quantal dose response relationships

quantal dose response curves

• average effect of a drug as a function of its dose in a population of individuals

  • observe for the presence or absence of a response

    • sleep or no sleep

    • alive at 12 months vs not alive at 12 months

• graph the % of individuals who response to each dose of a drug

• used to predict the effects of a drug when it is administered to a population of individuals and for determining population-based toxic and lethal doses

types of quantal dose response curves

gaussian distribution

• bars in frequency histogram represent the % of individuals with effect minus the % of individuals that response at lower dose

  • normal frequency distribution → most individuals response in middle portion of range of doses

  • bell shaped curve

  • fall to the right of the curve = more resistant to drug

  • fall to the left of the curve = hypersusceptible

sigmoid dose response

• add together the # of individuals responding at each consecutive dose

• cumulative responses

quantal dose response curves more in depth

• frequency distribution of doses of drug required to produce a specified effect

  • shaded boxes and bell-shaped curves

  • the % of animals that require a particular dose to exhibit the effect

• cumulative frequency distribution

  • open boxes and sigmoidal curves

  • log-normally distributed

• by the time you achieve the highest dose, essentially all individuals in the population will have responded

quantal dose response curves (ED, TD, LD)

• ED50

  • dose at which 50% of the subjects exhibit a therapeutic response to a drug

    • remember: Ec50 is dose at which a drug elicits a half max effect in an individual

• TD30

  • dose at which 50% of subjects exhibit a toxic effect to drug

• LD50

  • dose at which 50% of subjects exhibit a lethal response to drug

population sensitivity

sensitivity

• drugs A and C have the same mean sensitivity (1.0 log unit ~ 10 ug/kg)

• mean sensitivity to drug B is lower (2.2 log unit ~150 ug/kg)

  • need higher dose to achieve the same response

response

• population response is more homogenous for drug C then drug A despite same sensitivity (smaller standard deviation)

• same standard deviation of drug A and B (width of curve)

therapeutics

• therapeutic window = range of doses of a drug that elicits a therapeutic response WITHOUT unacceptable adverse effects (or toxicity) in a population of pts

• quantified as therapeutic index (TI)

  • TI = toxic (lethal) dose50/effective dose50

therapeutic index

• cumulative percentages of pts responding to 2 different drugs → warfarin (anticoagulant, narrow TI) and penicillin (antibiotic, large TI)

therapeutic index question

dose dependent relationship between desired biological effect and toxicity

calculate TI

• determine ED50 and TI50

• ED50 = 100

• TI50 = 1000

• TI = 1000/100 = 10

therapeutic index with non parallel curves

• TI = 10 in both graphs, however in graph B some pts are experiencing toxicity at ED50

• TI ratio is less helpful when the curves are not parallel

margin of safety

margin of safety = TD1/ED99

• ratio of the doses that cause toxicity in 1% of the population to that cause the desired effect in 99% of the population

• often used rather than TI when dose-response curves are NOT parallel