A survey of drug-dose calculation skills of Australian tertiary hospital doctors

Medication errors are a source of significant morbidity and mortality among hospital patients worldwide. A United States study found that drug complications were the most common type of adverse hospital event, accounting for 19% of all these events.1 An adverse drug event is defined as any injury related to the use of a drug.2 The risk of a medication error causing an adverse drug event is increased by difficult and time-critical circumstances.

A recent qualitative study highlighted a myriad of factors that may lead to a prescribing error — drug choice, route or dose, or drug omission.3 Each drug administration is a complex process, involving up to 40 individual steps.4 The risk of an adverse event is increased when the patient’s condition is unstable, or the drug is administered intravenously.1

Studies in the United Kingdom5,6 and the US7 have investigated hospital doctors’ ability to calculate and prescribe drug doses accurately, and the effect of education programs on this skill. Junior doctors were identified as being at particular risk of making medication errors and highlighted as a target for education.7,8 Studies have also tested calculation and prescribing skills of nurses9,10 and paramedics.11 A study of intensive care physicians found that most medication errors were in dosing, which is consistent with the finding that doctors have difficulty converting between ratios, mass concentration and percentages.5 To our knowledge, no similar research has been conducted in Australia.

This study aimed to describe the ability of doctors to calculate drug doses and their workplace prescribing and calculation habits at an Australian tertiary hospital.

This prospective, observational study was conducted at a 570-bed major metropolitan teaching hospital that serves both adult and paediatric populations. The study was approved by the hospital’s ethics committee.

The questionnaire was distributed to 190 doctors and returned by 142 (75% response rate). One respondent did not answer any demographic questions and was excluded, leaving 141 valid questionnaires for analysis.

Characteristics of the 141 participants are summarised in Box 3. There were few missing data (less than 5% for any specific variable).

This study found that doctors expected a higher level of skill in drug calculation from their peers than they were able to achieve themselves. Furthermore, junior doctors and those working in non-critical care areas scored lower on a drug-dose calculation test. Both these groups reported that their previous education in drug calculations was less than adequate when compared with more senior doctors and those working in critical care areas.

Doctors’ self-predicted and actual scores were similar, suggesting they have good insight into their own skill and limitations. However, the mean score judged as adequate was significantly higher than the mean score the doctors achieved themselves: 80% of participants expected a colleague to score 90% or more to practise adequately in a clinical environment. These high expectations, and the group’s failure to achieve them, raise medicolegal concerns about the criteria doctors use to judge their peers. In a US study, 83% of 175 respondents believed prescribing errors were unacceptable and should not occur.15

A UK study found that doctors generally had a poor level of skill in calculating drug doses.5,8 We found similarly that junior and newly graduated doctors perform most poorly, and that critical care doctors perform best. Within the critical care specialties, we surveyed a relatively large number of senior anaesthetists, partly explaining the higher scores in this group.

Strikingly, participants who stated they had “never” or “unlikely” ever made a mistake in a drug-dose calculation scored significantly lower (62.7%) in the calculation test than those who admitted to past errors (90.6%). This result may be accounted for by the more experienced doctors, who performed better but had longer careers in which to make a mistake. However, it also raises concern that some doctors may lack insight into their ability and overestimate their skill, thus being unaware of their current or past mistakes.

Reassuringly, most doctors in our study (89%) said they “mostly” or “always” double-check their own drug-dose calculations. This is a higher proportion than in a US study,15 which showed that only half of interns always double-checked their calculated doses. It is difficult to know whether our results truly reflect better workplace practices in Australia, as it has been shown repeatedly that self-reported compliance with desired behaviour is higher than objectively measured compliance.15,16 However, doctors who performed worst in the calculation test were most likely to have a second staff member check their calculated doses. This reflects awareness of their deficiencies and supports the belief that the self-reporting of workplace habits was accurate.

Our study also supports previous arguments for standardised drug labelling.5,6,17 Nearly all doctors preferred solutions to be expressed in mg/mL. This preference was supported by significantly higher scores for calculations involving concentrations expressed as mg/mL. Concentrations expressed as percentages or ratios resulted in more calculation errors, potentially leading to adverse events.5,6,18,19

Standardising the units for drug concentrations in solution to mass per unit volume would lessen the risk of error by reducing the complexity of dose calculation, particularly in time-critical, high-stress areas.8 These strategies for risk reduction have been effective in the aviation and nuclear industries2,5 and are well suited but underutilised in acute care medicine.

Some may argue that a written test is a poor predictor of the true performance of doctors in clinical practice. However, residents who show poor calculation skills in a written examination are likely to perform even more poorly under stressful conditions.18

It is of concern that over three-quarters of participants (79%) reported never being tested in the skill of drug-dose calculation during their careers, suggesting this skill is assumed. One doctor calculated a dose that was 1000 times the correct dose (Question 7, Box 2). Doctors need to be trained to identify “alarms” that a dose calculation is incorrect or dangerous.20 Directly achievable recommendations to reduce errors include encouraging safe workplace practices such as double-checking one’s own calculations, cross-checking with another staff member, and utilising web-based medication programs.

Our study had a number of limitations. The newly constructed questionnaire was not validated, although it was derived from previously used and validated surveys. We cannot exclude the possibility of selection bias, but the response rate was high (74%), from a large representative sample of the hospital’s medical staff, and few data were missing. Although some potential participants may have declined to participate if they expected to perform poorly, this would have biased towards higher actual scores, which is alarming given the generally poor scores achieved. Lastly, it was beyond the scope of this study to assess whether incorrect calculations would have led to clinical errors and affected patient outcomes.

This study showed that the doctors surveyed expected a higher level of skill in calculating drug doses from their colleagues than they achieved or expected of themselves. In addition, junior doctors and those in non-critical care specialties performed more poorly, clearly confirming the need for improved teaching of drug-dose calculations to medical students and junior staff.21,22

To address calculation, mathematical process and arithmetic errors, we recommend ongoing training and enforcement via formal, regular assessment of skill in calculating drug doses for all doctors.7,8,15,17,23,24 In this way, the skill levels of individual doctors may be more likely to reflect the high expectations they have of their colleagues. Since the completion of this study, we have been approached by the hospital’s medical education office to run formal training sessions on this skill for intern staff. This will enable us to conduct further, more robust, research.2,25