Error Assessment of Drug Dose in Pharmaceutical Mixtures

Abstract

This chapter describes a unique method to calculate the maximum potential error associated with drug dose in pharmaceutical mixtures and unit dosage forms, composed of an infinite number of ingredients that are measured on multiple balances of variable sensitivities, and thus provides instant guidance on the pharmaceutical ingredient preparation. The method also determines the sensitivity of the instruments measuring each of the components and the least allowable weight (LAW) of the drug within the predetermined assay standard. A great variety of solved examples with capsules, creams, and ointments as the finished products are used to demonstrate a step-by-step application of the method. The method was written in such a way to help you better understand the principles of balance operation, comprehend the relationship of the sensitivity requirement (SR) of a balance and the maximum allowable error in the dose, appreciate that sequential measurements carry a complicated error propagation on the result, and sharpen up your critical thinking by having to consider all possible consequences of any action involved in prescription preparation prior to actually performing relevant calculations. What follows is the description of the aliquot method of weighing based on the LAW as a method that allows weighing a drug quantity smaller than the sensitivity of the balance. Although the concept of the aliquot method of weighing based on the least allowable weight has been around for more than 50 years, this is really the first time that the theory of the method is developed and applied correctly. The method as described elsewhere ignores errors associated with multiple weighing of drug-excipient mixtures, and as a result, the dose error in the final product is underestimated. The topics are advanced but extremely important.

Exercises

• 2.1. Calculate the % maximum probable error in drug concentration x in the following clinical batch manufactured in a GMP-certified laboratory that should produce 12 unit doses, each weighing 300 mg. Drug x and excipients y, w, and z were measured on pharmaceutical scales of sensitivity 1 mg, 0.05 g, 60 mg, and 4 mg, respectively, that is, dx = 1 mg, dy = 50 mg, dw = 60 mg, and dz = 4 mg. The 12 capsules were measured on a balance of sensitivity dm = 1 mg.

  Drug x	2 mg
  Excipient, y	90 mg
  Excipient, w	200 mg
  Excipient, z	8 mg

  Mix and make one capsule. Dispense a total of 12 capsules.

  • (Answer: 7.64%)

• 2.2. Calculate the least allowable weight (LAW) of drug x in Exercise 2.1 that can be weighed on the specified electronic balances, with a maximum permissible error (MAE) of 2%.

  • (Answer: x = 105 mg, y = 4724.6 mg, w = 10,499 mg, z = 420 mg)

• 2.3. Determine the sensitivity of the balance that drug x needs to be weighed on if the MAE of drug x concentration in the mixture of Exercise 2.1 is 4%. The SR of the other balances are as described in that exercise.

  • (Answer: 121.6 μg)

• 2.4. Determine the sensitivity of the balance that drug x needs to be weighed on if the MAE of drug x concentration in the mixture of Exercise 2.1 is 2%. The SR of the other balances are as described in that exercise.

  • (Answer: The formulation cannot be prepared within a MAE of 2%)

• 2.5. A GMP-certified lab prepared the prescription shown in Example 2.7 with a 5% maximum allowable error. Drug was measured on a balance with an SR = 0.1 mg, lactose was measured on a balance of SR equal to 0.1 g, and the dosage form was measured on a balance with an SR equal to 6 mg.

  • (a) Calculate the % maximum possible error associated with Prednisone concentration in the compounded prescription.

  • (b) Calculate the minimum allowable drug quantity that conforms to the maximum allowable error.

  • (c) Determine the sensitivity of the balance that drug x needs to be weighed on to achieve an MAE in drug x concentration of 5%.

  • (d) Determine the sensitivity of the balance that lactose needs to be weighed on to achieve an MAE in drug x concentration of 5%.

    • (Answer: (a) 3.2%; (b) 25.23 mg; (c) 0.0537 mg; (d) 93.1 mg)

• 2.6. Fill the prescription of Example 2.6 with 8% maximum potential error. What is the LAW, the aliquot amount, the stock mixture, and the lactose mass?

  • (Answer: 150 mg, 150 mg, 937.5 mg, 787.5 mg)

• 2.7. Explain how you should weigh 32 mg of a drug with an error equal to 5%, using starch as the diluent, on a balance that has a sensitivity equal to 8 mg. The ratio of drug to starch in the prescription is 1/75.

  • (Answer: Aliquot, A = 2432 mg; Q = 171.27 mg, S = 13016.3 mg, starch = 12,845 mg)

• 2.8. You filled a prescription that called for 30 capsules of drug D using a balance of sensitivity equal to 9 mg. You weighed an aliquot quantity that was equal to the total powder mixture needed to fill the 30 capsules. The error associated with the drug q is 5%. The total weight of the stock powder made from drug and lactose was 41.539 g. After the capsules were filled using a capsule filler machine, it was found that the maximum error in the dose is 8%.

  • (a) What is the weight of each capsule?

  • (b) What is the aliquot amount?

  • (c) How much drug is needed to fill the prescription?

  • (d) Calculate the drug quantity per capsule.

    • Answer: (a) 300 mg; (b) 9 g; (c) LAW (Q) = 180 mg; (d) 1.3 mg)

• 2.9. ℞

  Drug D
  Lactose	q.s. ad	0.350
  M. et ft. caps no i, d.t.d caps no XL
  Sig. Caps i b.i.d. p.c. and h.s.

  The prescription above was prepared using the aliquot method of weighing with a 6% maximum potential error. The total weight of the stock powder was 44.3 g, and all ingredients were weighed on a class III prescription balance that had an SR equal to 7 mg.

  • (a) Calculate the total powder mixture needed to fill 40 capsules.

  • (b) How much drug is needed to fill the prescription?

  • (c) Calculate total lactose used to fill the prescription.

  • (d) What is the daily dose?

    • (Answer: (a) 14 g; (b) 175 mg; (c) 44.125 g; (d) 4.15 mg)

• 2.10. Pindolol could be used to treat hypertensive patients that also suffer from heart failure because it is a beta-blocker with intrinsic sympathomimetic activity (partial agonist), and as such, it lowers the blood pressure without decreasing cardiac output. Given the following prescription:

℞
Pindolol		0.005
Lactose	ad	0.150
M. et ft. caps no i, d.t.d caps no XX
Sig. i cap b.i.d., 10 days

• (a) Describe how you would fill the prescription above with a maximum potential error of 10% using a balance that has sensitivity requirement equal to 5 mg.

• (b) What is the daily dose?

• (c) What is the maximum potential error in the daily dose?

  • (Answer: (a) aliquot preparation is not needed; (b) pindolol 10 mg; (c) 8.33%)

• 2.11. Therapeutic doses of clonidine for cases of hypertension are usually between 0.2 and 1.2 mg daily. Explain how you could fill the prescription below, with a 3% error using a balance that has sensitivity requirement equal to 6 mg.

℞
Clonidine		0.001
Lactose	ad	0.150
M. et ft. caps no i, d.t.d caps no XVI
Sig. i cap b.i.d., 8 days

• (Answer: Prescription cannot be filled within the allowable error. A more sensitive balance is needed to fill the prescription)

• 2.12. The suppository form prescribed below is known to provide a longer duration of pain relief as compared to the corresponding oral administration of capsules mainly due to a better absorption of the drug and a less extensive metabolism (absence of a first pass effect). Describe how you would fill the prescription with a 5% error in the dose if the sensitivity requirement of the balance is 3 mg.

℞
Hydromorphone HCl		0.15% w/w
Cocoa butter	q.s. ad	2 g
M. et ft. supp. No. i, d.t.d. supp. # XII
Sig: Insert 1 suppository rectally every 12 h

• (Answer: LAW = 61.86 mg)

2.1.1 Additional Exercises

• 2.13. Prepare the prescription below using an electronic balance that has an SR of 0.1 mg, with a maximum potential error in the dose of 1%.

℞
Drug D	4 μg/mL
Infuse 1 L in D5W

• 2.14. Combination of thiazide and potassium-sparing diuretics is usually indicated to patients with hypertension or congestive heart failure who develop hypokalemia when thiazides or other kaliuretics are used alone. Explain how you should fill the prescription below, using the aliquot method of weighing on a prescription balance that has a SR = 4 mg with a 4.5% max allowable error in the dose.

℞
Amiloride		5 mg
HCTZ		50 mg
Lactose	q.s. ad	200 mg
M. et. Ft caps # i, d.t.d caps no 14
Sig: i caps daily

• (Answer: Amiloride LAW = 164 mg)

• 2.15. The formula below contains a decongestant, antihistaminic, and an opioid analgesic. It is commonly used to treat cough and to relieve congestion due to common cold or flu.

℞
Phenylephrine		5 mg/tsp
Chlorpheniramine		2 mg/tsp
Hydrocodone bitartrate		2.5 mg/5 mL
Sucrose		60 g
Purified water	ad	120 mL
Sig: i tsp. b.i.d and h.s.

• (a) Describe how you would fill the prescription with a 5% maximum potential error in the dose, if the sensitivity requirement of the balance is 6 mg?

• (b) How much sucrose did the pharmacist use all together?

• (c) How long is the medication going to last?

  • (Answer: (a) LAW for chlorpheniramine and hydrocodone bitartrate = 240 mg; (b) 60 g; (c) 8 days)

• 2.16. You prepare the prescription shown below for a diabetic patient who has a cough and suffer from nasal congestion, symptoms of a common cold.

℞
Phenylephrine		5 mg/tsp
Chlorpheniramine		2 mg/tsp
Hydrocodone bitartrate		2.5 mg/5 mL
Purified water	ad	120 mL
Sig: i tsp. b.i.d and h.s.

• (a) Describe how you would fill the prescription below with ≤5% error in the dose, if the sensitivity requirement of the balance was 6 mg.

• (b) What is the error in the dose?

  • (Answer: (a) Use a liquid aliquot for the chlorpheniramine and hydrocodone; (b) 5%)

• 2.17. The combination medicine below is used to relieve moderate to severe pain. Describe how you would fill the prescription with a 2% error in the dose if the sensitivity requirement of the balance was 5 mg. Is this method cost-effective?

Hydrocodone bitartrate	2.5 mg
Acetaminophen	500 mg
M. et ft. caps# i, d.t.d caps no 40
Sig: i caps q.6 h. for the pain

• (Answer: LAW = 497.5 mg, aliquot = 20,100 mg, total acetaminophen = 99,502.5 mg)

• 2.18.

  • (a) Fill the prescription below with a 3% maximum potential error in the dose using a balance that has a sensitivity requirement of 6 mg.

℞
Oxycodone HCl	0.105
Acetaminophen	9.75
M. et div. Caps# 30
Sig: i caps q.8 h. for the pain

• (b) What is the oxycodone daily dose?

• (c) How long is the medication going to last?

  • (Answer: (a) LAW = 511.28 mg of oxycodone HCl; (b) 10.5 mg; (c) 10 days)

• 2.19. You planned an experiment on animals to investigate whether there is a synergistic action of anti-inflammatory drugs against osteoarthritis. You have to prepare the formulation given below, mix each dose with food and then feed the five arthritic rats (average weight = 350 g) that participate in the study.

  Etoricoxib		286 μg/kg
  Indomethacin		0.25 mg
  Starch	q.s. ad.	0.250 g
  M. et ft. powders # i, d.t.d powders # 25

  Assuming that the sensitivity of the analytical balance available in the laboratory is 0.1 mg, answer the following if the maximum allowable error in the dose is 1%.

  • (a) Calculate the LAW in order to prepare the powders within the given maximum allowable error.

  • (b) How much starch is needed to prepare the formula?

  • (c) What is the % error associated with the measurement of indomethacin before and after scaling-up the formula?

    • (Answer: (a) 10.42 mg; (b) 26.015 g; (c) 1.6% and 0.4%)

• 2.20. Having reviewed your plan, your advisor suggested that you should include “control” experiments to provide a basis for comparison. Since the goal of the original plan was to investigate possible synergistic anti-inflammatory action (the total effect should be greater than the sum of the individual effects), the control experiments have to include each drug alone at twice as much dose compared to that in Exercise 2.7. The weight and number of the animals included in each study, the SR of the balance and percentage error are as stated in Exercise 2.7.

  Formulation #2:

  Etoricoxib		572 μg/kg
  Starch	q.s. ad.	0.250 g
  M. et ft. powders # i, d.t.d powders # 25

  Formulation #3:

Indomethacin		0.50 mg
Starch	q.s. ad.	0.250 g
M. et ft. powders # i, d.t.d powders # 25

• (a) What is LAW for formulation #2?

• (b) Calculate the starch needed to prepare formulation #2.

• (c) What is % error associated with indomethacin powders in formulation #3?

  • (Answer: (a) 10.42 mg; (b) 13,002 mg; (c) 0.84%)