Calculations and Biostats

Type 1 Error

false positives (null hypothesis was rejected in error)

Type 2 Errors

False negatives (null hypotheses was accepted in error)

Relative Risk (or Risk Ratio) Formula

Risk = (number of subjects in group w unfavorable event)/ (total number of subjects in group)

RR = risk in treatment group/ risk in control group

Relative Risk Reduction

RRR = (% risk in control group - % risk in treatment group)/ % risk in the control group

OR

RRR = 1 - RR

Absolute Risk Reduction

ARR = (% risk in control group) – (% risk in treatment group)

Number Needed to Treat/ Harm

NNT = 1/ (risk in control group – risk in treatment group)

OR

1/ARR

note: NNT is rounded up, NNH is rounded down

Odds Ratio

[outcome present (exposed group) x outcome absent (absent group)]/ [outcome absent (exposed group) x outcome present (absent group)]

Hazard Ratio

HR = Hazard rate in the treatment group/ Hazard rate in the control group

1 fluid oz = ? mL

30 mL

1 cup = ? oz

1 pint = ? cup

1 quart = ? pint

1 gallon = ? quarts

1 cup = 8 oz

1 pint = 2 cups

1 quart = 2 pints

1 gallon = 4 quarts

1 oz = ? grams

1 lb = ? grams

1 oz = 28.4 grams

1 lb = 454 grams

1 grain = ? mg

1 grain = 65 mg

mEq to mmol

1:1 for monovalent ions (eg Na, K

1: 0.5 for divalent ions (Mg, Ca)

1 inch = ? centimeters

1 inch = 2.54 centimeters

Specific Gravity

weight of a substance (g)/ weight of equal volume of water (g)

Alligation

(higher strength - desired strength) = part of lower strength

(desired strength - lower strength) = parts of higher strength

parts of desired strength = parts of lower + parts of higher

mOsmol

moles x # of particles x 1000

Isotonicity (E value)

E = (58.5 x i)/ (MW of drug x 1.8)

mEq

mmoles x valence

Enteral Nutrition Calories (Carbs, Protein, Fat)

carbs/proteins = 4 kcal/gram

fat = 9 kcal/gram

Parenteral Nutrition Calories (dextrose, amino acid solution, ILE 10%, ILE 20%, ILE 30%)

dextrose = 3.4 kcal/gram

amino acid solution = 4 kcal/gram

ILE 10% = 1.1 kcal/mL

ILE 20% = 2 kcal/mL

ILE 30% = 3 kcal/mL

Determining Fluid Needs

Weight > 20 kg: 1,500 mL + (20 mL)(weight in kg -20)

Can estimate using 30-40 mL/kg/day

Total Energy Expenditure

BEE x activity factor x stress factor

Grams of Nitrogen From Protien

nitrogen (g) = protein intake (g)/ 6.25

IBW (male and females); Adjusted BW

male = 50 kg + (2.3 kg) (inches over 5 feet)

females = 45.5 kg + (2.3 kg) (inches over 5 feet)

Adjusted BW = IBW + 0.4(TBW-IBW)

Which Weight to Use for Drug Dosing

All drugs (if underweight ie BMI 18.5) = TBW

Most drugs (if normal weight or obese) = TBW

Exceptions:

IBW (normal weight, obese): acyclovir, aminophylline, levothyroxine, theophylline

Adjusted BW (obese): Aminoglycosides

Dehydration

BUN: SCr > 20:1

CrCl

[(140 - age of patient)/ (72 x SCr)] x weight (kg) x 0.85 if female)

Anion Gap

Anion Gap = Na - Cl - HCO3

pH calculation (weak acid and weak base)

acid: pH = pKa + log (salt/acid)

base: pH = pKa + log (base/salt)

Absolute Neutrophil Count

ANC = WBC x [(% segs + % bands)/100]

Fahrenheit to Celsius Conversion

F = (C x 1.8) + 32

Incremental Cost Ratio

(C2 - C1)/ (E2 - E1) C = costs, E = effects

Correction Dose

[(blood glucose now) - (target blood glucose)]/ correction factor

LDL equation

LDL = TC - HDL - (TG*/5) *do not use if TG greater than 400

minimum weight quantity

MWQ = sensitivity requirement/ acceptable error rate (usually 0.05)

BSA

BSA (m2) = sqrt [ht (cm) x wt (kg)/ 3,600]

F (%) - bioavailability

F(%) = 100 x (AUCextravascular/ AUCintravascular) x (DOSEintravascular/ DOSE extravascular)

Volume of Distribution

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

Clearence

Cl = (F x dose)/ AUC

or

Cl = Ke x Vd

Elimination Rate Constant (ke)

ke = Cl/Vd

Predicting Drug Concentrations

C2 = C1 x e^-kt

half-life (t1/2)

t1/2 = (0.693)/ke

LD

(desired concentrations x Vd) / F

Lithium Drug Dose Conversion

5 mL lithium syrup = 300 mg lithium carbonate = 8 mEq Li ion

Loop Diuretic Conversions (Ethacrynic acid, furosemide, torsemide, bumetanide, furosemide IV: PO, Other Loops IV: PO)

Ethacrynic acid = 50 mg

furosemide = 40 mg

torsemide = 20 mg

bumetanide = 1 mg

furosemide IV: PO = 1:2

Other Loops IV: PO) = 1:1

Metoprolol IV: PO

IV:PO = 1:2.5