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7
Calculation of Doses: General
Considerations
OBJECTIVES
Upon successful completion of this chapter, the student will be able to:
Perform general dose calculations.
Perform calculations relevant to specific dosing regimens.
Apply dosing terminology correctly in performing pharmaceutical
calculations.
Dose Definitions
The dose of a drug is the quantitative amount administered or taken by a
patient for the intended medicinal effect. The dose may be expressed as a
single dose, the amount taken at one time; a daily dose; or a total dose,
the amount taken during the course of therapy. A daily dose may be
subdivided and taken in divided doses, two or more times per day
depending on the characteristics of the drug and the illness. The schedule
of dosing (e.g., four times per day for 10 days) is referred to as the
dosage regimen.
Quantitatively, drug doses vary greatly among drug substances; some
drugs have small doses, whereas other drugs have relatively large doses.
The dose of a drug is based on its biochemical and pharmacologic
activity, its physical and chemical properties, the dosage form used, the
route of administration, and various patient factors. The dose of a drug
for a particular patient may be determined in part on the basis of the
patient’s age, weight, body surface area, general physical health, liver and
kidney function (for drug metabolism and elimination), and the severity
of the illness being treated. Considerations of some specific patient
parameters in dosing are presented in Chapter 8, and an introduction to
pharmacokinetic dosing is presented in Chapter 22. Pharmacokinetic
dosing takes into account a patient’s ability to metabolize and eliminate
drugs from the body due to impaired liver or renal function, which often
necessitates a reduction in dosage.
The usual adult dose of a drug is the amount that ordinarily produces
the medicinal effect intended in the adult patient. The usual pediatric
dose is similarly defined for the infant or child patient. The “usual” adult
and pediatric doses of a drug serve as a guide to physicians who may
select to prescribe that dose initially or vary it depending on the assessed
requirements of the particular patient. The usual dosage range for a drug
indicates the quantitative range or amounts of the drug that may be
prescribed within the guidelines of usual medical practice. Drug use and
dose information is provided in the package inserts that accompany
manufacturers’ pharmaceutical products, from online resources, and
through a variety of references such as Drug Facts and Comparisons1;
Prescribers’ Digital Reference2; Pediatric Dosage Handbook: Including
Neonatal Dosing, Drug Administration, & Extemporaneous
Preparations3; Drug Information Handbook4; and the Food and Drug
Administration website.
5
The dose response of individuals varies as depicted in Figure 7.1 and
may require dosage adjustment in a given patient. For certain conditions,
as in the treatment of cancer patients, drug dosing is highly specialized
and individualized. Frequently, combinations of drugs are used, with the
doses of each adjusted according to the patient’s response. Many
anticancer drugs are administered cyclically, usually for 21 to 28 days,
with a rest period between dosing cycles to allow recovery from the toxic
effects of the drugs. As presented in Chapter 8, anticancer drugs are most
commonly dosed on the basis of the patient’s body surface area.
FIGURE 7.1 Drug effect in a population sample.
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The median effective dose of a drug is the amount that produces the
desired intensity of effect in 50% of the individuals tested. The median
toxic dose of a drug is the amount that produces toxic effects in 50% of
the individuals tested. Drugs intended to produce systemic effects must
be absorbed or placed directly into the circulation and distributed in
adequate concentrations to the body’s cellular sites of action. For certain
drugs, a correlation exists between drug dosage, the drug’s blood serum
concentration after administration, and the presentation and degree of
drug effects. An average blood serum concentration of a drug can be
measured, and the minimum concentration determined that can be
expected to produce the drug’s desired effects in a patient. This
concentration is referred to as the minimum effective concentration
(MEC). The base level of blood serum concentration that produces doserelated toxic effects is referred to as the minimum toxic concentration
(MTC) of the drug.
Optimally, appropriate drug dosage should result in blood serum drug
concentrations that are above the MEC and below the MTC for the period
of time that drug effects are desired. As shown in Figure 7.2 for a
hypothetical drug, the serum concentration of the drug reaches the MEC
2 hours after its administration, achieves a peak concentration in 4 hours,
and falls below the MEC in 10 hours. If it were desired to maintain the
drug serum concentration above the MEC for a longer period, a second
dose would be required at about an 8-hour time frame. In some cases,
incremental dose escalation is employed whereby the patient is started
on a known low dose of a drug followed by additional doses until the
desired effect is achieved.
FIGURE 7.2 Example of a blood level curve for a hypothetical
drug as a function of the time after oral administration. (MEC,
minimum effective concentration; MTC, minimum toxic
concentration.)
The frequency or scheduling of dosing is dependent on many factors,
including whether the illness or condition is responsive to short-term or
long-term treatment; the physical–chemical and biologic characteristics
of the drug substance itself; and features of the product formulation and
route of drug administration.
For certain drugs, a larger-than-usual initial dose may be required to
achieve the desired blood drug level. This dose is referred to as the
loading dose. Subsequent maintenance doses, similar in amount to usual
doses, are then administered according to the dosage regimen to sustain
the desired drug blood levels or drug effects. To achieve the desired drug
blood level rapidly, the loading dose may be administered as an injection
or oral liquid, whereas the subsequent maintenance doses may be
administered in other forms, such as tablets or capsules.
As discussed later in this chapter, there are certain instances in which
low-dose therapy or high-dose therapy is prescribed for a particular
patient. Also, for certain drugs, different doses may be required
depending on whether the use is for monotherapy, that is, as the primary
drug treatment, or adjunctive therapy, that is, additional to or supportive
of a different primary treatment.
Certain biologic or immunologic products, such as vaccines, may be
administered in prophylactic doses to protect the patient from contracting
a specific disease. Other products, such as antitoxins, may be
administered in therapeutic doses to counter a disease after exposure or
contraction. The doses of some biologic products, such as insulin, are
expressed in units of activity, derived from biologic assay methods.
Calculations pertaining to these types of products are presented in
Chapter 9.
Prefabricated products prepared on a large scale within the
pharmaceutical industry and dispensed in community and institutional
pharmacies generally contain the dosage strengths and dosage forms most
often used. However, in instances in which the desired strength or dosage
form is not available, pharmacists may be called upon to compound the
preparation. Pharmaceutical products may be prepared to contain one or
more therapeutic agents. Products containing more than one therapeutic
agent are termed combination products.
One of the primary responsibilities of the pharmacist is to check
doses specified in prescriptions based on knowledge of the usual doses,
usual dose ranges, and dosage regimens of the medicines prescribed. If
an unusual dose is noted, the pharmacist is ethically bound to consult the
physician to make certain that the dose as written or interpreted is the
dose intended and that it is suitable for the patient and condition being
treated.
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Routes of Drug/Dose Administration and
Dosage Forms
Doses of drugs are administered by a variety of dosage forms and routes
of administration, as shown in Table 7.1. In addition to the drug itself,
dosage forms contain pharmaceutical ingredients, which provide the
physical features, stability requirements, and aesthetic characteristics
desired for optimal therapeutic effects. Pharmaceutical ingredients may
be listed on the product labeling as “inactive ingredients” and are also
termed “excipients” in some references. Included in the array of
pharmaceutical ingredients are solvents, vehicles, preservatives,
stabilizers, solubilizers, binders, fillers, disintegrants, flavorants,
colorants, and others.
TABLE 7.1 SELECTED ROUTES OF ADMINISTRATION
AND REPRESENTATIVE DOSAGE FORMS
With added pharmaceutical ingredients, the quantity of an active
ingredient in a dosage form represents only a portion (often a small
portion) of the total weight or volume of a product. For example, a tablet
with 10 mg of drug could weigh many times that amount because of the
added pharmaceutical ingredients.
Definitions of the various dosage forms and drug delivery systems are
found in Appendix B.
Dose Measurement
In the institutional setting, doses are measured and administered by
professional and paraprofessional personnel. A variety of measuring
devices may be used, including calibrated cups and oral syringes for
liquid oral medications (Figs. 7.3 and 7.4). For pediatric patients, use of
oral syringes is recommended as a means of reducing medication dosing
errors.6 In hospitals, many medications are administered by injection and
by intravenous infusion.
FIGURE 7.3 An example of a calibrated medication cup for
administering oral liquid medication.
FIGURE 7.4 An example of a calibrated Exacta-Med Oral
Dispenser for administering liquid medication to pediatric
patients. (Courtesy of Baxter Healthcare Corporation.)
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In the home setting, the patient, the caregiver, or, in the case of a child,
the parent generally measures and administers oral medication. Liquids
are measured using household measures such as teaspoons and
tablespoons (Table 7.2), calibrated spoons or cups, oral syringes, or
drops. Patients being treated by home health care personnel may receive
medications by all routes of administration, including parenteral.
TABLE 7.2 USEFUL APPROXIMATE EQUIVALENT OF
HOUSEHOLD MEASURE
Teaspoon and Tablespoon
Household spoons vary greatly in capacities. Due to the variability in
capacity, the Food and Drug Administration has issued the following
statement: “Do not use common household spoons to measure medicines
for children since household spoons come in different sizes and are not
meant for measuring medicines.”7 Instead, the FDA urges the use of the
measuring device that accompanies a specific product or another device
that is calibrated to deliver the recommended dose. A calibrated oral
syringe often is a good option.
The National Institute of Standards and Technology defines a
teaspoonful as one-sixth of a fluidounce (4.93 mL) and a tablespoonful as
one-half of a fluidounce (14.79 mL).8 However, for practical purposes
and in dosage calculations, the teaspoon is considered to hold 5 mL of
volume and the tablespoon 15 mL (Table 7.2).9 Occasionally, a prescriber
will indicate a teaspoonful dose by using the fluidram symbol (flʒ, fʒ, or
ʒ
) in the Signa portion of a prescription, and the pharmacist interprets it
accordingly.
a
a
The fluidram (f?) is a quantity in the apothecaries’ system as presented in Appendix A.
The Drop as a Unit of Measure
The drop (abbreviated gtt) is used as a dose measurement for certain
dosage forms such as liquids administered by the ophthalmic or otic
route. A drop does not represent a definite volume, because drops of
different liquids issued from different droppers vary greatly due to
variations in flow characteristics. A dropper may be calibrated by
counting the drops of a liquid as they fall into a graduate until a
measurable volume is obtained. The number of drops per unit volume is
then established (e.g., 20 drops/mL). Most manufacturers include a
specially calibrated dropper along with their prepackaged medications for
use by patients in measuring dosage. Examples of calibrated droppers are
shown in Figure 7.5. Droppers used in administering pharmaceutical
products deliver approximately 25 to 50 microliters per drop.
10
FIGURE 7.5 Examples of calibrated droppers used in the
administration of pediatric medications.
If a pharmacist counted 40 drops of a medication in filling a graduate
cylinder to the 2.5-mL mark, how many drops per milliliter did the
dropper deliver?
CASE IN POINT 7.1
A physician asks a pharmacist to calculate the dose of a cough syrup
so that it may be safely administered dropwise to a child. The cough
syrup contains the active ingredient dextromethorphan HBr, 30 mg/15
mL, in a 120-mL bottle.
Based on the child’s weight and literature references, the
pharmacist determines the dose of dextromethorphan HBr to be 1.5 mg
for the child.
The medicine dropper to be dispensed with the medication is
calibrated by the pharmacist and shown to deliver 20 drops of the
cough syrup per 1 mL.
Calculate the dose, in drops, for the child.
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General Dose Calculations
A pharmacist often needs to calculate the size of a dose, the number of
doses, or the total quantity of medication to dispense. For these
calculations, the following equation is useful with the terms rearranged
depending on the answer required. In using the equation, the units of
weight or volume must be the same for the total quantity and size of the
dose.
Example Calculations of the Number of Doses
1. If the dose of a drug is 200 mg, how many doses are contained in 10
g?
Or, solving by dimensional analysis:
2. If 1 tablespoonful is prescribed as the dose, approximately how many
doses will be contained in 1 pint of the medicine?
3. If the dose of a drug is 50 μg, how many doses are contained in 0.02
g?
Example Calculations of the Size of a Dose
The size of the dose is expressed in whatever denomination is chosen for
measuring the given total quantity.
1. How many teaspoonfuls would be prescribed in each dose of an elixir
if 180 mL contained 18 doses?
2. How many drops would be prescribed in each dose of a liquid
medicine if 15 mL contained 60 doses? The dispensing dropper
calibrates 32 drops/mL.
Or, solving by dimensional analysis:
Example Calculations of the Total Quantity of
Product
It is convenient first to convert the given dose to the denomination in
which the total quantity is to be expressed.
1. How many milliliters of a liquid medicine would provide a patient
with 2 tablespoonfuls twice a day for 8 days?
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