Formulas Flashcards
odds ratio
odds of exposure among cases (a/c) versus odds of exposure among controls (b/d)
OR = (a/c)/(b/d) = ad/bc
relative risk
risk of developing disease in the exposed group divided by risk in the unexposed group
RR = (a/[a + b]) / (c/[c + d])
relative risk reduction
proportion of risk reduction attributable to the intervention as compared to a control
RRR = 1 - RR
attributable risk
difference in risk between exposed and unexposed groups
AR = (a/[a + b]) - (c/[c + d])
AR% = (RR - 1)/RR * 100
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])
number needed to treat
number of patients who need to be treated for one patient to benefit
NNT = 1/ARR
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
mortality rate
number of deaths within a population over a defined period
deaths/1000 people per year
attack rate
proportion of exposed people who become ill
(people who become ill)/(total people exposed)
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
posttest probability
posttest probability = posttest odds / (posttest odds + 1)
posttest odds = pretest probability * LR
sensitivity
true positive rate; proportion of all people with disease who test positive
= TP / (TP + FN)
= 1 - FN rate
specificity
true negative rate; proportion of all people without disease who test negative
= TN / (TN + FP)
= 1 - FP rate
positive predictive value
probability that a person who has a positive test result actually has the disease
PPV = TP / (TP + FP)
negative predictive value
probability that a person with a negative test result actually does not have the disease
NPV = TN / (TN + FN)
standard error
SE = SD/(square root of sample size)
statistical power
power = 1 - B
B: probability of making a type II error
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)
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
