration are also difficult todetermine.

It has been an almost universal experience withantihypertensive drugs that the doses used in estab-lished practice are significantly lower than the dosesused in early studies and the regimens recommendedwhen the drugs were first introduced. Doses of/J-blockers and thiazides used nowadays very rarelyreach the levels recommended in earlier years.1 ACEinhibitors and calcium antagonists are also used inmuch lower doses than those recommended initially.This in part reflects a failure to recognize the limita-tions of trial design including forced dose titration,time versus drug effects, and above all, the widervariability in response in the general population.Until very recently information on the dose-effectrelations of antihypertensive drugs was limited orabsent, and many drugs were claimed to have "flat"dose-response curves. This is probably incorrect andoriginated because early studies used high doses thatproduced drug concentrations on the upper plateauof a maximal effective dose (E^ ) relation so that thelower part of the dose-response curve was not ade-quately explored (Figure 1). Similar misunderstand-ings led to conclusions that there was no relationbetween the plasma level of antihypertensive drugsand their pharmacological effect. As discussed below,individual variability in drug plasma levels (i.e., phar-macokinetics) is probably the largest source of vari-ability in response to many antihypertensive drugs.

Variability in Response to Antihypertensive DrugsThe major pitfalls in blood pressure measurement

are well known and include observer bias, digitpreference, instrument calibration, and inappropri-ate cuff size20 in addition to "white coat" or "office"hypertension. In any evaluation of response to anantihypertensive drug, these potential sources oferror contribute to variability and must be excludedby using reliable, bias-free equipment and trained

100*

Tharapauttodoaa rang*

Log D O M

FIGURE 1. Schematic of a representative dose-responserelation, illustrating how, if the therapeutic dose range hasbeen established around the potential maximal effect, this maybe interpreted as a "flat" dose-response relation.

observers, or alternatively, regularly serviced, vali-dated semiautomated devices or even 24-hour ambu-latory recordings. In addition to instrument andobserver variables, there is the inherent variability ofblood pressure with established diurnal patterns andsuperimposed shorter term rhythms related to phys-ical or mental activity and behavioral influences.Even by standardizing the time of day and theconditions of recording, there will still be "biologi-cal" variability in blood pressure within individuals.This inherent variability may be reduced by makingmultiple recordings of blood pressure over 12- or24-hour periods.21

When an antihypertensive effect is being studiedand there is a drug-induced temporal change in bloodpressure imposed on diurnal variations, it is essentialto make measurements across the complete dosageinterval. Single measurements of blood pressurebetween 2 and 6 hours after dosing can give mislead-ing response information on effect, and similarly,measurements recorded at the end of the dosageinterval address only the duration of action and notthe magnitude of response. For accurate assessmentof the dose-response curve, the maximal effect andthe duration of action, it is necessary to measureresponse throughout the dose interval. The variationamong individuals not only in the profile but also inthe magnitude of antihypertensive effect makes itdifficult if not impossible to accurately identify thetime of maximal response without recording the fullblood pressure profile for each individual.

A further confounding factor in the assessment ofantihypertensive drugs is regression to the mean andthe associated observation of "placebo" responses22

or the converse white coat hypertension.23 There isstill no agreement on the optimal time of observationto eliminate these factors. However, 1 month can bea relatively short time interval, and 3-6 months maybe more appropriate in some patients. There isevidence that these problems may be less prominentif 24-hour ambulatory blood pressure recordings areused.24


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14 Hypertension Vol 16, No 1, July 1990

Variability in response to drugs is not unique toantihypertensive agents. It is widespread and is theresult of pharmacokinetic and pharmacodynamic fac-tors. Genetic and environmental factors do undoubt-edly exert a major effect on response but pharmaco-kinetic factors contribute the largest identifiablecomponent to the variability. In studies with ACEinhibitors,17 calcium antagonists25-26 and a-blockers,27-28 much of the intersubject variability inantihypertensive effect was attributable to individualdifferences in drug disposition and thus to plasmaand tissue drug levels. In contrast, demographic andbiochemical factors, such as age, sex, plasma reninactivity, and plasma noradrenaline, were compara-tively unimportant and did not significantly or inde-pendently influence the blood pressure responses ina group of salt-replete Caucasian patients with mild-to-moderate hypertension.1725-28

In other patient populations, specific dynamic fac-tors may assume greater importance: for example,when there is activation of the renin-angiotensinsystem due to diuretic treatment or salt and waterdepletion, the response to an ACE inhibitor drugmay be more markedly influenced by the level ofrenin or angiotensin II in plasma.1516 It is importantto continue attempts to clearly identify, in differentpatient groups, the contribution of genetic and otherfactors in determining the magnitude of hypertensivedrug response, but instead of focusing on patientswho show optimal or marginally suboptimalresponses, it may be more relevant to concentrate onpoor or nonresponders and to identify the reasons fortheir relative resistance to therapy.

Dose or Concentration-Response RelationsIt is surprising that accurate information on many

dose-response relations in hypertension has beenaccrued only recently. The commonly referenced flatdose-response relation for the antihypertensiveeffect of diuretics and £-blockers is particularly mis-leading. The relation is almost certainly not flat atlow drug concentrations, and the misunderstandinghas arisen from studies that have used large dosesand examined the plateau phase of a conventionaldose-response curve (Figure 1). In the case of diuret-ics, it appears that the dose-response curve for someof the adverse metabolic effects, such as hypokalemiaand hyperuricemia,29 may be steep over the thera-peutic range of doses used for hypertension. How-ever, the other metabolic effects of thiazide diureticson glucose and lipid metabolism may not be doserelated.29

Dose-response relations have been more clearlyidentified with vasodilator drugs like calcium antag-onists. However, to identify dose-response relationsit is necessary to undertake a study of sufficient size(power), of an appropriate design and of a suffi-ciently wide range of doses (low and high) to char-acterize the relation. Many of these same designfeatures must also be considered when evaluating theplasma drug concentration-effect relation.30 In addi-

tion to accurate and simultaneous measurements ofthe effect on blood pressure, it is also necessary tohave accurate quantitation of the drug or its activemetabolite concentration in plasma and to be able tofully characterize not only the time course of theeffect but also the plasma concentration-time profileand the pharmacokinetic properties of the drug.

There is some evidence that the response to anti-hypertensive drugs may be influenced by treatmentduration1-15: for example, it has been shown that ittakes several weeks to achieve maximal blood pres-sure response with captopril.15 In contrast, the anti-hypertensive effect with a-blockers may be maximalinitially and reduced during long-term treatment,27'28

whereas for calcium antagonists antihypertensiveeffect may be reduced31 or unchanged.26 A timediscrepancy between the attainment of maximumplasma concentration and the attainment of maxi-mum effect may be partly responsible. This discrep-ancy, which is common to many antihypertensivedrugs, presumably reflects a delay in achievingsteady-state drug concentrations at the site ofaction.32 Alternatively, for some drugs, including thecalcium antagonist verapamil, there may be a changein pharmacokinetics from acute to chronic dosinggiving rise to higher plasma concentrations duringlong-term treatment.25 However, it is clear thatdynamic counterregulatory mechanisms (e.g., tachy-cardia, renin release, and sodium retention) mayconfound interpretation as will later adaptivechanges such as baroreceptor reflex resetting. Manyof the studies that have claimed to show slowlydeveloping responses have used less than optimalstudy designs and a time effect has not always beendistinguished from a dose or concentration effect. Toinvestigate adequately changes in response with time,it is necessary to undertake a comprehensive assess-ment not only of blood pressure but also of plasmadrug levels over a dosing interval both acutely andafter weeks or months of therapy. When this isundertaken, there is little evidence, at least forcalcium antagonists26 or ACE inhibitors,17 that theresponse is a function of time.

Many early studies with antihypertensive drugsfailed to identify a relation between plasma concen-tration and the fall in blood pressure,33-34 but somereports did show a concentration-effect relation afteracute intravenous dosing. The failure may reflectstudy designs or the type of drug such as reserpine ordiuretics. In animals35 and humans,36 there was arelation between the antihypertensive effect andplasma drug concentrations for the a2 agonist cloni-dine. In this case, the relation was not linear but "bellshaped" due to opposing depressor (low concentra-tion) and pressor (high concentration) influences.37

Concentration-effect relations for other antihyper-tensive drugs have been investigated including a-blockers38-39 and 0-blockers.33-40 In the latter case,the relations were most prominent between plasmalevels and the pharmacological effect of cardiac /3receptor antagonism40 and less clearly defined for


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Drug conon

FIGURE 2. Schematic drawing of an anticlockwise hysteresisof effect and drug concentration.

changes in blood pressure. As described below, stud-ies with a) antagonists in both normotensive41 andhypertensive27-28 subjects have provided the clearestevidence of concentration-dependent falls in bloodpressure after oral administration in humans. Thesestudies, together with investigations of our group andothers with calcium antagonists25-26-42--*4 and ACE in-hibitors,17 have led us to the view that a clear definitionof concentration-effect relations can help rationalizethe choice of dose and dose interval for individualpatients and can offer a sound pharmacokinetic basisfor individualized therapy in the future.

Concentration-Effect ModelingAs already suggested, pharmacokinetic factors

contribute the largest identifiable component to thevariability in response to antihypertensive drugs. Thesimplest relation between pharmacokinetics andpharmacodynamics is a direct proportionalitybetween the observed effect and the drug plasmaconcentration measured. Provided that the measure-ments of concentration and effect are simultaneous,the analysis is entirely model independent at least interms of the pharmacokinetics as the correlation ofconcentration and effect is dependent on a series ofsimultaneous and independent measurements of thetwo variables. However, the data from antihyperten-sive drug studies often produces a plot of plasmadrug concentration versus antihypertensive effect,which is not a simple linear relation, and furtheranalysis reveals an anticlockwise hysteresis loop (Fig-ure 2). This loop characterizes a relatively small fallin blood pressure or the presence of high concentra-tions of drug immediately after drug administrationand, subsequently, an increased hemodynamicresponse in the face of falling drug concentrations.This is the result of a delay between the concentra-tion of the drug in plasma and its concentration atthe "effector" site. This delay can be accounted forby augmenting a conventional pharmacokineticmodel with an explicitly defined "effect compart-ment" in such a way that this modification does notinfluence the pharmacokinetic parameters defined bythe original model.45 The analysis then focuses on therelation between concentration and effect as defined

Langmulr

10 50 200 1000Log Drug Concentration

E- m.OI Llmar

0 100 200 300 400 SOOUnear Drug Concentration

FIGURE 3. Representative examples of concentration-effectcurves with the alternative mathematical forms that may beapplied to describe the concentration-response relation. E,measured effect; E^n, theoretical maximum effect; ECxi,concentration of drug that elicits an effect 50% of EmtI; X, isa number influencing the slope of the curve; m, slope of thelinear relation between drug concentration effect; and i,intercept term for a linear correlation.

by a chosen model. This model may be characterized inmany different ways including irreversible binding toreceptor sites or rectilinear, log linear, or an E ^ modelwith the latter based on either the Langmuir or Hillequation32 (Figure 3). The Sheiner approach to theintegrated, quantitative description of plasma concen-tration-response time data has been applied to anumber of drugs in a range of therapeutic areas. Theseinclude the prolongation of the QT interval in responseto disopyramide46 and quinidine,47 the change in theforce of muscle contraction after administration ofD-tubocurarine,45 and the improvement in respiratoryfunction in response to theophylline.48

We first applied this approach to antihypertensivedrugs in normotensive subjects after single doses.49

The quinazoline aj-adrenergic receptor antagonistdrugs lent themselves to such analysis because of thereadily measurable fall in blood pressure in nor-motensive subjects and the differing profiles ofhypotensive activity between structurally relatedcompounds.41 In a comparison of intravenous pra-zosin, doxazosin, trimazosin, and placebo, falls insystolic blood pressure, corrected for placebochanges, in individual subjects were successfullyrelated to drug concentration measurements usingthe effect modeling approach. Contending models(linear, E ^ or Sigmoid E^^ Langmuir; and Hill)were fitted to the effect data, and for all three drugsthe simple linear model proved on statistical testing


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to be adequate for fitting the blood pressure profilein all individuals. On theoretical grounds, it is some-what surprising that such a simple relation mostappropriately characterizes the drug concentration-effect relations as the implication is that an infiniteresponse will be elicited by very high drug concentra-tions. However, over the range of doses studied thelinear model was "best" fitted to the concentration-effect data, and furthermore, there is good reason tobelieve that more physiologically based relationsbased on receptor occupancy (Hill and Langmuirequations) may not necessarily be any more appro-priate when blood pressure response is also influ-enced by counterregulatory mechanisms such asbaroreceptor reflex activation or renin release. Fromthe linear model, the response in each individual wascharacterized by the slope effect/concentration andthus had units of fall in blood pressure (in mm Hg)per unit of drug concentration. This parameter canthus be considered as an index of drug potency interms of a drug concentration-effect relation asdistinct from a dose-effect relation. The meanresponsiveness terms for doxazosin and prazosinresponses were comparable with mean slope valuesof 2.3 and 2 mmHg/ng/ml drug (1.04 and 0.84mm Hg/nM). In contrast, however, that for trima-zosin was very much smaller at 2.0 mm Hg/)ug/ml (1.5mm Hg//xM) reflecting lower potency and the needfor 100-fold or higher doses. In addition to havingdifferent pharmacokinetic half-lifes, the drugsshowed different degrees of anticlockwise hysteresis(as represented in Figure 2) consistent with observeddifferences in rates of onset and offset of action. Inthe case of trimazosin, concentration-effect analysiswas extended to demonstrate that the biphasichypotensive response to the drug could be accountedfor by pharmacological activity of both the parentdrug and its major metabolite. Subsequent work withboth oral and intravenous trimazosin provided fur-ther evidence of a pharmacologically active metabo-lite contributing significantly to the overall hemody-namic response.50

Modeling of Response in Essential HypertensionAn important aspect of any mathematical model is

the potential to extend understanding by generatingtestable hypotheses, for instance, from intravenous tooral dosing or from single to multiple doses. This isapplicable to conventional pharmacokinetics and tointegrated pharmacodynamic data. Models may beused to predict events in alternative situations. Thepredictions generated can then be prospectivelytested. The prediction of drug effect on long-termoral therapy, after steady state has been achieved,from the first dose response may be regarded as oneof the principal, practical aims of concentration-effect modeling. It is thus important to be able tocharacterize the concentration-response relation inpatients with essential hypertension after acute oraladministration and also at steady state to validatesingle dose predictions of response. Such an evaluation

has been undertaken in a series of parallel placebo-controlled studies with a variety of antihypertensivedrugs including prazosin,27 doxazosin,28 ketanserin,51

nifedipine,26 verapamil,25 and enalapril.17 All studiesfollowed essentially the same design. Existing antihy-pertensive therapy was withdrawn for at least 4 weeks,and patients then received placebo for at least a further2 weeks followed by 6 weeks of active treatment in asingle-blind manner. The patients underwent a series ofintensive study days, with frequent blood pressurerecordings and coincident plasma drug concentrationmeasurements made over 12-24 hours. Patients werestudied after placebo, the first dose of active drug, andafter at least 4-6 weeks of active treatment.

A number of interesting and contrasting featuresemerged from these studies. As earlier, with nor-motensive subjects, the blood pressure response toacute and chronic prazosin and doxazos was ade-quately described by a linear model.27-28 Response tothe first dose of doxazosin in individual patientscorrelated well with the response after 1 and 6 weeksof treatment, although the magnitude of responsesystematically diminished by about 30%.27-28 When asimilar approach was used with verapamil, despite asignificant decrease in drug clearance betweenacute and steady-state therapy, the response interms of blood pressure fall per unit drug concen-tration was the same.25 Similar findings wereobtained with nifedipine26 and enalapril17 with goodagreement between the response on first dosing andat steady state. After enalapril, however, reductionin blood pressure as a function of drug concentra-tion was best described by a Langmuir ~Ema model(Figure 3A), the parameters of which are E ^ , thetheoretical maximum response to the drug, andCeso, the steady-state concentration that elicits afall in blood pressure that is 50% of

Prediction of Response to Antihypertensive DrugsThe close correlation of the response parameters

obtained on first administration and at steady statewith both enalapril17 and nifedipine26 suggests thatthe acute response to each drug may be a usefulpredictor of the steady-state response to that drug,and this concept has now been evaluated in patientswith essential hypertension.52 For both nifedipineand enalapril after 4-6 weeks of treatment, theresponses (before dosing and 4 hours after dosing)predicted from the analysis of the first dose pharma-cokinetic and pharmacodynamic data were in closeagreement with the observed responses with onlysmall, nonsignificant discrepancies. With enalapril,the observed and predicted blood pressure profilesover a 12-hour study period were well correlated in allpatients. With nifedipine, however, although therewas generally good agreement, a few individualsshowed significant overprediction or underprediction.

We believe that the potential value of the effectmodeling approach for predicting steady-state anti-hypertensive response to nifedipine and enalaprilusing fixed doses and dosage regimen has been


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established. It is reasonable to suggest that the sameapproach might also be used to predict the effects ofdifferent therapeutic regimens such as changes ofdose or dosing intervals. Simulation of the effect ofdifferent dosage regimens on the steady-state antihy-pertensive profile of enalapril reveals several fea-tures. In only two of 13 patients studied does aregimen of 20 mg enalapril given as a single dailydose produce a placebo-corrected "trough/peak"response ratio of greater than 50%, where the troughis the drug effect at steady state measured immedi-ately before dosing and peak is the maximum fall inblood pressure over a steady-state dosage interval. Incontrast with both 10 mg and 5 mg b.i.d., the trough/peak ratio exceeds 60% in all patients. In addition,the average hourly blood pressure fall at steady stateover a 12-hour dosage interval with 5 mg b.i.d. didnot differ significantly from that achieved with 20 mgonce daily.

In conclusion, it is now apparent that concentra-tion-effect and dose-effect relations can be identifiedfor many antihypertensive drugs. A simple linearrelation can only be identified in a few cases usuallyafter intravenous administration. In the absence ofsuch a direct relation it may be necessary to use morecomplex and sophisticated data analysis techniquesto integrate pharmacokinetics, pharmacodynamics,and time.44 Such an approach can consistently dem-onstrate concentration-effect relations for a range ofantihypertensive drugs with differing pharmacologi-cal actions including calcium antagonists, o-blockers,and ACE inhibitors. Furthermore, the concentra-tion-effect relation derived from the first dose ofenalapril or nifedipine can predict the blood pressureresponse to long-term treatment.52 We believe thatthe definition of individual concentration-effect rela-tions may be of considerable value in the rational useof antihypertensive therapy. In particular, it canprovide valuable information on dose-effect relationsand optimal choice of dose intervals in drug devel-opment that may be of considerable benefit in prac-tice, but as yet this remains unproven.

AcknowledgmentsWe are grateful for the helpful comments and

critical review of this manuscript by our colleaguesBrian Whiting, Andrew Kelman, Richard Donnelly,and Henry Elliott and to our many clinical andlaboratory assistants who have contributed to thisprogram of research. We also thank JeannetteHamilton for preparation of the manuscript.

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KEY WORDS • antihypertensive drugs • angiotensin convertingenzyme inhibitors • calcium antagonists • dose response •pharmacokinetics


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J L Reid and P A MeredithConcentration-effect analysis of antihypertensive drug responses.

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Concentration-Effect Analysis of Antihypertensive Drug Responses