# Clinical dose calculations

| Home | | Pharmaceutical Drugs and Dosage | | Pharmaceutical Industrial Management |

## Chapter: Pharmaceutical Drugs and Dosage: Pharmacy math and statistics

The dose of a drug represents the amount of the drug substance that a patient must take at one time.

Clinical dose calculations

The dose of a drug represents the amount of the drug substance that a patient must take at one time. This amount is designed with an expectation of producing the optimum therapeutic effect while minimizing the unwanted side effects. In the current pharmacokinetic paradigm, the designed therapeutic dose for a patient is usually based on the desired target concentration of the drug substance in the patient’s central compartment body fluids, that is, blood, or the target site of action.

Any changes in the patient’s profile or pathophysiological status that may affect the drug’s pharmacokinetics can change the drug’s concentration reached in the patient’s body fluids for the same dose. These changes, for example, can include patient-to-patient differences in body weight, body surface area (BSA), age, and renal function. The usual adult dose mentioned for most medications reflects the amount of drug required for an average 180-lb adult with normal body functions. The drug’s dose for an individual patient is often adjusted to reflect one more of these differences, so as to optimize the patient’s exposure to the drug substance.

### Dosage adjustment based on body weight or surface area

In many cases, the target dose is expressed in terms of BSA or body weight. For example, meperidine hydrochloride (Demerol®) has a dose of 6 mg/ kg/day in divided doses to be taken 4–6 times daily, while isoniazid has a recommended daily dose of 450 mg/m2 BSA/day to be administered in a single dose. Therefore, the daily dose is calculated based on the patient’s weight or BSA and divided by the number of doses per day to determine an individual dose amount. A set of doses administered over a period of time as a part of a treatment plan is termed dosage regimen.

For example, for a patient of 180-lb body weight, the daily dose of meperidine hydrochloride would be 220/2.2 × 6 = 600 mg. For a patient recommended q.i.d. (Latin, quaque in die, four times a day) dosing for 3 days, the dose would be 600/4 = 150 mg/dose. Therefore, the patient may take three tablets of 50 mg four times a day. The total number of tablets to be dispensed would be = 3 × 4 × 3 = 36 tablets.

Dosage calculation based on the BSA is often utilized for the IV admin-istration of drugs and fluids. The BSA can be calculated by Mosteller’s formula, using the body weight and height information as follows:

Another, more common, approach to the estimation of BSA is the use of a nomogram (graphical calculation device). Figure 5.1 illustrates a typi-cal adult nomogram. To estimate the surface area, use a ruler to mark the patient’s height and weight in his or her respective scales in a straight line. The point at which this straight line intersects the surface area line is the BSA of the patient.

Figure 5.1 Example of a typical adult nomogram for the calculation of body surface area for patients weighing more than 65 lbs or 3-feet tall. (From http:// www.smm.org.)

### Calculation of children’s dose

In addition to the height and the weight, the BSA is also a function of the age and gender of an individual. For example, the average BSA of an adult men (~1.9 m2) is higher than that of an adult women (~1.6 m2) and children (~1.1 – 1.3 m2 for 9- to 13-year-old children). An average adult’s (150–154 lbs) BSA is assumed to be 1.73 m2. This is often used in the calculation of children’s doses. For example,

Child’s dose = Adult dose ( Child’s BSA in m2 / 1.73 m2 )          (5.6)

Estimation of BSA for children uses a different nomogram, illustrated in Figure 5.2.

Less frequently, a child’s dose is also calculated using the age of child in months (Fried’s rule) or years (Young’s rule) or using the weight of the child in pounds (Clark’s rule). The formulas are illustrated as follows:

Figure 5.2 Example of a typical child nomogram for the calculation of body surface area for patients weighing less than 65 lbs or 3 feet tall. (From http://www.smm.org.)

Child’s dose = Adult dose ( Child’s weight in pounds / 150 pounds )

The choice of a formula for dose calculation depends on the conventional practice of the pharmacy or hospital for a given drug. Attention should also be paid to the overall metabolic status of the patient and the thera-peutic index of the drug. For drugs eliminated by the kidney, the renal function, measured by creatinine clearance (Cr Cl), plays an important role in dose adjustment of potent compounds. Creatinine clearance of greater than 80 mL/min is considered normal. For compromised Cr Cl, the formularies usually have a recommended table of doses, depending on the therapeutic index of the drug and the percentage of drug eliminated by the kidney.

### Dose adjustment for toxic compounds

For the administration of highly toxic compounds with a narrow thera-peutic window, such as the cytotoxic anticancer compounds, dosage cal-culation becomes very critical. These compounds are dosed at very high levels, close to but lower than their maximum tolerated dose (MTD), to maximize their therapeutic benefit to the patient. Therefore, interpatient variability in drug exposure has serious implications on drug effectiveness and toxicity to the patients. The variation in drug exposure arises from differences in drug metabolism and elimination. For example, the total body clearance of carboplatin can range from 20 to 200 mL/min owing to interpatient differences in renal function, since most of the drug is elimi-nated by glomerular filtration. Similarly, topotecan clearance correlates with renal function.

Different dosage adjustment strategies are followed in these cases, depending on the drug being administered. For drugs with clinically estab-lished exposure–physiological parameter correlations, dosage adjustment for an individual patient is done a priori, based on the patient’s physiolog-ical parameters, such as genotype and/or phenotype of the metabolizing enzymes, renal clearance, serum protein, or hepatic function. In addition, for drugs that are dosed repeatedly or continuously, dosage modification can be based on the measurement of blood levels of the drug and toxici-ties in the patient, for example, for etoposide and fluorouracil.5 Another dose individualization strategy involves administration of a low test dose of the compound to determine the exact pharmacokinetic parameters for an individual patient, followed by modifying the dose to achieve a target drug exposure. In other cases, clinical oncologists frequently use the BSA for drug dose scaling between individuals. Other physiological scaling parameters, such as age, gender, weight, and body mass index, are also used in specific circumstances.

### Dose adjustment based on creatinine clearance

Renal function is often determined in terms of a patient’s Cr Cl. Creatinine is a cyclic derivative of the nitrogenous organic acid, creatine (Figure 5.3), found in the muscle. Creatinine is eliminated by filtration through the kid-neys and is not reabsorbed. Therefore, the correlation of its blood and urine levels is an indication of the rate of filtration of blood plasma through the kidney (glomerular filtration rate [GFR]), which indicates renal function. Glomerular filtration rate can be calculated using the concentration of a chemical, such as inulin, that is freely filtered through the kidney but not secreted or reabsorbed.

GFR = (Urine concentration × Urine flow ) /Plasma concentration

The use of creatinine is preferred over inulin, since extraneous administra-tion is not required for creatinine. However, a small amount of creatinine is also secreted by peritubular capillaries, which can contribute to some error (overestimation) in the calculation of Cr Cl. However, this error becomes significant only in the cases of severe renal dysfunction.

Creatinine clearance is estimated by determining blood creatinine con-centration (which is relatively steady) and the amount of creatinine secreted in urine collected over a period of 24 h. For example, if 2 mg/mL of creati-nine is detected in 1 L of urine collected over a period of 24 h and the blood creatinine concentration is 0.01 mg/mL, then:

This is indicative of the rate of filtration of plasma volume through the kidneys per unit time. Creatinine clearance is often also corrected for the BSA to normalize dose calculation. Assuming 1.73 m2 as the average-sized man’s BSA, Cr Cl is expressed as:

Cr Cl (corrected) = Cr Cl × (1.73/BSA) mL/min/1.73m2

Creatinine clearance estimation requires and assumes complete urine col-lection over a 24 h period. To avoid this assumption for outpatients, creati-nine clearance can be estimated on the basis of serum creatinine level alone. For example, Cockcroft–Gault formula estimates creatinine clearance as:

Cr Cl = { (140 age) × weight(kg)×[0.85,if female] } / {72 × serum creatinine level(mg/dL)}

The normal range of GFR is 100–130 mL/min/1.73 m2. It varies with age, race, and kidney function. Glomerular filtration rate correlates with different stages of chronic kidney disease (CKD) as follows:

Stage 1 CKD—GFR greater than 90 mL/min/1.73 m2: normal

Stage 2 CKD—GFR 60–89 mL/min/1.73 m2: mild

Stage 3 CKD—GFR 30–59 mL/min/1.73 m2: moderate

Stage 4 CKD—GFR 15–29 mL/min/1.73 m2: severe

Stage 5 CKD—GFR less than 15 mL/min/1.73 m2: kidney failure

Dose adjustment based on Cr Cl are provided for most drugs by the manu-facturers based on the results of clinical trials. These are mainly based on the percentage of drug eliminated by the kidneys. For highly toxic compounds, Cr Cl is utilized for the calculation of pharmacokinetic parameter, such as the elimination rate constant, which is then used with the drug’s pharmacokinetic model for dose calculation.

The dosage regimen for a renal-compromised patient is usually adjusted by either reducing the dose or prolonging the dosing interval. Reduction in dose is recommended for cases where relatively constant blood level is desired, for example, β-lactam antibiotics. For drugs whose efficacy may be related to their peak level, for example, fluoroquinolone antibiotics, prolongation of the dosing interval is recommended.

Related Topics