You have been asked to review a new “Drug X” as to whether it should be added to the ICU formulary. It is administered over 7 days for cardiogenic shock to improve ejection fraction (EF). The following study data has been provided:
| Outcome | ||
|---|---|---|
| Improved EF | Unchanged EF | |
| Drug X (n=100) | 96 | 4 |
| Placebo (n=100) | 92 | 8 |
For this set of data:
a. Calculate and explain the odds ratio (OR) (2 marks)
b. Calculate and explain the relative risk reduction (RRR) (2 marks)
c. Calculate and explain the number needed to treat (NNT) (2 marks)
d. List the additional information that would aid your decision-making regarding the addition of the drug to the ICU formulary (4 marks)
Syllabus topic/section: 2.5.1 Research and Evidence Based Practice in Intensive Care
This SAQ was a direct repeat of an SAQ from the previous paper this year. While the pass rate has improved for this topic, candidates still appeared to have knowledge gaps in very straightforward statistical terminology and calculations. Repeat SAQs are a standard feature of the SP written section and candidates are advised to revise past papers, particularly those SAQs which explore important topics or have a prior low pass rate.
In part d) most candidates were able to provide a list with adequate detail; answers could have been improved by linking back to the information provided for the first 3 parts. Candidates who used structure often scored higher marks as they were able to provide more detail. For example, listing decision making information under the headings of drug factors (ie. Storage, pharmacokinetic and pharmacodynamic information), Organisational factors (Cost, staff education, administration concerns) and Patient factors (case mix and cohort requirements) would have provided an example of an above standard answer.
That past SAQ was Question 2 from the first paper of 2025, which had so many formulae in it that the author had to install mathjax.
a) Calculate and explain the odds ratio (OR) (2 marks)
|
Outcome |
||
|
Improved EF |
Unchanged EF |
|
|
Drug X (n=100) |
96 |
4 |
|
Placebo (n=100) |
92 |
8 |
So,
OR: odds ratio; the odds that an outcome will occur given a particular exposure, compared to the odds of the outcome occurring in the absence of that exposure
$ OR = \dfrac{Odds_{treatment}}{Odds_{control}} $
$ Odds_{treatment} = \dfrac{a}{b} $
$ Odds_{control} = \dfrac{c}{d} $
ergo, $ OR = \dfrac{a/b}{d/c} = \dfrac{ad}{bc} $
thus:
$ Odds_{treatment} = \dfrac{96}{4} = 24 $
$ Odds_{control} = \dfrac{92}{8} = 11.5 $
$ OR = \dfrac{24}{11.5} = 2.08 $
or, $ OR = \dfrac{96 \times 8}{92 \times 4} = 2.08 $
b) Calculate and explain the relative risk reduction (RRR) (2 marks)
RRR: the difference in event rates between two groups expressed as a proportion of the event rate in the untreated group
where
$ RR = \dfrac{AR_{treatment}}{AR_{control}} $
$ = \dfrac{96 / (96+4)}{92 / (92+8)} $
$ = \dfrac{0.04}{0.08} $
$ = 0.5 $
so
c) Calculate and explain the number needed to treat (NNT) (2 marks)
NNT: the number of patients you need to treat to prevent one additional bad outcome; the reciprocal of ARR.
$ ARR = \dfrac{a}{a+b} - \dfrac{c}{c+d} $
$ = \dfrac{96}{100} - \dfrac{92}{100} $
$ = 0.04 $
$ \text{thus, } NNT = \dfrac{1}{0.04} = 25 $
Further information needed for decision making? NNT is meaningless without context.
Consider:
Barratt, Alexandra, et al. "Tips for learners of evidence-based medicine: 1. Relative risk reduction, absolute risk reduction and number needed to treat." Canadian Medical Association Journal 171.4 (2004): 353-358.
Scott, Ian. "Interpreting risks and ratios in therapy trials." Australian Prescriber 31.1 (2008).
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Murad, M. Hassan, et al. "Methods for deriving risk difference (absolute risk reduction) from a meta-analysis." bmj 381 (2023).
Peretti-Watel, Patrick. La société du risque. La découverte, 2010.
Gifford, Sandra M. "The meaning of lumps: a case study of the ambiguities of risk." Anthropology and epidemiology: interdisciplinary approaches to the study of health and disease. Dordrecht: Springer Netherlands, 1986. 213-246.
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