Without stating the direction of the effect, the alternative treatment, the treatment period, and the follow‐up period, information in terms of NNTs is uninterpretable. Thus when quoting an NNT one should always give the basic information about which treatments are compared, the treatment period, the follow‐up period, and the direction of the effect.
Example – Importance of Considering both Absolute Risk and Relative Risk
Women of reproductive age not using the combined oral contraceptive pill have a risk of deep vein thrombosis (DVT) of about 2 per 10 000 women per year (Stegeman et al. 2013). Use of combined oral contraceptives increases the risk of DVT compared with non‐use by a relative risk of 4 to 8 per 10 000 women per year, which would seem a large extra risk. However, the absolute increase in risk is 8/10 000 – 2/10 000 = 6/10 000 = 0.0006, or an additional 6 women with DVTs in 10 000 years of exposure. This increased risk is very small and hence may be considered worth taking, when balanced against other factors such as cost or convenience. Also, it is worth mentioning that a pregnant woman has a risk of a DVT of about 11 per 10 000 per year (Kourlaba et al. 2016); so the risk of DVT if you are pregnant is greater than the risk of a DVT when using the contraceptive pill, of 8 per 10 000 per year. Thus when one reads in the newspapers about a new risk to health that has been discovered, often only the relative risk is quoted, but one should ask about the baseline risk or incidence of the outcome (given you are not exposed to the risk factor) and the ARD, which may be negligible. If you are at very low risk, then you will remain at very low risk even when exposed to a hazard, unless the relative risk for the hazard is enormous!
Summarising Binary Data – Odds and Odds Ratios
A further method of summarising the results is to use the odds of an event rather than the probability. The odds of an event are defined as the ratio of the probability of occurrence of the event to the probability of non‐occurrence, that is, p/(1−p).
Using the notation of Table 3.3 we can see that the odds of a positive outcome for the test group relative to the odds of a positive outcome for control group, the odds ratio (OR), is:
The odds ratio (OR) from Table 3.3 is
What does an odds ratio of less than 1 mean? There is a negative association between exposure and outcome (people in the exposed group less likely to experience outcome of interest). What does an odds ratio of more than 1 mean? There is a positive association between the exposure and outcome (people in the exposed group more likely to experience the outcome of interest).
Example – Summarising Results from a Clinical Trial– Corn Plasters: Odds Ratio
From Table 3.4, the odds of the corn resolving by three‐months in the plaster group is 0.337/(1 − 0.337) = 0.508; whilst the odds of resolution in the scalpel group is 0.213/(1 − 0.213) = 0.270. Thus, the odds ratio for the corn resolving by three months in the plaster compared to the scalpel treated group is 0.508/0.270 = 1.88. You can also calculate the odds ratio by using the four cell counts in the 2 × 2 contingency table of Table 3.3. The odds ratio for the corn resolving in the plaster group compared to the scalpel group is OR = (32 × 74)/(20 × 63) = 1.88.
The OR = 1.88 and RR = 1.58 with these trial data are clearly different. However, when the probability of an event happening is rare, the odds and probabilities are close, because when a is much smaller than c then the risk a/(a + c) is approximately a/c. Further if b is much smaller than d then b/(b + d) is approximately b/d, then RR = (a/c)/(b/d). Thus, the OR approximates the RR when the successes are rare, say with a maximum incidence less than 10% of either pTest or pControl Sometimes the odds ratio is referred to as ‘the approximate relative risk’. The approximation is demonstrated in Table 3.6.
Table 3.6 Comparison of RR and OR for different baseline rates.
| p Test | p Control | RR | OR | RR and OR |
|---|---|---|---|---|
| 0.05 | 0.1 | 0.5 | 0.47 | Close |
| 0.1 | 0.2 | 0.5 | 0.44 | Close |
| 0.2 | 0.4 | 0.5 | 0.38 | Not close |
| 0.4 | 0.2 | 2 | 2.66 | Not close |
| 0.2 | 0.1 | 2 | 2.25 | Close |
| 0.1 | 0.05 | 2 |
2.11
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