2.3 Pharmaceutical Calculations & Literature Evaluation

Why This Matters

Pharmaceutical calculations are among the most heavily weighted and most missed items on the NAPLEX. A single arithmetic slip changes the answer entirely, so a disciplined method matters more than speed. Literature evaluation tests whether you can judge whether a study's result is real, large enough to matter, and applicable to a patient — core skills for evidence-based dispensing decisions.

A Reliable Calculation Method

1. Write down what is asked and the target unit.
2. List every given value with its unit.
3. Set up dimensional analysis so units cancel to the target.
4. Solve, then sanity-check magnitude (is a 5,000 mg dose plausible?).
5. Round only at the end to the clinically appropriate precision.

Weight-Based and Dose Calculations

mg/kg Dosing

A patient weighs 70 kg and the order is 15 mg/kg per dose.

Dose = 15 mg/kg x 70 kg = 1,050 mg per dose

If the drug is supplied as 250 mg/5 mL:

Volume = 1,050 mg x (5 mL / 250 mg) = 21 mL

Body Surface Area (BSA)

Many chemotherapy and pediatric doses use BSA in m². Mosteller formula:

BSA (m²) = sqrt[(height cm x weight kg) / 3600]

For a patient 180 cm and 80 kg:

BSA = sqrt[(180 x 80) / 3600] = sqrt[4.0] = 2.0 m²

If a regimen is 100 mg/m², the dose is 100 x 2.0 = 200 mg.

IV Infusion Rate Calculations

Rate in mL/hr

Order: infuse 1,000 mL over 8 hours.

Rate = 1,000 mL / 8 hr = 125 mL/hr

Drops per Minute (gtt/min)

With a drop factor of 15 gtt/mL at 125 mL/hr:

gtt/min = (125 mL/hr x 15 gtt/mL) / 60 min/hr = 31.25 ≈ 31 gtt/min

Dose-Based Infusion

A dopamine drip is ordered at 5 mcg/kg/min for an 80 kg patient using 400 mg in 250 mL.

• Dose rate = 5 mcg/kg/min x 80 kg = 400 mcg/min = 0.4 mg/min
• Concentration = 400 mg / 250 mL = 1.6 mg/mL
• Pump rate = (0.4 mg/min x 60 min/hr) / 1.6 mg/mL = 15 mL/hr

Electrolyte and Osmolarity Calculations

Milliequivalents (mEq)

mEq = (mg / molecular weight) x valence

For potassium chloride (KCl, molecular weight 74.5, valence 1), 1,490 mg of KCl provides:

mEq = (1,490 / 74.5) x 1 = 20 mEq

Osmolarity

Osmolarity (mOsm/L) = (grams per liter / molecular weight) x number of dissociated species x 1,000

For 0.9% sodium chloride (NaCl): 9 g/L, molecular weight 58.5, dissociates into 2 species.

(9 / 58.5) x 2 x 1,000 ≈ 308 mOsm/L

This is why 0.9% NaCl is called isotonic — it approximates normal serum osmolarity (~285-295 mOsm/L).

Alligation

Alligation determines how many parts of a higher-strength and a lower-strength preparation are needed to make an intermediate strength. Place the desired strength in the center; subtract diagonally.

Worked Example

Prepare a 5% hydrocortisone cream using a 10% cream and a 1% cream.

Total = 9 parts. To make 90 g of 5% cream:

• 10% cream: (4 / 9) x 90 g = 40 g
• 1% cream: (5 / 9) x 90 g = 50 g

Verify: (40 g x 0.10) + (50 g x 0.01) = 4 g + 0.5 g = 4.5 g active in 90 g = 5%.

Drug Literature Evaluation: Study Designs

NAPLEX expects you to rank evidence quality and recognize each design's strengths and biases.

Intention-to-treat (ITT) analysis keeps patients in their assigned group regardless of adherence; it preserves randomization and is the conservative standard for superiority trials.

Risk, Number Needed to Treat, and Statistical Significance

For a trial where event rate is 20% in control and 12% in treatment:

• Absolute risk reduction (ARR) = 0.20 - 0.12 = 0.08 (8%)
• Relative risk (RR) = 0.12 / 0.20 = 0.60 (a 40% relative risk reduction)
• Number needed to treat (NNT) = 1 / ARR = 1 / 0.08 = 12.5, round up to 13

Treat about 13 patients to prevent one event. Number needed to harm (NNH) uses the same formula with the absolute risk increase; a large NNH is desirable.

Confidence Intervals and p-Values

• A p-value < 0.05 conventionally indicates statistical significance — the result is unlikely under the null hypothesis. It does not measure effect size or clinical importance.
• A 95% confidence interval (CI) gives the plausible range for the true effect. For a ratio (RR, odds ratio, hazard ratio), if the CI includes 1, the result is not statistically significant. For a difference (ARR, mean difference), the null value is 0. Narrow CIs indicate more precise estimates.