Formulas Flashcards by Taylor Flynn

odds ratio

odds of exposure among cases (a/c) versus odds of exposure among controls (b/d)

OR = (a/c)/(b/d) = ad/bc

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relative risk

risk of developing disease in the exposed group divided by risk in the unexposed group

RR = (a/[a + b]) / (c/[c + d])

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relative risk reduction

proportion of risk reduction attributable to the intervention as compared to a control

RRR = 1 - RR

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attributable risk

difference in risk between exposed and unexposed groups

AR = (a/[a + b]) - (c/[c + d])
AR% = (RR - 1)/RR * 100

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absolute risk reduction

difference in risk (not the proportion) attributable to the intervention as compared to a control

ARR = (c/[c + d]) - (a/[a +b])

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number needed to treat

number of patients who need to be treated for one patient to benefit

NNT = 1/ARR

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number needed to harm

number of patients who need to be exposed to a risk factor for one patient to be harmed

NNH = 1/AR

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mortality rate

number of deaths within a population over a defined period

deaths/1000 people per year

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attack rate

proportion of exposed people who become ill

(people who become ill)/(total people exposed)

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likelihood ratio

LR+ = (probability of positive result in a patient with disorder) / (probability of positive result in patient without disorder)
= (sensitivity) / (1 - specificity)
= (TP rate) / (FP rate)

LR- = (probability of a negative result in a patient with disorder) / (probability of negative result in patient without disorder)
= (1 - sensitivity) / (specificity)
= (FN rate) / (TN rate)

LR+ >10 = highly specific test
LR- < 0.1 = high sensitive test

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posttest probability

posttest probability = posttest odds / (posttest odds + 1)

posttest odds = pretest probability * LR

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sensitivity

true positive rate; proportion of all people with disease who test positive

= TP / (TP + FN)
= 1 - FN rate

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specificity

true negative rate; proportion of all people without disease who test negative

= TN / (TN + FP)
= 1 - FP rate

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positive predictive value

probability that a person who has a positive test result actually has the disease

PPV = TP / (TP + FP)

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negative predictive value

probability that a person with a negative test result actually does not have the disease

NPV = TN / (TN + FN)

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standard error

SE = SD/(square root of sample size)

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statistical power

power = 1 - B

B: probability of making a type II error

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confidence interval

range of values within which the true mean of the population is expected to fall

CI = 1 - a

CI for sample mean = mean +/- Z(SE)

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coefficient of determination

r^2

Michaelis-Menten equation

v = Vmax * [S]/(Km + [S])
v = rate of reaction (rate for formation of product)
Vmax = maximum rate achieved
[S] = concentration of substrate
Km = [S] at 1/2 Vmax

volume of distribution (Vd)

Vd = (amount of drug in body) / (plasma drug concentration)

compartment = intravascular: low Vd
compartment = ECF: medium Vd
compartment = all tissues (including fat): high Vd

clearance (CL)

CL = (rate of elimination of drug) / (plasma drug concentration)
CL = Vd * Ke

Ke = elimination constant

half life (t1/2)

t1/2 = 0.7(Vd) * CL

(for first-order elimination)

loading dose, maintenance dose

loading dose = Cp * Vd / F

maintenance dose = Cp * CL * T / F

Cp = target plasma concentration
Vd = volume of distribution
CL = clearance
T = dosage interval (time between doses)
F = bioavailability

bioavailability (F)

F = (AUC oral * Dose iv) / (Dose oral * AUC iv)

therapeutic index

TI = TD50/ED50 TD50 = median toxic dose TD50 = median effective dose drugs with lower TI values require monitoring: warfarin, theophylline, digoxin, antiepileptic drugs, lithium

corrected reticulocyte count

also called reticulocyte production index (RPI) RPI = % reticulocytes * (actual Hct / normal Hct) / maturation time

cardiac wall tension

wall tension = pressure * radius wall stress is proportional to (wall tension)/(2*(wall thickness))

stroke volume

SV = EDV - ESV

ejection fraction

EF = SV/EDV = (EDV - ESV)/EDV

cardiac output

CO = Q = SV * HR CO = (rate of oxygen consumption) / (arterial O2 content - venous O2 content)

pulse pressure

PP = systolic blood pressure (SBP) - diastolic blood pressure (DBP) PP is increased in hyperthyroidism, aortic regurgitation, aortic stiffening, obstructive sleep apnea, anemia, and exercise PP is decreased in aortic stenosis, cardiogenic shock, cardiac tamponade, advanced HF

mean arterial pressure

MAP = CO * TPR MAP = 2/3 DBP + 1/3 SBP = DBP + 1/3 PP

resistance (cardio)

resistance = driving pressure / Q = (8(viscosity) * length)/(pi * r^4)

capillary fluid exchange (net fluid flow)

Jv = Kf[(Pc - Pi) - sigma(pi.c - pi.i)]

inspiratory capacity

IRV + VT (tidal volume) air that can be breathed in after normal exhalation

functional residual capacity

RV + ERV volume of gas in lungs after normal expiration; outward pulling force of chest wall is balanced with inward collapsing force of lungs

vital capacity

IRV + VT + ERV maximum amount of air that can be expired after a maximal inspiration

total lung capacity

IRV + VT + ERV + RV = VC + RV volume of gas present in lungs after a maximal inspiration

determination of physiologic dead space

VD = VT * (PaCO2 - PeCO2)/PaCO2 PaCO2: arterial PCO2 PeCO2: expired air PCO2

minute ventilation

VE = VT * RR total volume of gas entering lungs per minute

alveolar ventilation

VA = (VT - VD) * RR volume of gas that reaches alveoli each minute

pulmonary vascular resistance

PVR = (pressure in pulmonary artery - pulmonary artery occlusion pressure)/Q Q = cardiac output

alveolar gas equation

PAO2 = PIO2 - PaCO2/RQ = 150 mm Hg - PaCO2/0.8

oxygen content

O2 content = (O2 bound to hemoglobin) + (O2 solubilized in plasma) = (1.34 * Hb * SaO2) + (0.003 * PaO2) SaO2 = percent saturation of arterial blood with O2 0.003 = solubility constant of O2 PaO2 = partial pressure of O2 in arterial blood