# Presentation: 035215

## DOSE-EFFECT RELATIONSHIP

**The intensity and duration of a drug’s effects are a function of the drug dose and drug concentration at the effect site**
**Frank M. Balis, M.D.**
**January 25, 2007**

**Notes:**
The intensity and duration of a drug’s pharmacologic effects are indirectly proportional to the dose of the drug administered and directly proportional to the concentration of the drug at its site of action - the effect site.
Dose is a drug’s most important parameter - if the dose is to low, less than the optimal therapeutic effect is achieved and if the dose is too high, there may be unacceptable toxicity.
As a result, early phases of clinical development of a new drug focus on defining the optimal dose by defining the relationship between dose and the drug’s therapeutic and toxic effects.

## Monitoring Dose-Effect

**Level**
**Molecular (e.g, enzyme inhibition)**
**Cellular (*****in vitro***** tissue culture, blood cells)**
**Tissue or organ (*****in vitro***** or *****in vivo*****)**
**Organism**
**Endpoint used to measure effect may be different at each level**
**Overall effect = sum of multiple drug effects and physiological response to drug effects**

**Notes:**
A drug’s pharmacological effects can be monitored and quantified at several levels, including at a molecular level if the receptor or mechanism of action of the drug is known, at a cellular level in vitro, in a tissue or organ in vitro or in vivo, or at the organism level.
The endpoint used to measure drug effect may be different at each level (CLICK on this to go to FTI example)
At the tissue, organ or organism level, the overall drug effect could be the sum of multiple effects and the physiologic response to the drug effects. For example, change in BP with an antihypertensive agent.

## Dose-Effect Endpoints

**Graded**

**Quantal**

**•****	****Continuous scale**** (********dose**** ******** ********effect)**
**•****	****Measured in a single biologic unit**
**•****	****Relates dose to intensity of effect**

**•****	****All-or-none pharmacologic effect**
**•****	****Population studies**
**•****	****Relates dose to frequency of effect**

**Notes:**
Endpoints used to quantify drug effect can be categorized into 2 types, graded and quantal. 
Graded - The graded dose-effect is measured on a continuous scale and the intensity of the effect is proportional to the dose, such as measuring the change in blood pressure after administering an antihypertensive agent.  Graded dose-effect relationships can be measured in a single biologic unit that is exposed to a range of doses.  A graded dose-effect study relates the dose to the intensity of the effect.
Quantal - Conversely a quantal effect is an all-or-none effect such as alive or dead, asleep or awake, pain-free or in pain.  Quantal dose-effect studies are performed in populations of subjects who are treated with a range of doses, and dose is related to the frequency of the all-or-none effect, such as the % of subjects who survived.

## Erythropoietin and Anemia

**Erythropoietin and Anemia**

**Erythropoietin Dose [units/kg]**

**Peak Hematocrit Increment [%]**

**Eschbach et al. NEJM 316:73-8, 1987**

**Notes:**
This is an example of a graded dose-effect study of erythropoietin in patients with end-stage renal failure.
Erythropoietin is a naturally-occurring hematopoietic growth factor that stimulates hematopoietic precursors to produce red cells - it is the physiologic regulator of red cell production, and it is essential for terminal maturation of erythroid cells. 
EPO is produced in the kidney in response to hypoxia.  Patients in renal failure are EPO deficient and as a result they are usually severely anemic and frequently transfusion-dependent.
This graph shows the results of a dose-finding study in 18 patients with end stage renal disease and severe anemia.  The dose-effect relationship for EPO was studied over a range of doses from 1.5 to 500 units/kg in 3-5 patients per dose level. IV 3 x weekly.
The effect of EPO is measured as the peak absolute increment in the hematocrit.  These patients had pretreatment hematocrits less than 20%.
There was no effect at the two lowest dose levels of 1.5 and 5.0 units/kg.  Starting at a dose of 15 units/kg, the hematocrit increased by 4 to 22% depending on the dose of EPO administered.
This is a typical dose-effect curve.  The characteristics of this relationship in graphical form are:
The effect increases as the dose is increased
The shape of the dose-effect curve is that of a rectangular hyperbola, which approaches a maximum effect as the dose is increased.
There is diminishing return at higher doses - the increment in hematocrit is smaller with each increment in the dose of EPO.

## Drug-Receptor Interactions

**k****1**

**k****2**

**Drug**

**Receptor**

**Effect**

**Drug-****Receptor ****Complex**

**(K****D**** = k****2****/k****1****)**

**Ligand-binding domain **

**Effector domain **

**Notes:**
This relationship between dose and effect with EPO and most other drugs is governed by the mechanism by which drugs produce their effects - by interacting with cellular macromolecules called receptors.
A receptor can be any cellular macromolecule with which a drug interacts to initiate its pharmacologic effect.  Proteins are the most important class of drug receptors
Cellular proteins that are receptors for endogenous regulatory ligands, such as hormones, growth factors, neurotransmitters, are also the most important drug receptors. These proteins have a ligand binding domain where the drug interacts and an effector domain that propagates the message - leading to an effect.
Other receptors include enzymes (acetylcholinesterase), transport proteins (Na+, K+-ATPase), structural proteins (tubulin), and nucleic acids
The drug’s chemical structure is the primary determinant of the class of receptors with which the drug will interact.
The intensity of the effect produced by a drug is proportional to the fraction of receptors occupied by drug and the maximal effect occurs when all receptors are occupied (receptor occupation theory).
The drug-receptor interaction is reversible and conforms to the law of mass action that govern chemical reactions, assuming that 1) response to drug is directly proportional to the fraction of total receptor occupied by the drug and 2) the amount of drug bound to receptor is negligible so the concentration of free drug remains constant.  The drug concentration doesn’t change during the reaction - only the proportion of free and occupied receptors changes.
In the reaction scheme k1 and k2 are the proportionality constants for the formation and dissociation of the drug-receptor complex (the interaction is reversible). 
CLICK. At equilibrium, the reaction can also be expressed by this equation which takes the same form as the Michaelis-Menten equation where [Drug] is the concentration of free drug, maximal effect is the effect achieved when all of the receptors are occupied by drug, and KD is the dissociation rate constant for the complex.  CLICK. KD is equal to k2/k1, the ratio of the proportionality constants.

## Dose-Effect Relationship

**Dose-Effect Relationship**

**Notes:**
Examine this equation more closely by rearranging it slightly - the maximal effect is essentially a proportionality constant and
[Drug]/(KD + [Drug]) represents the fraction of receptors occupied by drug, which is proportional to the drug’s effect
The maximal effect occurs when all receptors are occupied, which occurs when the [Drug] exceeds the dissociation constant and the expression [Drug]/(KD + [Drug]) approaches 1.

## Graded Dose-Effect Curve

**Graded Dose-Effect Curve**

**% of Maximal Effect**

**[Drug]**

**EC****50**

**Maximal effect**

**Notes:**
The mathematical relationship from the previous slide takes on the shape of a hyperbolic function when presented graphically.  This is a dose-effect or dose-response curve.  In this form of the dose-effect curve, the free drug concentration along the X-axis is a linear scale.
 Drug effect asymptotically approaches the maximal effect as the drug concentration increases.
This is a graded dose-response relationship, because the responding system is capable of showing progressively increasing effect with increasing dose.
The EC50 is the drug concentration at which the drug is half-maximally effective.  If the relationship between receptor occupancy and response is linear then KD = EC50.
If there is amplification between receptor occupancy and response, such as when the receptor has catalytic activity when the receptor ligand is bound, then the EC50 lies to the left of the KD.
Once the dose exceeds the EC50, there is diminishing return with increasing dose.  There is a smaller increment in effect with a fixed dose increment.

## Log Dose-Effect Curve

**Log Dose-Effect Curve**

**% of Maximal Effect**

**[Drug]**

**EC****50**

**Notes:**
It is more customary to plot the dose-effect relationship using a log scale for drug dose or concentration to evaluate the quantitative aspects of the action of a single drug or to compare the actions of several drugs
When the dose is transformed to a log scale - the dose response curve is sigmoidal - the midpoint or inflection point of the curve is the dose at which 50% of the maximum effect is elicited.
This method of presentation allows for a better assessment of the effects of low doses and for a wide range of doses on the same plot.

## Lidocaine Graded Dose-Effect

**Lidocaine Graded Dose-Effect**

**Lidocaine Blood Level [μg/ml]**

**Analog**
**Pain Score**

**Ferrante et al. Anesth Analg 82:91-7, 1996**

**Notes:**
This is an example of a graded dose-effect study performed in patients.
The effect of intravenous lidocaine on neuropathic pain was studied. Effect, relief of pain, was measured using an analog visual pain score - the higher the score, the greater the pain and maximal effect was no pain, which is a score of 0.
Each patient received gradually increasing doses and the degree of pain was scored after each dose increment. Effect is plotted against the steady state blood level.
The dose effect curve is very steep (the pain decreased over a concentration range of 0.62 μg/ml), indicating that the response to IV lidocaine is characterized by a precipitous break in pain over a narrow range in serum drug concentrations.

## Theophylline Dose-Effect

**Theophylline Dose-Effect**

**PDE Inhibition**

**Relaxation**

**% ****Control**

**Theophylline [μM]**

**Rabe et al. Eur Respir J 8:637-42, 1995**

**Notes:**
Graded dose-effect studies can be used to elucidate the site of action of a drug.
This graph shows the dose-effect study for theophylline in vitro at a molecular level (against the target enzyme, phosphodiesterase in human bronchial homogenates) and at a tissue level (in human bronchial rings).
Theophylline is a methylxanthine that relaxes human bronchial smooth muscle.  It has many effects (multiple receptors) including mutually antagonist actions on mast cell by increasing cyclic AMP (a second messenger in cell signaling pathways) levels by inhibiting phosphodiesterase (PDE), which catabolizes cyclic-AMP; and by blocking adenosine receptors (adenosine causes bronchial constriction in asthmatics).
In this in vitro study, the inhibition of PDEs and relaxation of bronchial rings occurs over a similar range of theophylline concentrations.
The EC50 for relaxation is about 80 μM (14 μg/ml).
The IC50 of theophylline for PDE inhibition is 190 μM.
In these dose-response studies, correlating the dose-effect curve in the effected tissue with the dose-effect for the presumed receptor (PDE) helps to elucidate the mechanism of action of the drug.
However, the limitations of these studies is that the concentrations of theophylline required to produce relaxation of the bronchial segments in vitro is considerably higher than the concentrations required in vivo.

## Metformin Dose-Response

**Decrease in FPG from Placebo [mg/dl]**

**Decrease in HbA****1c**** from Placebo [%]**

**Dose [mg/d]**

**Garber et al. Am J Med 102:491-7, 1997**

**Notes:**
Here is a more topical example. This study evaluated the dose-effect relationship for the anti-hyperglycemic agent metformin.
The endpoints monitored - fasting plasma glucose levels and levels of glycated hemoglobin, a surrogate of chronic hyperglycemia
451 patients with a fasting plasma glucose exceeding 180 mg/dl were randomized to receive an 11 week course of placebo or metformin at a dose of 500, 1000, 1500, 2000 or 2500 mg daily.
FPG at the end of the study period declined by 19 to 84 mg/dl compared with the placebo group at the 500 to 2000 mg dose levels, and HbA1c declined by 0.6% to 2.0%.
There was a not unexpected disproportionate decrease FPG compared to HbA1c due to the slow turnover of Hgb (full effect would not be achieved in 11 weeks).
Metformin lowered fasting plasma glucose and HbA1c in a dose-related fashion and the maximum effect occurred at the upper limits of the recommended daily dose range (2000 mg).
The minimum effective dose was 500 mg, not 1500 mg as previously thought

## Dose-Effect Parameters

**P****OTENCY****:**

**E****FFICACY****:**

**The sensitivity of an organ or tissue to the drug**

**The maximum effect**

**Notes:**
Graded dose-effect curves are also a good way to compare agents that produce the same effect.
Drugs that produce the same effect differ in terms of potency and efficacy, which are parameters that can be assessed from the dose-response curves of the agents.
Potency is a measure of the sensitivity of a target organ or tissue to the effect of the drug.  It is relative term that relates the amount of one drug required to produce a desired effect compared with another agent.  On a dose response curve the more potent agents are to the left (have a lower EC50 or ED50).
Efficacy is the drug property that allows the receptor-bound drug to produce its pharmacological effect.  The relative efficacy of 2 drugs that elicit the same effect can be measured by comparing the maximum effects of the drugs.

## Comparing Dose-Effect Curves

**% of Maximal Effect**

**[Drug]**

**Drug A**

**Drug C**

**Drug B**

**Notes:**
Here are the dose-effect curves of 3 drugs that produce the same effect.
Drug A is more potent than Drug B.
Drugs A & B are more efficacious than Drug C.
Comparing the dose-response curves of drugs that produce the same pharmacological effect can also provide information about the site of action of the drugs.
Drugs A and B have dose response curves with identical shapes and the same maximal level of response - the curves are parallel.  This suggests that the the 2 drugs act through the same receptor.
Conversely, if 2 drugs that produce the same effect have non-parallel dose-effect curves, such as Drug A and Drug C, they probably have different sites of action.
If we return to the issue of potency and keeping in mind the equation (CLICK) that describes the relationship between drug effect and dose, the only way that unequal doses of 2 drugs can produce the same effect is if their dissociation constants (KD) differ.  So the dissociation constant is a measure of the affinity of the drug for its receptor, just like the Michaelis-Menten constant, Km, is a measure of the affinity of a substrate for its enzyme.

## Thiopurine Cytotoxicity

**Cytotoxic Effect**

**Thiopurine [M]**

**Thioguanine**

**Mercaptopurine**

**Adamson et al. Leukemia Res 18:805-10, 1994**

**Notes:**
These are dose-effect curves comparing 2 thiopurine analogs, thioguanine and mercaptopurine.  These drugs are antimetabolites that used for the treatment of acute leukemia.
Both drugs have multiple sites of action, but their primary mechanism of action is felt to be the result of incorporation into DNA - so in this case the receptor is a nucleic acid.
The effect on the Y-axis of this plot is the % of leukemic cells surviving compared to untreated controls in vitro using 3 different leukemia cell lines.
Thioguanine is about one-log more potent than mercaptopurine, despite the fact that they have very similar chemical structures (CLICK) and that they are converted to the same active intracellular metabolite prior to their incorporation into DNA.
[CLICK on thioguanine or mercaptopurine for metabolic pathway.]
Considerable weight is placed on these in vitro cytotoxicity studies for anticancer drugs, because it has not been possible to define therapeutic concentrations in vivo in animal models or in patients.

## Receptor-Mediated Effects

**% Maximum Effect**

**[Drug]**

**Notes:**
The type of effect produced by a drug can be classified from its dose-effect curve.
Drugs that bind to a receptor and mimic the effect of an endogenous ligand are called agonists.
There are other types of drug receptor interactions that can occur that are shown here graphically.  If a drug produces less than a full effect even at doses that saturate the receptor, it is a partial agonist.  Partial agonist are less efficacious.
An antagonist is a drug that binds to a receptor but does not produce an effect.  Antagonists produce a pharmacological effect by inhibiting the effect of an agonist.
Drug receptor interactions can be complex and the dose-effect curve can take on a shape other than the sigmoidal curve that we have discussed today.  The pharmacological effect can be the sum of the interactions of a drug with multiple receptors.  There are also drugs that produce a pharmacological effect that is not mediated through a receptor, such as antacids.

## Drug Interactions

**% of Maximal Effect**

**[Drug]**

**Agonist**

**Agonist + competitive antagonist**

**Agonist + non-competitive antagonist**

**Notes:**
Graded dose-effect curves are also useful for studying pharmacodynamic drug interactions.
This plot shows the dose-effect curves for an agonist alone, in yellow, the agonist combined with a competitive antagonist in blue, and combined with a non-competitive antagonist in green.
A competitive antagonist combines reversibly with the same binding site as the agonist or active drug and can be displaced from the binding site by an excess of the agonist.  The maximal effect of the agonist can still be achieved if sufficient agonist is used.  A competitive inhibitor lowers the potency of the agonist but does not alter its efficacy.
A non-competitive antagonist binds irreversible to the receptor binding site or interacts with other components of the system to decrease or eliminate the effect of the drug binding to the receptor.  A non-competitive antagonist prevents the agonist, at any concentration, from producing its maximum effect.  Typically, the dose response curve with this type of antagonist reveals reduced apparent efficacy, but the potency is not altered.
Using the dose-effect curve to study drug interactions can obviously be helpful in elucidating the mechanism of the drug interaction.

## Graded Dose-Effect Analysis

**Identify the therapeutic dose/concentration**
**Define site of drug action (receptor)**
**Classify effect produced by drug-receptor interaction (agonist, antagonist)**
**Compare the relative potency and efficacy of drugs that produce the same effect**
**Assess mechanism of drug interactions**

## Quantal Dose-Effect Distribution

**Threshold Dose**

**# of**
**Subjects**

**ED****50**

**Notes:**
This is an example of a population-based dose-effect study with an all-or-none or quantal endpoint.
By gradually increasing the dose in each subject, the minimally effective dose of the drug that evokes the all-or-none response is identified - this is called the threshold dose.
This graph is a frequency distribution of the threshold doses for the population.
The first obvious observation is that a wide range of doses are required to produce an effect in a population of subjects.  The maximum frequency of the effect occurs in the middle portion of the dose range.
The frequency distribution takes on the shape of a bell-shaped curve aka a normal frequency distribution.

## Cumulative Dose-Effect Curve

**Dose**

**Cumulative % of Subjects**

**Notes:**
A more convenient way to express a quantal dose-effect curve is to plot the dose vs. the cumulative percentage of subjects experiencing a response or effect at a given dose.  In the case of the study on the previous slide, the normal distribution is transformed into what should be a familiar S-shaped or sigmoidal curve.
Although this curve resembles the graded dose-effect curve, remember that the graded dose-effect curve expresses the relationship between change in effect and a change in the dose, whereas the quantal curve shown here is a measure of the variation in the threshold dose required to produce a defined all-or-none effect in a group of subjects.
The median effective dose (ED50) for the quantal dose-effect curve is  the dose at which 50% of the population responds.

## Cumulative Dose-Effect Study

| Dose Level | No. of Subjects | No. Responding | % Response |
| --- | --- | --- | --- |
| 1 | 10 | 0 | 0 |
| 2 | 10 | 1 | 10 |
| 3 | 10 | 3 | 30 |
| 4 | 10 | 5 | 50 |
| 5 | 10 | 7 | 70 |
| 6 | 10 | 8 | 80 |
| 7 | 10 | 9 | 90 |
| 8 | 10 | 10 | 100 |

**Notes:**
Defining the threshold dose in each subject in animal and human trials is usually not practical, so the way studies are typically performed is to treat groups of subjects at different dose levels.  The fraction of subjects responding at each dose level would then be the those subjects for which the dose is at or above their threshold dose.
This represents essentially a cumulative response at each dose level.

## Therapeutic and Toxic Effects

**Therapeutic and Toxic Effects**

**Dose**

**% Responding**

**Therapeutic**

**Toxic**

**ED****99**

**TD****1**

**ED****50**

**TD****50**

**Indices**

**Notes:**
In this dose-effect plot, the therapeutic and toxic effects are plotted.
This study illustrates an important principle when a drug is administered to an organism - there is no single dose-effect curve relationship that can adequately characterize the full spectrum of activity of a drug.  All drugs produce at least 2 effects and therefore have at least 2 quantal dose-response curves - one for the therapeutic effect and one or more for the toxic effect.
The safety of a drug depends on the degree of separation between the doses producing a therapeutic effect and the doses which produce side effects, both of which can be characterized by quantal dose-effect curves.
BUTTON

## Doxorubicin Cardiotoxicity

**Total Doxorubicin Dose [mg/m****2****]**

**Probability of CHF**

**0**

**0.20**

**0.40**

**0.60**

**0.80**

**1.0**

**0**

**200**

**400**

**600**

**800**

**1000**

**von Hoff et al. Ann Intern Med 91:710-7, 1979**

**Notes:**
This is a quantal dose-effect curve for doxorubicin cardiotoxicity.
Doxorubicin is an anticancer drug that causes permanent myocardial damage as one of its toxic effects.
The cumulative probability of developing clinical congestive heart failure is plotted against the total lifetime dose of doxorubicin.
This analysis was the first demonstration that the cardiotoxicity of doxorubicin was related to the cumulative dose of the drug and based on this analysis, safe cumulative dose levels were defined and patient’s doses are now limited to <450 or 400 mg/m2 to lower the risk of CHF.

## Lidocaine Quantal Dose-Effect

**Lidocaine Quantal Dose-Effect**

**% Achieving Complete Analgesia**

**Total Lidocaine Dose (mg)**

**Ferrante et al. Anesth Analg 82:91-7, 1996**

**Notes:**
This is the same data from the study of lidocaine in neuropathic pain in patients that I showed you earlier.  The previous plot was a graded dose-effect curve and this is the same data plotted as a quantal dose response curve.  
The all-or-none response in this study is complete analgesia.
CLICK.  The ED50 is 400 mg and the ED90 is 490, so the quantal dose-effect curve is also very steep.

## Antihypertensive Dose-Effect

**Johnston Pharmacol Ther 55:53-93, 1992**

|  | Dose Range [mg] |  | Lowest Effective Dose [mg] |
| --- | --- | --- | --- |
| Drug | Early Studies | Present Dose |  |
| Propranolol | 160-5000 | 160-320 | 80 |
| Atenolol | 100-2000 | 50-100 | 25 |
| Hydrochlorthiazide | 50-400 | 25-50 | 12.5 |
| Captopril | 75-1000 | 50-150 | 37.5 |
| Methyldopa | 500-6000 | 500-3000 | 750 |

**Notes:**
Identifying the dose-effect relationship is an important component of early clinical trials performed during the initial stages of drug development.  These trials frequently follow a dose escalation design.
Johnston reported a detailed review of the dose-effect studies performed with a variety of antihypertensive agents.  He compared the dose range studied in the initial clinical trials and the initial recommended dosage range with the currently recommended dose and the lowest effective dose identified in randomized trials.
Based on this dose-effect meta-analysis, he concluded that a variety of antihypertensive agents were introduced into clinical practice at excessively high doses.
He attributed this to the reliance on dose-escalation trial design where doses are doubled and failure to define the lower part of the dose-effect relationship.
In many cases the initial dose produced the maximum effect and the dose was escalated without any clear evidence of increased efficacy.
In other cases the dose was escalated before the maximum antihypertensive effect was achieved at the previous dose.
This table shows examples of drugs for which excessively high doses were recommended based on the initial trials.
He also summarized his analysis with a graph (BUTTON).

## Antihypertensive Drugs

**Log Dose**

**% with Maximal Effect**

**Adverse Effects**

**Desirable Dose Range**

**Dose Range most often used**

**Notes:**
Most agents were recommended to be administered in doses that appeared to be on the plateau rather than in the desired range.
The problem with this is that in very minimal added benefit, but significantly greater risk for toxicity.

## Dose Intensity in Breast Cancer

**Response Rate (%)**

**Relative Dose Intensity**

**RDI**

**Hryniuk & Bush J Clin Oncol 2:1281, 1984**

**Notes:**
This is a different type of dose-effect analysis that has been used to assess the importance of dose rate of anticancer drugs in breast cancer.
This is a metanalysis, meaning that the data from multiple clinical trials were used - each point on this graph represents a different clinical trial of the three drug combination of cyclophosphamide, adriamycin and fluorouracil.
Dose intensity, rather than dose is related  to the response rate (at least a 50% decrease in the size of tumor). Dose intensity is the amount of drug per week administered.
Because the data for this analysis comes from multiple clinical trials using different doses and schedules of each of the three agents, the dose intensity has been normalized to an arbitrarily selected standard regimen, and the relative dose intensity is the average of the three drugs for each regimen. BUTTON
In this graph dose intensity is plotted on a linear scale, but despite this the dose-effect curve is very steep.  The response rate increases from 10 to over 80% with a 2-fold increase in dose intensity.

## Doxorubicin Dose in Osteosarcoma

**Dose Intensity (mg/m****2****/wk)**

**% with >90% Necrosis**

**Smith et al. JNCI 83:1460, 1993**

**0**

**100**

**200**

- 0

- 5

- 10

- 15

- 20

- 0

- 20

- 40

- 60

- 80

- 100

**Notes:**
In this meta-analysis performed, RDI was not calculated. Instead, the role of individual agents was assessed by relating the % of patients achieving >90% tumor necrosis after neoadjuvant therapy to the dose intensity of each agent administered in the neoadjuvantly.
This is a bubble plot - the difference between this plot and a scattergram is that the size of the bubble reflects the number of patients treated in the trial.
There appeared to be a strong relationship between doxorubicin dose-intensity and response.
These dose intensity analyses are useful in defining the optimal dose of drugs when a relationship is seen, but they should not be used to determine which drugs are active and which are inactive.

## Relating Dose to Effect In Vivo

**Dose**

**Effect**

**Age**
**Absorption**
**Distribution**
**Elimination **
**Drug interactions**

**Tissue/organ sensitivity (receptor status)**

**Notes:**
This relationship between dose and effect is linked through the concentration of drug achieved at the target site. CLICK
The discipline that describes the time course of drug concentrations in the body is pharmacokinetics. CLICK
There have been other talks of pharmacokinetics , so I will not discuss it in this talk, but there are a couple of points that I would like to make.
PK BUTTON
The discipline that relates drug concentration to Effect is pharmacodynamics. CLICK
PD BUTTON
One might say that the dose-effect relationship provides the scientific basis for studying pharmacokinetics and pharmacodynamics.
PK and PD models can be linked to predict the time course of a drug effect EFFECT BUTTON

## Effect Compartment (PK/PD Model)

**Notes:**
The pharmacodynamic models described above relate drug concentration at the effect site to the drug’s pharmacological effect.  Under steady state conditions, the plasma concentration, which is assumed to be proportional to the steady state effect site concentration, can be substituted into the equation as [C].
However, under non-steady state conditions, such as after a single bolus dose, the time course of the drug effect is derived by linking pharmacokinetic models, which describe the time course of drug concentrations in the central and peripheral compartments, to a pharmacodynamic model (usually a maximum-effect model).
An effect compartment can be linked to the central compartment or to a compartment describing the disposition of an active metabolite via a first-order rate constant.  Linking pharmacokinetic and pharmacodynamic models describes the drug effect over time and allows for simulation of drug effect with different drug doses or administration schedules.
Example of a pharmacokinetic/pharmacodynamic model incorporating an effect compartment that is linked to the central compartment, where C and Ce are the drug concentrations in the central and effect compartments at time t, Xp is the amount of drug in the peripheral compartment at time t, Vc and Ve are the volumes of the central and effect compartments, k0 is the drug infusion rate, k12 and k21 are the first-order rate constants for exchange of drug between the central and peripheral compartments, k10 is the first-order drug elimination rate constant from the central compartment, k1e is the first-order rate constant for drug entry into the effect compartment, ke0 is the first-order rate constant for elimination of drug from the effect compartment, E(t) is the intensity of drug effect at time t, Emax is the maximum drug effect, EC50 is the drug concentration at the effect site required to achieve half of the maximum effect, and H is the Hill constant (see text).  The amount of drug entering the effect compartment is assumed to be insignificant (k1e is very small) relative to the amount of drug in the linked central compartment, and therefore back diffusion from the effect compartment into the linked central compartment is ignored for simplicity.

## Concentration and Effect vs. Time

**Conc./ Amount**

**Effect**
**[% of E****max****]**

**Time**

**Central Compartment**

**Peripheral Compartment**

**Effect Compartment**

**Effect**

**Non-Steady State**

**Notes:**
Simulation of drug concentrations in the Central, Peripheral and Effect compartments and the Effect as a percentage of Emax, based on the linked pharmacokinetic/pharmacodynamic model.

## Hysteresis and Proteresis Loops

**Plasma Drug Concentration**

**Intensity of Drug Effect**

**Intensity of Drug Effect**

**Hysteresis Loop (Counterclockwise)**

**Proteresis Loop (Clockwise)**

**Equilibration delay in plasma and effect site conc.**
**Formation of active metabolite**
**Receptor up-regulation**

**Tolerance**
**Receptor tachyphylaxis**

**Notes:**
Under non-steady state conditions, the drug concentration at the effect site may not directly parallel the plasma concentration, and, as a result, the time course of the intensity of the drug’s effect may not parallel the time course of plasma drug concentrations.
This can be evaluated by plotting the plasma drug concentration-effect data and connecting the points in time sequence.
A counterclockwise or hysteresis loop could indicate a delay in equilibrium between the plasma and effect site drug concentrations, the formation of an active metabolite or the up-regulation of the drug receptor.
A clockwise or proteresis loop is consistent with the development of tolerance or receptor tachyphylaxis.
If properly designed, the linked pharmacokinetic/pharmacodynamic models, such as those described on the previous slides, can account for these more complex concentration-effect relationships.

## Role of Dose-Effect Studies

**Drug development**
**Site of action**
**Selection of dose and schedule**
**Potency, efficacy and safety**
**Drug interactions**
**Patient management**
**Therapeutic drug monitoring**
**Risk-benefit (therapeutic indices)**

**Notes:**
I started out this talk by saying that the dose-effect relationship was pervasive in pharmacology and I have tried to illustrate through examples how this principle of pharmacology is important in basic research on the
Site of action (theophylline)
Selection of the appropriate dose and schedule - PK/PD models
Quantification of the potency and efficacy of drugs that have the same effect
And the study of drug interactions.
Also in the clinical arena the dose-effect relationship provides the basis for rational and individualized dosing methods such as therapeutic drug monitoring, and allows us to assess risk benefit ratios for patients receiving drug therapy by comparing the dose-effect curves for the therapeutic and toxic effects.

## Endpoints to Monitor Drug Effect

| LEVEL | ENDPOINT |
| --- | --- |
| Molecular | Farnesyltransferase inhibition |
| Cellular | Proliferation rate, apoptosis |
| Tumor | Response (change in tumor size) |
| Organism | Survival, quality of life |

**Farnesyltransferase Inhibitors for Cancer**

## Thiopurine Metabolic Activation

## Therapeutic Indices

**Therapeutic Ratio =**

**= 2.5**

**Notes:**
Therapeutic indices are calculated from dose-effect curves in order to quantify the relative safety of a drug.
Using these curves we can calculate a therapeutic ratio using the TD50 and ED50. The TD50/ED50 ratio for the drug shown on the previous graph is about 2.5, which means that about 2.5 times as much drug will cause a toxic effect in half the subjects as is needed to produce a therapeutic effect in the same proportion of subjects.  However this ratio of toxic to therapeutic dose may not hold across the entire dose range if the dose-effect curves are not parallel.
The aim of drug therapy is to achieve the desired therapeutic effect in all patients without the producing toxicity in any.  A ratio that uses the lowest toxic and highest therapeutic doses is more realistic and consistent with this aim.  The certain safety factor (CSF) is the ratio of TD1/ED99. A CSF > 1 indicates that the dose effective in 99% of the population is less than that which would be toxic in 1%.  If the CSF < 1, there is overlap between the maximally effective and minimally toxic doses.
Unlike the therapeutic ratio this measure is independent of the shapes of the quantal dose-effect curves for the therapeutic and toxic effects.
The Standard Safety margin uses the same extremes and derives the percentage by which the ED99 has to be increased before the TD1 is reached.

## Relative Dose Intensity

|  |  | Dose Rate mg/m2/wk | R.D.I. |  |
| --- | --- | --- | --- | --- |
| Regimen | Drugs |  | Drugs | Regimen |
|  | Cyclo | 350 | 1 |  |
| CAF-1 | Doxo | 15 | 1 | 1 |
|  | FU | 250 | 1 |  |
|  | Cyclo | 125 | 0.36 |  |
| CAF-2 | Doxo | 12.5 | 0.83 | 0.56 |
|  | FU | 125 | 0.50 |  |

## Oral Mercaptopurine

**MP Dose (mg/m****2****)**

**MP AUC [μM•hr]**

**Balis et al. Blood 92:3569-77, 1998**

**Notes:**
Dose may not be predictive of plasma concentration
Variable

## Pharmacodynamic Models

**Fixed effect model**
**Linear model**
**Log-linear model**
**E****max**** model**
**Sigmoid E****max**** model**

***Effect = E******0****** + S•[Drug]***

***Effect = I + S•Log([Drug])***

**Notes:**
These are the most commonly used pharmacodynamic models that relate drug concentration to effect at steady state
Notice that at steady state these models are time independent.
The fixed effect model is a statistical approach that quantifies the likelihood or probability that a given concentration will produce an all-or-none effect.  For example, a digoxin plasma concentration of 2 ng/ml is associated with a 50% probability of developing digoxin toxicity.  This is only a useful model in the clinical setting.
CLICK. The linear model assumes direct proportionality between drug concentration and effect.  E0 is the baseline effect with no drug present and S is the slope of the line. This is the intuitively most popular model, but it rarely applies.  The most obvious limitation of the model is that it does not predict for a maximal effect.  Changes in drug effect are not directly proportional to changes in the dose.
CLICK. The log-linear model (I is the intercept) may be applicable over narrow dosage ranges around the EC50, but has the same limitations as the linear model at extreme doses.
CLICK. The Emax and Sigmoid Emax models have the same form as the equation describing the interaction of drug and receptor, which is not a coincidence since receptor occupancy is proportional to the effect.  This general equation has also been called the Hill equation (first developed to describe O2-hemoglobin interactions) and the exponent, know as the Hill constant or slope factor, determines the steepness of the curve.
The Emax model is a Sigmoid Emax model with a slope of 1.

## Sigmoid Emax PD Model

**[Drug]**

**Effect (%)**

**Effect (%)**

**EC****50**

**EC****50**

**H = 0.1**

**H = 5**

**H = 2**

**H = 1**

**H = 0.5**

**Notes:**
I hope by now that you could predict the shape of the curves (concentration-effect curves) with the Sigmoid Emax model.
I have plotted them using a linear and log scale for drug concentration.
For this series of curves the Emax and EC50 are the same and I have varied the slope factor to illustrate the effect it on the shape of the curve. 
Remember an H of 1 is the Emax model.

## Theophylline Pharmacodynamics

**Theophylline [mg/L]**

**FEV****1**** (% normal)**

**E****max**** = 63%**
**EC****50**** = 10 mg/L**

**Mitenko & Ogilvie NEJM 289:600-3, 1973**

**Notes:**
This is one of the original pharmacodynamic studies of theophylline performed in patients.
The effect that was measured is the improvement in FEV1, which is normalized to normal control values.
6 subjects were studied after a placebo and then 3 incremental doses of theophylline.  Serum theophylline concentrations were measured and related to the effect.
In the original manuscript a linear model was fit to the data, but more recently other investigators have fit an Emax model and the Emax curve and parameters are shown.
They defined a therapeutic range for theophylline from this study of 10 to 20 μg/ml and defined the loading dose and infusion rate to achieve this level based on the PK studies.

## Carboplatin PK/PD

**Carboplatin AUC [μg•hr/ml]**

**Creatinine Clearance [ml/min]**

**% Decrease Platelet**

**Carboplatin Cl****TB**** [ml/min]**

**Van Echo et al. Semin Oncol 16:1-6, 1989**

## Carboplatin Adaptive Dosing

**ADULTS**

**CHILDREN**