It's Just Math—Unless It's Toxic!

Abstract

Objective

The objective was to determine emergency medicine residents’ ability to perform pharmaceutical calculations.

Methods

A six‐question needs‐assessment survey of emergency medicine residents was conducted at a citywide conference in 2016. Residents performed simple pharmaceutical calculations and were queried regarding resources they typically use to aid in performing calculations.

Results

Fifty‐three emergency medicine residents out of 110 attendees (48%) completed the survey (postgraduate year [PGY]‐1 n = 27, PGY‐2 n = 13, PGY‐3 n = 8, PGY‐4 or above n = 5). Nearly 80% (n = 42) of all residents responded correctly to at least four of six questions (PGY‐1 = 70%, PGY‐2 = 86%, PGY‐3 = 88%, and PGY‐4 and above = 100%). Sixty‐five percent of PGY‐1s, 50% of PGY‐2s, and 75% of PGY‐3s thought that it was very important to correctly perform basic calculations. Google and Up To Date were frequently used to assist with calculations. More than 70% of all residents utilize clinical pharmacy (PharmD) staff for calculating doses. PharmD services were available at all times in the majority of survey responses.

Conclusions

Emergency medicine residents performed poorly when completing pharmaceutical calculations. This may contribute to increased patient morbidity and mortality. Internet resource use increased as the years of training increased. PharmD services were extensively utilized by all resident regardless of years of training.

More than 250,000 deaths are reported in the United States every year because of medical errors making it the third leading cause of death after heart disease and cancer.1 Medication errors contribute to higher mortality rate and cost of health care.2 Lack of knowledge and proficiency in pharmaceutical calculations may be contribute to medication errors.3

The difficulties practitioners encounter when performing calculations is compounded by inconsistencies in the labeling of drug strengths. Concentrations of drugs in solution are expressed most commonly as mass per unit volume (e.g., mg/mL), ratios (e.g., 1:1,000), and percentages. The ratio system is based on thousands and percentages are based on hundreds adding to the potential for confusion and increasing the numbers of medication errors.4

Methods

All emergency medicine residents representing six training programs who attended a regional conference in September 2016 were invited to participate in a needs‐assessment survey. This survey was approved by our institutional review board. A convenience sample of emergency medicine residents were asked six multiple‐choice questions (Figure 1). Questions on the survey involved calculating the concentration of drug solutions expressed as a percentage, a ratio, and mass concentration; calculating the correct volume; and mathematical unit conversions. No statistical analysis was performed due to small sample size.

Figure 1.

The six questions about pharmaceutical calculations (correct answers marked in bold).

Results

Fifty‐three emergency medicine residents completed the survey out of 110 attendees (48%). The numbers of residents per training year included: PGY‐1 n = 27, PGY‐2 n = 14, PGY‐3 n = 8, PGY‐4 and above n = 4. The mean score was 4 of 6 for all participants. Question 2 concerning the percentage of ethanol in 100‐proof whiskey was answered correctly by 96% of participants (n = 49).

Only 51% (n = 27) chose the correct amount of epinephrine in 1 mL of a 1:1,000 solution. More than half of the participants were able to correctly answer questions involving mathematical unit conversions (question 4 = 70%, question 5 = 86%). Nearly 80% (n = 42) of all residents responded correctly to at least four of six questions (PGY‐1 = 19/27, PGY‐2 = 12/14, PGY‐3 = 7/8, and PGY‐4 and above = 4/4). However, only 47% of all residents were able to answer five of six questions correctly. The most common incorrectly answered question (question 3) required residents to convert epinephrine concentrations.

More than half of the participants thought that it was very important to correctly perform basic calculations. Google (55%) and Up‐to‐date (52%) were the most commonly utilized resources followed by phone applications (45%) and Wikipedia (15%). More than 70% of residents consult clinical pharmacists for assistance in calculating doses. Clinical pharmacy services were available at all times in the majority of survey responses (72%).

Discussion

Medication miscalculations and lack of understanding of drug concentrations may result in medication errors.3 Wheeler et al.5 conducted a Web‐based multiple‐choice questionnaire in the United Kingdom to determine whether physicians who had completed training were familiar with medications expressed as a ratio, a percentage, or mg/mL. They found that physicians perform poorly when calculating drug doses and have poor understanding of the various ways in which the drug concentrations in solutions are expressed.5

Glover and Sussmane6 evaluated the calculation skills of pediatric residents. They found insufficient mathematical calculation competency in all 3 years of residency based on a 10‐ question test. Their overall average test score was 65%. The years of clinical training did not improve test scores. None of the 21 residents who completed the test identified any of three infusion‐related errors. Seven residents made 10‐fold dosing errors and one resident made a 1,000‐fold dosing error.

Honey et al.7 studied the frequency and type of resident prescribing errors in a pediatric outpatient setting. They compared the accuracy of residents in pediatrics (n = 16), family medicine (n = 9), internal medicine (n = 4), and medicine/pediatrics (n = 9) training programs. Thirty‐eight residents wrote 2,941 prescriptions during the study. The prescribing error rate was 5.88% for all residents. Error rates were greatest for family medicine residents (11%) and lowest for pediatric residents (4%). The most common error type was medication overdose although the authors did not specify if a miscalculation led to the overdose.

Our survey of emergency medicine residents had similar findings to Wheeler et al.5 Difficulties occurred when calculating the correct dose, especially when the drug concentration units were not uniformly expressed. In question 3 the epinephrine concentration was expressed as a ratio and the concentration needed to be calculated. Only 51% of all emergency residents were able to calculate this correctly.

Calculation errors resulted when drug concentrations were expressed as a percentage (questions 1 and 6). Although more than half of the residents answered question 1 correctly, this was the most common incorrectly answered question for both the PGY‐2 and PGY‐3 residents.

Contrary to the pediatric resident findings of Glover and Sussmane, emergency medicine residency classes performed better as their years of training increased for the majority (four of six) of correctly answered questions, i.e., PGY‐1 = 70%, PGY‐2 = 86%, PGY‐3 = 88%, and PGY‐4 or above = 100% in our study.6 This result could be attributed to increased Internet use as the years of residency training increased. While the years of experience may improve residents’ ability to perform calculations, our results illustrating only 47% of residents were able to correctly answer five of six questions demonstrates inconsistencies with experience (PGY‐1 = 52%, PGY‐2 = 43%, PGY‐3 = 75%, and PGY‐4 or above = 50%). The most commonly missed question (question 3, epinephrine concentration conversion) across all years of training suggests that drug concentrations expressed as a ratio are confusing for all and that the level of experience does not improve residents’ ability to perform such calculations.

Overall, we found that emergency medicine residents could not correctly perform these calculations. This inability was greatest when drug concentrations were expressed as ratios and percentages. These deficiencies have the potential to cause dosing errors that may result in patient harm and poor outcomes.

Our results of emergency medicine residents were similar to findings of practicing physicians (mean experience length = 14.8 years) in a similar survey of dosage calculations.4 Necessary skills for performing dosage calculations should be a priority in medical school coursework. Emergency medicine residents would benefit from additional training in calculating drug doses. Medication doses calculated using computer‐assisted dosing programs (e.g., heparin, conscious sedation medication) may be overridden by the prescriber and are not error proof. Residents should consult clinical pharmacy services to assist in calculating dosages, check doses, and prevent dosage errors.

Limitations

Study limitations include the small number of survey responses and the variable sample size between the residency classes. Residents who are intimidated by calculations may have chosen not to take part. The survey was conducted in a controlled environment and the results may be an underestimation of the magnitude of calculation errors made by emergency medicine residents in a chaotic emergency department milieu. This was a convenience sample of residents from six emergency medicine programs and the results may not be representative of emergency medicine residents from other training programs.

Conclusion

Emergency medicine residents performed poorly on a survey of pharmaceutical calculations. Uncertainty existed when calculating the correct dose using drug concentrations expressed as both a ratio and a percentage. Improved performance trends and utilization of web‐based resources were seen with increased years of residency training.

Standardization of drug concentrations in solution as mg/mL may mitigate errors resulting from calculating drug doses. Practicing calculations in a simulated environment may also identify difficulties so that residents can be remediated.

AEM Education and Training 2020;4:64–67.