Three primary methods for calculation of medication dosages exist; Dimensional Analysis, Ratio Proportion, and Formula or Desired Over Have Method. We are going to explore the Ratio-Proportion Method, one of these three methods, in more detail.
Ratio-Proportion Method allows us the ability to compare numbers, units of measurement, or values.
Clinicians must define a ratio and proportion. Ratios often expressed in fraction format, are mathematical works of art, designed in relationship patterns which explore comparisons between like units, words, numbers. As in any relationship, key players forge a bond to make the association stronger or manageable. Proportions are those key players, formed by equality of ratios. A complicated relationship simplified by utilization and strategic placement of key players of like units or volumes. Ratios and proportions expressed as fractions, canceled out by cross multiplication or division, provide for ease in problem-solving using this method of drug calculation.
Numerators (top) numbers or denominators (bottom) numbers multiplied and divided after same units are canceled out. Some equations or formulas get expressed with a colon (:) or backslash (/) to indicate division and its subsequent deployment in this problem-solving technique.
For ease of calculation, a person should place the numerator of the fraction to the left of the colon or slash. In completion of this relationship, the denominator gets put on the right of the slash or colon. Unknown amounts, unknown quantities or unknown desired amounts are depicted as an (x) in the equation and solved. The symbol (x) placement is to the left of the equation, making cross multiplication and division for (x) a simple undertaking. Keeping in mind the fundamental principle regarding the same units of measurement; numbers or units on the top and bottom of a fraction possess the ability to cancel each other out.
It is common for healthcare workers to use a calculator to calculate drug dosages. Calculators may be useful to decrease medication errors related to a calculation issue but are not helpful in recognition of a conceptual error (Savage, 2015).
One study by Boyle and Eastwood found there were (40%) conceptual errors, (60%) arithmetical errors, and (25%) computational errors amongst study participants in a paper-based drug calculation questionnaire of twenty paramedics where no calculator was allowed (Boyle & Eastwood, 2018).
This study highlighted the need for ongoing education modules to improve basic arithmetic skills, for example, proper use of formulas, ability to construct a mathematical equation, and ability to perform long division without the use of a calculator. Calculators are not always available in a prehospital environment, and cell phone coverage with the use of apps may be spotty at best. The study concluded that a basic knowledge of performing manual drug calculations be a part of training modules by educators (Boyle & Eastwood, 2018).
Using 1 of the 3 methods of drug calculation as discussed above will ease the performance of manual drug calculations; Ratio and Proportion, Desired Over Have or Formula, and Dimensional Analysis. Whichever method is employed by the healthcare provider, a second method may be of use as a check for the first method. A second check further decreases the chance of a medication error related to an incorrect dosage calculation.
Ratio and Proportion Method
The Ratio and Proportion Method has been around for years and is one of the oldest methods utilized in drug calculations. Addition principals is a problem-solving technique that has no bearing on this relationship, only multiplication, and division is used to navigate our way through a ratio and proportion problem, not adding. An example listed below will help us provide a better explanation using a fraction or a colon format:
A provider orders lorazepam 4 mg intravenous (IV) push for a CIWA score of 25. On hand, the clinicians has 2 mg/mL vials. How many milliliters are required to carry out the ordered dose?
In colon format, you would use H:V::D:X and multiply means DV and Extremes HX.
Desired Over Have or Formula Method
Desired over Have or Formula Method uses a formula or equation to solve for an unknown quantity (x) much like ratio proportion. Drug calculations require the use of conversion factors, such as when converting from pounds to kilograms or liters to milliliters. Simplistic in design, this method affords us the opportunity to work with various units of measurement, converting factors to find our answer (as cited in Boyer, 2002) [Lindow, 2004]. Useful in checking the accuracy of the other methods of calculation as above mentioned, thus acting as a double or triple check.
For example, a provider requests lorazepam 4 mg IV Push for a patient in severe alcohol withdrawal. On hand, the clinician has 2 mg/mL vials. How many milliliters should they draw up in a syringe to deliver the desired dose?
Remember, units of measurement must match such as milliliters and milliliters, or you will need to convert to like units of measurement. In the example, above, the ordered dose was in mg, and the have dose was in mg, both would cancel out leaving milliliters (answer called for milliliters), so no further conversion required.
Dimensional Analysis Method
An order placed by a provider for lorazepam 4 mg IV PUSH for CIWA score of 25 or higher, follow CAGE Protocol for subsequent dosages based on CIWA scoring.
Zeros can be canceled out in the same way as like units. Look at the example listed below for clarification:
Having addressed zeros, the following is a look at 1.
Medication errors can be detrimental and costly to patients (Chen, Hsiao, Shen & Wu, 2017). Drug calculation and basic mathematical skills play a role in the safe administration of medications. Pediatric populations are especially vulnerable to medication errors due to the need to calculate dosages incorporating many factors; height, weight, body surface area, and growth and development level (Ozyazicioglu et al., 2018). The higher the complexity of the math, the increased risk potential for dose calculation errors.
According to a study of intensive care nurses (ICU) in 2016, 80% of nurses considered knowledge on drug dosage calculation essential to decrease medication errors during the preparation of intravenous drugs (Di Muzio, Tartaglini, De Vito & La Torre, 2016).
High-risk medications such as heparin and insulin often require a second check on dosage amounts by more than one provider before administration of the drug. Follow institutional policies and recommendations on the double-checking of dose calculations by another licensed provider.
One study by a group of oncology nurses in 3 Swiss hospitals published in 2018, discusses the process of double-checking and its limitations in the current healthcare environment, specifically, increased nurse workload and time constraints, distracting environments, and lack of resources. The study concluded that oncology nurses strongly believed in the effectiveness of double checking medication despite reporting limitations of the procedure in clinical practice (Schwappach, Taxis & Pfeiffer, 2018).
Effect of Education of Principles of Drug Prescription and Calculation through Lecture and Designed Multimedia Software on Nursing Students' Learning Outcomes., Valizadeh S,Feizalahzadeh H,Avari M,Virani F,, Electronic physician, 2016 Jul 25 [PubMed PMID: 27648199] | |
Maths anxiety and medication dosage calculation errors: A scoping review., Williams B,Davis S,, Nurse education in practice, 2016 Sep [PubMed PMID: 27589091] | |
Factors associated with nursing students' medication competence at the beginning and end of their education., Sulosaari V,Huupponen R,Hupli M,Puukka P,Torniainen K,Leino-Kilpi H,, BMC medical education, 2015 Dec 18 [PubMed PMID: 26683623] | |
Evaluation of students' knowledge about paediatric dosage calculations., Özyazıcıoğlu N,Aydın Aİ,Sürenler S,Çinar HG,Yılmaz D,Arkan B,Tunç GÇ,, Nurse education in practice, 2018 Jan [PubMed PMID: 28942096] | |
Developing nurse medication safety training in a health partnership in Mozambique using behavioural science., Bull ER,Mason C,Junior FD,Santos LV,Scott A,Ademokun D,Simião Z,Oliver WM,Joaquim FF,Cavanagh SM,, Globalization and health, 2017 Jul 4 [PubMed PMID: 28676121] | |
Use of digital applications in the medicament calculation education for nursing., Fernandes Pereira FG,Afio Caetano J,Marques Frota N,Gomes da Silva M,, Investigacion y educacion en enfermeria, 2016 Jun [PubMed PMID: 28569933] | |
Validation of a questionnaire for ICU nurses to assess knowledge, attitudes and behaviours towards medication errors., Di Muzio M,Tartaglini D,De Vito C,La Torre G,, Annali di igiene : medicina preventiva e di comunita, 2016 Mar-Apr [PubMed PMID: 27071322] | |
Educational audit on drug dose calculation learning in a Tanzanian school of nursing., Savage AR,, African health sciences, 2015 Jun [PubMed PMID: 26124816] | |
Investigating the Causes of Medication Errors and Strategies to Prevention of Them from Nurses and Nursing Student Viewpoint., Gorgich EA,Barfroshan S,Ghoreishi G,Yaghoobi M,, Global journal of health science, 2016 Aug 1 [PubMed PMID: 27045413] | |
An evaluation of the drug calculation skills of registered nurses., Fleming S,Brady AM,Malone AM,, Nurse education in practice, 2014 Jan [PubMed PMID: 23831386] | |
What is the easier and more reliable dose calculation for iv phenytoin in children at risk of developing convulsive status epilepticus, 18 mg/kg or 20 mg/kg?, Prasad M,Shenton P,Dietz S,Saroha V,Whitehouse WP,, BMC pediatrics, 2013 Apr 21 [PubMed PMID: 23601207] | |
Undergraduate paramedic students cannot do drug calculations., Eastwood K,Boyle MJ,Williams B,, World journal of emergency medicine, 2012 [PubMed PMID: 25215067] | |
Drug calculation ability of qualified paramedics: A pilot study., Boyle MJ,Eastwood K,, World journal of emergency medicine, 2018 [PubMed PMID: 29290894] | |
Improvement of drug dose calculations by classroom teaching or e-learning: a randomised controlled trial in nurses., Simonsen BO,Daehlin GK,Johansson I,Farup PG,, BMJ open, 2014 Oct 24 [PubMed PMID: 25344483] | |
The cost-saving effect and prevention of medication errors by clinical pharmacist intervention in a nephrology unit., Chen CC,Hsiao FY,Shen LJ,Wu CC,, Medicine, 2017 Aug [PubMed PMID: 28834903] | |
Medication calculation and administration workshop and hurdle assessment increases student awareness towards the importance of safe practices to decrease medication errors in the future., Wallace D,Woolley T,Martin D,Rasalam R,Bellei M,, Education for health (Abingdon, England), 2016 Sep-Dec [PubMed PMID: 28406100] | |
Educational audit on drug dose calculation learning in a Tanzanian school of nursing., Savage AR,, African health sciences, 2015 Jun [PubMed PMID: 26124816] | |
Investigating the Causes of Medication Errors and Strategies to Prevention of Them from Nurses and Nursing Student Viewpoint., Gorgich EA,Barfroshan S,Ghoreishi G,Yaghoobi M,, Global journal of health science, 2016 Aug 1 [PubMed PMID: 27045413] | |
Mapping drug calculation skills in an undergraduate nursing curriculum., Elliott M,Joyce J,, Nurse education in practice, 2005 Jul [PubMed PMID: 19038203] | |
Dose Calculation, Gage CB,Toney-Butler TJ,,, 2018 Jan [PubMed PMID: 28613586] | |
Dose Calculation (Dimensional Analysis, Factor-Label Method), Toney-Butler TJ,Hughes J,,, 2018 Jan [PubMed PMID: 28613475] | |
Students who developed logical reasoning skills reported improved confidence in drug dose calculation: Feedback from remedial maths classes., Shelton C,, Nurse education today, 2016 Jun [PubMed PMID: 27138475] | |
Oncology nurses' beliefs and attitudes towards the double-check of chemotherapy medications: a cross-sectional survey study., Schwappach DLB,Taxis K,Pfeiffer Y,, BMC health services research, 2018 Feb 17 [PubMed PMID: 29454347] |