Concentration-Effect Relationships and Implications for Trough-to-Peak Ratio

Transcription

1 AJH 1996;9:66S-70S Concentration-Effect Relationships and Implications for Trough-to-Peak Ratio Peter A. Meredith and Henry L. Elliott The guidelines on trough-to-peak ratio identified an index of the duration of action of an antihypertensive drug (relative to its dosage interval) to prevent the use of inappropriately large doses of drug simply to extend the apparent duration of action. In some instances, however, trough-to-peak ratio may be dose-dependent and this analysis examines the contribution that the underlying concentration-antihypertensive effect relationship makes to the dose dependency of trough-to-peak ratio. Where this concentrationeffect relationship is essentially linear the troughto-peak ratio is almost invariably dose- T here is increasing evidence that optimal blood pressure control requires treatments that consistently reduce blood pressure (BP) over a full 24-h period. 1 This demands drug and treatment regimens capable of a full 24-h antihypertensive activity and, until recently, it was assumed that all agents licensed for once daily administration would be appropriately long-acting and therapeutically equivalent. It is increasingly apparent, however, that drugs may differ significantly in their duration of action and the Cardiovascular and Renal Drugs Advisory Committee of the Food and Drug Administration (FDA) of the United States proposed draft guidelines in 1988 for the evaluation of antihypertensive drugs including recommendations concerning the duration of action. The guidelines were formu- From the University Department of Medicine and Therapeutics, Gardiner Institute, Western Infirmary, Glasgow, Scotland. Address correspondence and reprint requests to Peter A. Meredith, University Department of Medicine and Therapeutics, Gardiner Institute, Western Infirmary, Glasgow Gll GNT, Scotland. independent. In contrast, where the relationship is identified as being of a sigmoid-emax type the trough-to-peak ratio is likely to be dosedependent. The nature of the concentration-effect relationship also influences the duration of action beyond the dosage interval whereby "linear" drugs are superior to "'Em,x'" drugs by virtue of the greater persistence of the antihypertensive effect. Am J Hypertens 1996;9:66S-70S KEY WORDS: Trough-to-peak blood pressure responses, concentration-effect relationships, Food and Drug Administration guidelines, antihypertensive drug dosing. lated in response to evidence that a relatively shortacting drug might have its duration of action prolonged by the administration of larger doses than were necessary or desirable. 2 Although the FDA Guidelines on Trough-To-Peak Ratio were initially formulated over concerns about the potential risks associated with a profound fall in BP at the time of peak drug effect, it is increasingly recognized that the trough-to-peak ratio, when appropriately characterized, provides additional information about the duration and consistency of action of an antihypertensive drug over the recommended dosage interval. The draft guidelines did not specifically address the issue of possible dose-related differences in trough-to-peak ratio, but it is implicit that an antihypertensive drug should have a trough-to-peak ratio that is essentially constant and independent of dose across the recommended dosage range. However, despite the intention to prevent "supra-therapeutic" dosing, there appears to have been a lack of consistency in the implementation of the guidelines. For example, the angiotensin converting enzyme (ACE) 1996 by the American Journal of Hypertension, Ltd /96/$15.00 Published by Elsevier Science, Inc. PII S (96)

2 AJH-OCTOBER 1996-VOL. 9, NO. 10, PART 2 CONCENTRATION-EFFECT AND TROUGH-TO-PEAK RATIO 67S inhibitor quinapril has been licensed and marketed as being suitable for once daily administration but, presumably on the recommendation of the FDA, some of its advertising material carried a footnote that "in some patients the antihypertensive effect may diminish towards the end of the once daily dosage interval. In such patients an increased dosage or twice daily administration may be warranted." While the suggestion of increasing the dosage frequency is entirely consistent with the trough-to-peak guidelines, the suggestion of an increased single daily dose appears to be directly contrary to their basic intent. EFFECT OF DRUG DOSE ON TROUGH-TO- PEAK RATIO The trough-to-peak ratio, for any given antihypertensive agent, is not identified by any single immutable numerical value. It obviously is directly related to the selected dosage interval and, as a consequence of intraindividual variability in response, it is subject to interpatient variation and, with some drugs, may be dose-dependent. For example, in a metaanalysis of studies that satisfied certain predetermined criteria, the ACE inhibitor lisinopril was found to have trough- (A) o systolic BP -10 (rnmhg) o systolic BP -10 (mmhg) (B) 2.Stag od lomg od 20rag od 80mg od 1 i'-i Trough I~ Peak lo mg bd 'N 24% 34% 57% 55% T:P ratio I~l'rough I~Peak 50% 48% T:P ratio 20 mg bd 30 mg bd FIGURE 1. Dose response and trough-to-peak ratios for lisinopril ( A) and nifedipine retard (B ). T:P, trough-to-peak; od, once daily; bd, twice daily. to-peak values in the range 40% to 80%, 3 Differences in the underlying methodology account for some of this variability but dose-dependent differences also contribute. This dose-dependence is well illustrated by the results of a separate dose-ranging study 4 (Figure 1A) that shows that low dose lisinopril produced a trough-to-peak ratio of <30% for systolic BP whereas the ratio can be improved to >50% by increasing the dose to 20 mg and above. It is of clinical importance that this change from a suboptimal to an acceptable trough-to-peak ratio occurred over the recommended therapeutic range of the lowest dose that might be recommended for the initiation of antihypertensive treatment to the usual maintenance dose of 20 mg. This creates practical problems for the prescribing physician in that both the lowest and highest recommended doses are deemed equally suitable for once daily administration. Dose dependency for trough-to-peak ratio does not occur with all antihypertensive agents. For example, nifedipine retard in the dose range of 10 to 30 mg twice daily maintains a consistent (although not particularly impressive) trough-to-peak ratio across this range of doses (Figure 1B). 5 Generally, dose dependency of trough-to-peak ratio and the associated differences in the duration of action appear to be relevant for ACE inhibitors and fl-blockers but of little or no importance for calcium antagonist drugs. CLINICAL PHARMACOLOGICAL FACTORS CONTRIBUTING TO DOSE DEPENDENCY Over the last 50 years the management of essential hypertension has evolved from a position of relative therapeutic impotence to one of relative therapeutic success. However, one salient failing has persisted throughout this period, ie, a relative inability to clearly define the dose response relationship during the drug development process, such that it has been an almost universal experience that the doses used in established clinical practice are significantly lower than those recommended when the drugs were first introduced. 6 This, in part, has been a result of the claim that many antihypertensive drugs have "flat" dose response curves 6 and this false concept has arisen largely due to the use of doses that are inappropriately high and that lie on the upper plateau of the dose response curve. The problem has been compounded by the strong desire for drugs that can be administered as once daily treatment. Sometimes this can only be achieved by the use of inappropriately high doses. Although this reflects poor therapeutic practice, which may reflect the dose dependency of the trough-to-peak ratio, there are other clinical pharmacological characteristics which influence the trough-to-peak ratio. For example, the disposition characteristics of the drug may

3 68S MEREDITHANDELLIOTT AJH-OCTOBER 1996-VOL. 9, NO. 10, PART 2 not obey first order (linear) pharmacokinetics and, at some point within the therapeutic range, the pharmacokinetic profile becomes zero order. Thus, there is a reduced rate of drug clearance and a disproportionate rise in plasma drug levels for a given increment in dose and this disproportionate increase in plasma drug levels and persistence apparently exaggerated response to the drug. However, most antihypertensive agents in current therapeutic practice exhibit linear pharmacokinetics over their recommended dosage range, although verapamil and, to some extent, diltiazero have been shown to exhibit nonlinearity in pharmacokinetics, particularly in translation from acute to steady-state therapy. 7 This leads to increases in peak concentration and area under the concentration time curve, with prolongations in half-life. This phenomenon cannot simply be attributed to dose-dependency over the therapeutic range, but instead reflects hepatic enzyme inhibition or changes in hepatic blood flow. Although dose-dependency in the trough-to-peak ratio has also been reported for modified release formulations of verapamil, 8 this reflects the characteristics of the formulation and not the drug itself. 2 ACE inhibitors constitute the only other class of antihypertensive agents that consistently exhibit nonlinear pharmacokinetics in association with saturable binding of the active drug moiety to angiotensin converting enzyme, both in plasma and in tissues. 9 However, this nonlinearity in pharmacokinetics contributes significantly to the dose-dependency of the trough-to-peak ratio only at very low doses, such as those used for initiating treatment in complex patients. Since the recommended maintenance doses usually exceed the dose required to saturate all ACE binding sites by at least a factor of 10, the pharmacokinetic parameters over the therapeutic dose range are essentially linear. It is often said that there is no relationship between the circulating plasma concentrations of an antihypertensive drug and its effect on BP. However, once allowance has been made for potential confounding factors, it is apparent that integrated pharmacokineticpharmacodynamic modeling approaches can describe the relationship between concentration and effect with most classes of antihypertensive drug. 6 Even the potentially confounding effects of nonlinear pharmacokinetics cannot conceal that there is some relationship between the disposition characteristics of a drug and its antihypertensive effect. Concentration-effect relationships may be characterized by a number of different models but, in general, the antihypertensive response has been most appropriately characterized by one of the three models detailed below or by logarithmic transformation of the linear model. The equations for the three models are: E = mce + i (Linear Model) E - E - Emax" Ce (Langmuir Model) Ces0 + Ce Emax" Ce ~ (Hill Model) Ce~'0 + Ce ~ where E = measured effects; i = an intercept term; E... = the theoretical maximal effect elicited by the drug; Ce = the concentration of drug in the effect compartment; and Ces0 = the concentration eliciting 50% of the maximal effect; and 3/is a coefficient characterizing the sigmoidicity of the nonlinear relationship. While generalization is potentially dangerous, the model that most appropriately characterizes the concentration-antihypertensive effect relationship is relatively consistent for each class of agent. Thus, the antihypertensive response to calcium antagonists and c~blockers is most appropriately described by a linear relationship while, with angiotensin converting enzyme inhibitors and fl-adrenoceptor antagonists, the nonlinear sigmoid E~a relationships are more appropriate. 6 Recognizing that the underlying concentration-effect relationship may be different, it is possible to predict on theoretical grounds the influence of dose on the calculated trough-to-peak ratio for different drugs. For example, using simulations based upon concentration-effect relationships characterized either by the linear model or by the Langmuir model, it is possible to predict the profiles of antihypertensive response for two stylized antihypertensive drugs with these discrepant concentration-effect relationships (Figure 2). Both drugs elicit their maximal or peak effects at 6 h after dosing and in both instances the highest dose elicits a trough effect that is 60% of the peak effect. The effect of dose increments on the responses to these two agents is also shown in Figure 2 and it is apparent for the drug with a linear concen- % of peak 100 ~ 4-80rag N._'-.. ~ 75 " ~ i I, hours post dose 100 % o-f Peak i i, hours po~ dose FIGURE 2. Effect of dose on trough-to-peak ratio for two hypothetical drugs, one with a "'linear" relationship between concentration and antihypertensive effect, the other with an "E,,,x" relationship.

4 AJH-OCTOBER 1996-VOL. 9, NO. 10, PART 2 CONCENTRATION-EFFECT AND TROUGH-TO-PEAK RATIO 69S tration-effect relationship that the trough-to-peak ratio is independent of dose and remains within the range 50% to 60% over the fourfold range of doses. In contrast, for the drug with a sigmoid Emax concentration-effect relationship, there is a clear dose dependent effect upon trough-to-peak ratio, such that at the highest dose the trough-to-peak ratio is 60% but at the lowest dose the trough-to-peak ratio is less than 30%. It is thus apparent that the dose dependent trough-to-peak ratio observed with lisinopril and the dose independent trough-to-peak ratio observed with nifedipine are entirely consistent with their differing concentration effect relationships. DURATION OF ACTION BEYOND THE DOSAGE INTERVAL If trough-to-peak ratio is to be regarded as a definitive and useful arithmetic index of duration of action, it follows that a high trough-to-peak ratio predicts the effectiveness of a drug throughout, but also beyond, its dosage interval. When a dose is omitted or taken belatedly, such a continuing duration of action is particularly important, especially given the well recognized patterns of poor compliance in hypertensive patients. 1 Thus, an antihypertensive drug with a good trough-to-peak should automatically sustain its effect for a significant period beyond the end of the dosage interval. Figure 3 shows the discrepant characteristics of the two stylized agents already considered in Figure 2 with respect to their ability to sustain an antihypertensive effect in the 24 h after a dosage omission. It is clear that there are differences in offset of effect that are related to the nature of the underlying concentration-effect relationship (Figure 3) and the loss of antihypertensive effect is likely to be more rapid with an "Emax" drug than with a "linear" drug. A number of studies have deliberately sought to estab- % of peak 6O 4O 2O m I m I ~ = " = " i. = hours post dose FIGURE 3. The offset of antihypertensive effect for two hypothetical antihypertensive drugs with differing concentration-effect relationships. = lish the effect of a delayed or missed dose on antihypertensive efficacy These studies confirm that a high trough-to-peak ratio translates into the maintenance of the treatment effect significantly beyond the end of the dosage interval. Such studies additionally support the concept that the nature of the relationship between drug concentration and drug effect is an important and independent further determinant of this maintenance effect. There is one cautionary note, however. Where the high trough-to-peak ratio is attributable to a modified release drug formulation, it is likely that the maintenance of effect will be more dependent upon the specific characteristics of the formulation rather than the concentration-effect. CONCLUSION A "satisfactory" trough-to-peak ratio indicates that the duration of action of an antihypertensive drug is appropriate for the chosen dosage interval. It further suggests that BP control will be consistently maintained throughout that dose interval and that there will be some persistence of the antihypertensive effect beyond the end of the dosage interval in the event of the patient being poorly compliant. It might be suggested that the validity of this arithmetic index is compromised because some agents display dose-dependent differences in trough-to-peak ratio. However, this phenomenon reflects the nature of the underlying pharmacokinetic-pharmacodynamic relationship and this determines whether or not the trough-to-peak ratio can be improved by increasing the dose. As a deliberate strategy, enhancement of the trough-to-peak ratio by increasing the drug dosage runs counter to the philosophy underlying the FDA Guidelines and caution should be exercised when interpreting studies based on a single relatively high dose level that suggest a favorable trough-to-peak ratio for a drug. REFERENCES 1. Meredith PA, Perloff D, Mancia G, Pickering T: Blood pressure variability and its implications for antihypertensive therapy. Blood Pressure 1995;4: Elliott HL, Meredith PA: Trough:peak ratio: clinically useful or practically irrelevant? J Hypertens 1995; 13: Zannad F: Trandolapril: how does it differ from other angiotensin converting enzyme inhibitors? Drugs 1993; 46 (suppl 2): M6nard J, Bellet M, Brunner HR: Clinical development of antihypertensive drugs: can we perform better? in Laragh JH, Brenner BM (eds): Hypertension: Pathophysiology, Diagnosis and Management, 1st ed. Raven Press Limited, New York, 1990, pp Meredith PA, Donnelly R, Elliott HL: Prediction and optimisation of the antihypertensive response to nifedipine. Blood Pressure 1994;3:

5 708 MEREDITH AND ELLIOTT AJH-OCTOBER 1996-VOL. 9, NO. 10, PART 2 6. Meredith PA, Reid JL: The use of pharmacodynamic and pharmacokinetic profiles in drug development for planning individual therapy, in Laragh JH, Brenner BM (eds): Hypertension: Pathophysiology, Diagnosis and Management. Raven Press, New York, 1995, pp Meredith PA, Elliott HL, Pasanisi F, et al: Verapamil pharmacokinetics and apparent hepatic and renal blood flow. Br J Clin Pharmacol 1985;20: McMahon FG, Reder RF: The relationship of dose to antihypertensive response to verapamil-sustained release in patients with mild to moderate essential hypertension. J Clin Pharmacol 1989;29: Francis RJ, Brown AN, Kler L, et al: Pharmacokinetics of the converting enzyme inhibitor cilazapril in normal volunteers and J Cardiovasc Pharmacol 1987;9: QUESTIONS AND ANSWERS Dr. Rabkin: My question is related to the different sites of action of drugs and how you can prove your thesis that serum levels are related to drug action and blood pressure effect when you have some drugs that act on the brain, heart, and vascular smooth muscle. How do you relate serum concentrations of drugs when the drug may have multiple sites of action? Dr. Meredith: I think it is important to avoid attributing any physiological relevance to our approaches to modeling. We are simply using them as tools to relate drug concentration to effect and the assumptions we make are not related to the pharmacokinetics of drugs such as the angiotensin converting enzyme inhibitors. 10. Meredith PA: Therapeutic implications of drug 'holidays.' Eur Heart J 1996; 17(suppl A): Anderson A, Morgan O, Morgan T: Effectiveness of blood pressure control with once daily administration of enalapril and perindopril. Am J Hypertens 1994; 7: Zanchetti A, Bianchi L, Bozza M, et al for the Italian Nifedipine GITS Study Group: Antihypertensive effects of nifedipine GITS on clinic and ambulatory blood pressures in essential hypertensives. J High Blood Pressure 1994;3: Vaur L, Dutrey-Dupagne C, Boussac J, et al: Differential effects of a missed dose of trandolapril and enalapril on blood pressure control in hypertensive patients. J Cardiovasc Pharmacol 1995;26 ( 1 ): Dr. Lipicky: If you do an acute dosing study with a drug and then examine its response at steady state after multiple dosing you may have to take into account other factors, such as changes in organ systems or sites of action. Dr. Meredith: Our studies have been confined to the short-term effects and it is difficult to speculate on what might happen with prolonged therapy, such as after a year or more. Drug effects after prolonged treatment may indeed be different from those seen after a period of weeks, but this is currently only speculation since concentration-effect studies have generally not be done after prolonged therapy.