Dose-Response Relationship

DOSE-RESPONSE RELATIONSHIP

When a drug is administered systemically, the doseresponse relationship has two components:

doseplasma concentration relationship and plasma concentrationresponse relationship. The former is determined by pharmacokinetic considerations and ordinarily, descriptions of doseresponse relationship refer to the latter, which can be more easily studied in vitro.

Generally, the intensity of response increases with increase in dose (or more precisely concentration at the receptor) and the doseresponse curve is a rectangular hyperbola (Fig. 4.11). This is because drugreceptor interaction obeys law of mass action, accordingly—

                    Emax × [D]

E = —————           ...(3)

K_D + [D]

Where E is the observed effect at a dose [D] of the drug, Emax is the maximal response, K_D is the dissociation constant of the drugreceptor complex, which is equal to the dose of the drug at which half maximal response is produced. If the dose is plotted on a logarithmic scale, the curve becomes sigmoid and a linear relationship between log of dose and the response is seen in the intermediate (30–70% response) zone, as can be predicted from equation (3). This is not peculiar to drugs. In fact all stimuli are graded biologically by the fractional change in stimulus intensity, e.g. 1 kg and 2 kg weights held in two hands can be easily differentiated, but not 10 kg and 11 kg weights. Though the absolute difference remains 1kg, there is a 100% fractional change in the former case but only 10% change in the latter case. In other words, response is proportional to an exponential function (log) of the dose.

Other advantages of plotting log doseresponse curves (DRC) are:

          i)   A wide range of drug doses can be easily displayed on a graph.

    ii) Comparison between agonists and study of antagonists becomes easier.

Therapeutic  Window  Phenomenon

This is an unusual feature seen with certain drugs: optimal therapeutic effect is exerted only over a narrow range of plasma drug concentrations or drug doses; both below and above this range, beneficial effects are suboptimal, i.e., the effect declines if the doses are increased beyond a certain level. Examples are:

§ Tricyclics (imipramine etc.) exert maximal antidepressant effect when their plasma concentration is maintained between 50–150 ng/ml.

§ Clonidine lowers BP over a plasma concentration range of 0.2–2.0 ng/ml; BP may rise at concentrations above 2 ng/ml.

§ Glipizide exerts poorer glycaemia control at doses > 25 mg/day.

The pharmacological basis of this phenomenon is not well understood, but may be due to dual or complex actions of the drug—different facets of which become prominent at different concentrations.

The log doseresponse curve (DRC) can be characterized by its shape (slope and maxima) and position on the dose axis.

Drug Potency And Efficacy

The position of DRC on the dose axis is the index of drug potency which refers to the amount of drug needed to produce a certain response. A DRC positioned rightward indicates lower potency (Fig. 4.12). Relative potency is often more meaningful than absolute potency, and is generally defined by comparing the dose (concentration) of the two agonists at which they elicit half maximal response (EC₅₀). Thus, if 10 mg of morphine = 100 mg of pethidine as analgesic, morphine is 10 times more potent than pethidine. However, a higher potency, in itself, does not confer clinical superiority unless the potency for therapeutic effect is selectively increased over potency for adverse effect.

The upper limit of DRC is the index of drug efficacy and refers to the maximal response that can be elicited by the drug, e.g. morphine produces a degree of analgesia not obtainable with any dose of aspirin—morphine is more efficacious than aspirin. Efficacy is a more decisive factor in the choice of a drug.

Often the terms ‘drug potency’ and ‘drug efficacy’ are used interchangeably, but these are not synonymous and refer to different characteristics of the drug. The two can vary independently:

§  Aspirin is less potent as well as less efficacious analgesic than morphine.

§  Pethidine is less potent but equally efficacious analgesic as morphine.

§  Furosemide is less potent but more efficacious diuretic than metolazone.

§  Diazepam is more potent but less efficacious CNS depressant than pentobarbitone.

Depending on the type of drug, both higher efficacy (as in the case of furosemide confering utility in renal failure) or lower efficacy (as in the case of diazepam confering safety in overdose) could be clinically advantageous.

The slope of the DRC is also important. A steep slope indicates that a moderate increase in dose will markedly increase the response (dose needs individualization), while a flat one implies that little increase in response will occur over a wide dose range (standard doses can be given to most patients). Hydralazine has a steep, while hydrochlorothiazide has a flat DRC of antihypertensive effect (Fig. 4.13).

Selectivity

Drugs seldom produce just one action: the DRCs for different effects of a drug may be different. The extent of separation of DRCs of a drug for different effects is a measure of its selectivity, e.g. the DRCs for bronchodilatation and cardiac stimulation (Fig. 4.14) are quite similar in case of isoprenaline, but far apart in case of salbutamol—the latter is a more selective drug.

The gap between the therapeutic effect DRC and the adverse effect DRC defines the safety margin or the therapeutic index of a drug. In experimental animals, therapeutic index is often calculated as:

       median lethal dose

Therapeutic index =  —————————–

        median effective dose

                               LD₅₀

or   ——–

                              ED₅₀

But this is irrelevant in the clinical set up where the therapeutic range is bounded by the dose which produces minimal therapeutic effect and the dose which produces maximal acceptable adverse effect (Fig. 4.15). Because of individual variability, the effective dose for some subjects may be toxic for others; defining the therapeutic range for many drugs is a challenging task. A drug may be capable of inducing a higher therapeutic response (have higher efficacy) but development of intolerable adverse effects may preclude use of higher doses, e.g. prednisolone in bronchial asthma.

Risk-Benefit Ratio

This term is very frequently used, and conveys a judgement on the estimated harm (adverse effects, cost, inconvenience) vs expected advantages (relief of symptoms, cure, reduction of complications/mortality, improvement in quality of life). A drug should be prescribed only when the benefits outweigh the risks. However, riskbenefit ratio can hardly ever be accurately measured for each instance of drug use, because ‘risk’ is the probability of harm; and harm has to be qualified by its nature, quantum, timecourse (transient to lifelong) as well as the value that the patient attaches to it. None of these can be precisely ascertained. As such, the physician has to rely on data from use of drugs in large populations (pharmacoepidemiology) and his own experience of the drug and the patient.