2.1 Paediatric & Adult Dose Calculations

2.1 Paediatric & Adult Dose Calculations

Introduction to Clinical Dose Calculations

Dose calculation is a core clinical competency tested on the PSI Equivalence Examination. Pharmacists practicing in Ireland must accurately calculate, verify, and individualise drug doses across diverse patient cohorts—from neonates and paediatric patients to elderly individuals with renal or hepatic impairment. Inaccurate dosing calculations can lead to therapeutic failure or severe toxicity, especially with narrow therapeutic index (NTI) medications such as aminoglycosides, digoxin, and cytotoxic agents.

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1. Weight-Based Dosing

Weight-based dosing expresses medication doses relative to patient body weight, typically in milligrams per kilogram per day (mg/kg/day) or per individual dose (mg/kg/dose). This dosing methodology is standard in paediatric practice and for specific adult regimens (e.g., low-molecular-weight heparins, vancomycin, and aminophylline).

Fundamental Principles & Unit Conversions

• Always convert patient body weight into kilograms (kg) before initiating calculations: $\text{Weight (kg)} = \frac{\text{Weight (lb)}}{2.2046}$
• Determine whether the dosage guideline specifies total daily dose (which must be divided into discrete administration intervals) or a single dose amount: $\text{Total Daily Dose (mg)} = \text{Dose (mg/kg/day)} \times \text{Weight (kg)}$ $\text{Single Dose (mg)} = \frac{\text{Total Daily Dose (mg)}}{\text{Number of Doses per Day}}$

Maximum Daily Dose Verification

Calculated weight-based doses for paediatric or adolescent patients must never exceed the standard maximum adult dose. For example, if a 60 kg adolescent is prescribed amoxicillin 30 mg/kg/day for acute otitis media, the calculated dose is $1,800\text{ mg/day}$. If the recommended maximum adult dose is $1,500\text{ mg/day}$, the dose must be capped at $1,500\text{ mg/day}$ ($500\text{ mg}$ TID).

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2. Body Surface Area (BSA) Calculations

Body Surface Area (BSA), expressed in square metres (m²), provides a more accurate correlation with physiological parameters such as cardiac output, basal metabolic rate, glomerular filtration rate, and extracellular fluid volume than body weight alone. It is widely used in paediatric oncology, chemotherapy protocols, and for drugs with narrow therapeutic windows.

Mosteller Formula

The standard equation used in clinical pharmacy practice and required for the PSI examination is the Mosteller formula: $\text{BSA (m}^2\text{)} = \sqrt{\frac{\text{Height (cm)} \times \text{Weight (kg)}}{3600}}$

Steps to Calculate BSA-Based Dosing:

1. Calculate the patient's BSA in m² using the Mosteller formula.
2. Multiply the target dose rate (mg/m²) by the calculated BSA (m²).
3. Verify the final dose against toxicity caps and rounding rules.

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3. Dose Adjustments for Age & Organ Impairment

Paediatric Pharmacokinetic Differences

• Neonates & Infants: Higher proportion of total body water (up to 80% of body weight in preterm infants), reduced plasma albumin binding (higher free drug fraction), and immature hepatic CYP450 enzyme systems and glomerular filtration.
• Clinical Impact: Neonatal dosing often requires lower mg/kg starting doses and extended dosing intervals (e.g., gentamicin administered every 24–48 hours in neonates compared to every 8–24 hours in older children).

Renal Function Assessment: Cockcroft-Gault Equation

Renal excretion is the main elimination route for many drugs. Estimated Creatinine Clearance (CrCl) calculated via the Cockcroft-Gault formula is used to guide renal dosage adjustments: $\text{CrCl (mL/min)} = \frac{(140 - \text{Age}) \times \text{Weight (kg)} \times F}{0.814 \times \text{Serum Creatinine (}\mu\text{mol/L)}}$ Where:

• $F = 1.23$ for males
• $F = 1.04$ for females

(Note: If serum creatinine is supplied in mg/dL, use $\text{CrCl} = \frac{(140 - \text{Age}) \times \text{Weight (kg)}}{72 \times \text{Serum Creatinine (mg/dL)}} \times 0.85\text{ for females}$).

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4. Step-by-Step Worked Numerical Examples

Worked Example 2.1.1: Paediatric Weight-Based Dosing

Clinical Scenario: A 4-year-old child weighing 16 kg is prescribed oral Amoxicillin suspension for acute otitis media at a dose of 40 mg/kg/day divided into 3 equal doses. The available stock is Amoxicillin 250 mg/5 mL suspension. Calculate the volume (in mL) to be administered per single dose.

Solution:

• Step 1: Calculate Total Daily Dose (mg) $\text{Total Daily Dose} = 16\text{ kg} \times 40\text{ mg/kg/day} = 640\text{ mg/day}$
• Step 2: Calculate Single Dose Amount (mg) $\text{Single Dose} = \frac{640\text{ mg}}{3\text{ doses}} = 213.33\text{ mg per dose}$
• Step 3: Calculate Volume of Suspension per Dose (mL) $\text{Volume per Dose} = \frac{213.33\text{ mg}}{250\text{ mg}} \times 5\text{ mL} = 4.2667\text{ mL} \approx 4.27\text{ mL}$ (In clinical practice, this is measured using a 5 mL oral dosing syringe rounded to 4.3 mL).

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Worked Example 2.1.2: BSA Calculation using Mosteller Formula

Clinical Scenario: An adult oncology patient measuring 170 cm in height and weighing 68 kg is prescribed Carboplatin at a target dose of 360 mg/m². Calculate the total dose of Carboplatin to administer.

Solution:

• Step 1: Calculate BSA using Mosteller formula $\text{BSA} = \sqrt{\frac{170 \times 68}{3600}} = \sqrt{\frac{11560}{3600}} = \sqrt{3.2111} = 1.792\text{ m}^2$
• Step 2: Calculate Total Dose (mg) $\text{Total Dose} = 1.792\text{ m}^2 \times 360\text{ mg/m}^2 = 645.12\text{ mg}$ (Rounding to standard clinical precision yields 645 mg).

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Worked Example 2.1.3: Renal Dose Adjustment using Cockcroft-Gault

Clinical Scenario: A 72-year-old female patient weighing 58 kg presents with a serum creatinine of $140\ \mu\text{mol/L}$. Her target antibiotic dose requires reduction if her CrCl is $<50\text{ mL/min}$. Calculate her estimated CrCl.

Solution:

• Step 1: Apply Cockcroft-Gault Formula for Females ($F = 1.04$) $\text{CrCl} = \frac{(140 - 72) \times 58 \times 1.04}{0.814 \times 140}$
• Step 2: Solve Numerator & Denominator $\text{Numerator} = 68 \times 58 \times 1.04 = 4101.76$ $\text{Denominator} = 0.814 \times 140 = 113.96$
• Step 3: Calculate Final CrCl $\text{CrCl} = \frac{4101.76}{113.96} = 35.99\text{ mL/min} \approx 36.0\text{ mL/min}$
• Clinical Conclusion: Because CrCl ($36.0\text{ mL/min}$) is $<50\text{ mL/min}$, the dose must be adjusted according to renal impairment guidelines.

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5. Summary & Key Comparison Table