Ch04-9781975113285

Useful Formulae

4

Thomas M. De Fer

INTRODUCTION

• The most important formula for the intern year:

(discharges + transfers) (admissions + cross cover) 2

Sleep (h) =

× number of interns

• Many of these formulae can be found on applications for your electronic devices or on Web sites. A-a O 2 GRADIENT

− Pa O

A-a gradient = PA O 2

2

2  × 713) −  (PaCO 2

PAO

 = (FiO

/0.8)

2

( all units in mm Hg )

• Estimate for upper limit of normal in room air (in mm Hg) by age (years) = (age/4) + 4. • Causes of increased A-a gradient: V/Q mismatch, intrapulmonary right-to-left shunt, intracardiac right-to-left shunt, impaired diffu- sion (room air only) ANION GAP (SERUM)

AG = [Na + ]  −  ([Cl − ] + [HCO 3 – ])

( all in mmol/L )

• Normal = 8 to 12 mmol/L • See Chapter 15, Acid-Base Disorders, for differential diagnosis.

1 0

Useful Formulae   1 1

ANION GAP (URINE)

) − U

UAG = (U

 + U

[Na + ]

[K + ]

[Cl − ]

( all in mmol/L )

• Normal = slightly positive • UAG is negative in diarrhea-induced nongap metabolic acidosis ( enhanced urinary NH 4 + excretion). • UAG is positive in distal RTA-induced nongap metabolic acidosis ( impaired urinary NH 4 + excretion). • See Chapter 15, Acid-Base Disorders, for differential diagnosis. BODY MASS INDEX

BMI = wt/(ht) 2 ( wt in kg, ht in m )

• <18.5 = underweight • 18.5-24.9 = normal weight • 25-29.9 = overweight • >30 = obese • >40 = morbidly obese CREATININE CLEARANCE/GLOMERULAR FILTRATION RATE

Estimated (Cockcroft-Gault Formula) CrCl = [(140  −  age) × weight]/[serum Cr × 72] × 0.85 ( if female ) ( weight in kg, Cr in mg/dL) Estimated (MDRD) eGFR = 175 × (SCr) − 1.54  × age −0.203 × 0.742 ( if female ) × 1.21 ( if black ) ( eGFR in mL/min per 1.73m 2 , Cr in mg/dL )

1 2   INTERNSHIP SURVIVAL GUIDE

• Um, yeah, like you’re going to calculate those exponents in your head. Obviously, this is too complicated without a calculator. • If you care, MDRD stands for Modification of Diet in Renal Disease (study). • MDRD is fairly accurate for patients with known chronic kidney disease and who are not hospitalized. Estimated (The Chronic Kidney Disease Epidemiology Collaboration) eGFR = 141 × min (SCr/ κ , 1) α  × max (SCr/ κ , 1) −1.209  × 0.993 age

× 1.018 ( if female ) × 1.159 ( if black ) ( eGFR in mL/min per 1.73m 2 , Cr in mg/dL )

• Again, ain’t no way anyone can calculate that in his/her head. • More accurate when GFR is close to normal. Measured (24-h) CrCl = (U [Cr]  × U volume )/(P [Cr]  × 24 × 60) ( Cr in mg/dL, volume in mL, and time in min )

CORRECTED SERUM CALCIUM

Corrected serum Ca = [Ca +2 ] +  [ 0.8 × (4.0  −  [albumin]) ] ( [Ca +2 ] in mg/dL, albumin in g/d )

CORRECTED SERUM SODIUM

Corrected serum Na = [Na + ] +  [ 0.016 × ([glucose]  −  100) ] ( [Na + ] in mmol/L, [glucose] in mg/dL )

FRACTIONAL EXCRETION OF SODIUM

FE

 = (U

 × P

)/(P

 × U

) × 100

Na

[Na + ]

[Cr]

[Na + ]

[Cr]

(U

and P

in mmol/L; U

and P

in mg/dL)

[Na + ]

[Na + ]

[Cr]

[Cr]

Useful Formulae   1 3

• FE Na <1% in prerenal states, early acute tubular necrosis, contrast or heme-pigment nephropathy, and acute glomerulonephritis. • Not valid when diuretics have been given. • See “Acute Kidney Injury” section in Chapter 12, Top 10 Workups.

FRACTIONAL EXCRETION OF UREA

FE

 = [(U

 × P

)/(P

 × U

)] × 100

urea

[urea]

[Cr]

[urea]

[Cr]

( all units in mg/dL )

• FE

<35% in prerenal states.

urea

• Not affected by diuretics. • See “Acute Kidney Injury” section in Chapter 12, Top 10 Workups.

MEAN ARTERIAL PRESSURE

Mean arterial pressure = [SBP + (2 × DBP)]/3

MODEL FOR END-STAGE LIVER DISEASE

MELD = (3.78 × Ln[bilirubin]) + (11.2 × Ln INR) + (9.57 × Ln[SCr]) + 6.43 ( [bilirubin] and [Cr] in mg/dL ) • Who remembers what a nature log is? Rhetorical… Only included to provide the interpretation (Table 4-1).

OSMOLALITY (SERUM, ESTIMATED)

Calculated serum osm = (2 × [Na + ]) + ([glucose]/18) + ([BUN]/2.8)

( [Na + ] in mmol/L; [glucose] and [BUN] in mg/dL )

• To correct for methanol + ([MeOH]/3.2). • To correct for ethanol + ([EtOH]/4.6).

1 4   INTERNSHIP SURVIVAL GUIDE

MORTALITY BASED ON MODEL FOR END-STAGE LIVER DISEASE (MELD) SCORE

TABLE 4-1

MELD Score

Observed Mortality (over 3 mo) (%)

>40

71.3 52.6 19.6

30-39 20-29 10-19

6.0 1.9

<9

Adapted from Wiesner R, et al. Model for end stage liver disease (MELD) and allocation of donor livers. Gastroenterology 2003;124:91-6, with permission.

• To correct for isopropyl alcohol + ([IPA]/6). And in this case, IPA does not stand for India pale ale.

• To correct for ethylene glycol + ([EG]/6.2). • To correct for mannitol + ([mannitol]/18.2). OSMOLAL GAP

−  calculated S

Osmolal gap = measured S osm

osm

• Causes of increased osmolal gap: decreased serum water, hyper- proteinemia, hypertriglyceridemia, and presence of unmeasured osmoles (e.g., sorbitol, glycerol, mannitol, ethanol, isopropyl alco- hol, acetone, ethyl ether, methanol, and ethylene glycol) • Every time you drink alcohol you have an osmole gap! Unless you correct for it as mentioned. RETICULOCYTE INDEX Reticulocyte index = [reticulocyte count × (Hct/45)]/maturation factor Maturation factor = 1 + (0.5 × [(45  − Hct)/10]) • Good marrow response = 3.0-6.0. You go marrow! • Borderline response = 2.0-3.0 • Inadequate response = <2.0. Gosh marrow, is that the best you can do?

Useful Formulae   1 5

MEDICAL EPIDEMIOLOGY

• Yeah, can you believe this stuff actually matters? • The letters in the following refer to a standard 2 × 2 table presented in Figure 4-1. • Sensitivity: the percentage of patients with the target disease/ condition who have a positive result [A/(A + C)]. The greater the sensitivity, the more likely the test will detect patients with the disease. High sensitivity tests are useful clinically to rule OUT a disease (SnOUT) (i.e., a negative test result would virtually exclude the possibility of the disease). • Specificity: the percentage of patients without the target disease/ condition who have a negative test result [D/(B + D)]. Very spe- cific tests are used to confirm or rule IN the presence of disease (SpIN). • Positive predictive value : the percentage of persons with positive test results who actually have the disease/condition [A/(A + B)]. • Negative predictive value : the percentage of persons with negative test results in which the disease/condition is absent [D/(C + D)]. • Number needed to treat : the number of patients who need to be treated to achieve one additional favorable outcome; calculated as 1/absolute risk reduction, rounded up to the nearest whole number • Number needed to harm : the number of patients who, if they received the experimental treatment, would lead to one additional person being harmed compared with patients who receive the con- trol treatment; calculated as 1/absolute risk increase

1 6   INTERNSHIP SURVIVAL GUIDE

All with positive test = A + B Positive predictive value (PPV) = [A/(A + B)] All with negative test = C + D

Negative predictive value (NPV) = [D/(C + D)]

D

B

Disease No disease

False positive (FP)

True negative (TN)

All without disease = B + D Specificity = [D/(B + D)]

A

C

Positive test True positive (TP)

Negative test False negative (FN)

All with disease = A + C Sensitivity = [A/(A + C)]

Figure 4-1. Medical epidemiology.