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1. Introduction
To ensure clear and valid assessment of new therapies, data must be appropriately collected and analysed. Once one has good data, the methods of analysis and the presentation of results can be chosen separately.
Results of clinical trials that compare the rates or proportions achieving an outcome, such as pain relief, can be analysed and presented in several ways. Common methods of comparing rates or proportions are the relative risk (RR), the difference in proportions, which is also known as the absolute risk reduction (ARR), the odds ratio (OR) and the log OR. As an example, consider a randomized trial of antifungal prophylaxis for stem-cell transplant recipients, which compared itraconazole with fluconazole.[1] In the first 6 months after transplantation, invasive fungal infections occurred in 6 of 71 (8%) itraconazole recipients and 17 of 67 (25%) fluconazole recipients. The overall mortality rates were 32 ÷ 71 = 45% in the itraconazole group versus 28 ÷ 67 = 42% in the fluconazole group. For mortality, the difference between the rates, the ARR, was 3% (95% CI -13.2, 19.8): the death rate might be approximately 20% higher or 13% lower on itraconazole than fluconazole. The outcomes measures ARR, RR and OR are shown in table I, with the calculations. The benefit of itraconazole in reducing infection rates is expressed by the ARR of -16.9%, a decrease; by an RR of 0.33, which indicates that the infection rate is a third of the rate on fluconazole; and by the OR of 0.28.
Table I. Summary statistics for antifungal trial[1] [Table omitted.]
A measure called the 'number needed to treat' (NNT), the inverse of the difference in rates, has been advocated in medical journals, first in the context of randomized controlled trials (RCTs).[2-4] In the antifungal trial, the infection rate on itraconazole is 16.9% lower than on fluconazole, and the inverse of this is 100 ÷ -16.9 = -6, to the nearest whole number. The difference between the mortality rates for itraconazole versus fluconazole is 3.3 ÷ 100, and the inverse of this is 100 ÷ 3.3 = 30. The NNT statistic is quite subtle, and expressing it correctly requires considerable care. We must consider whether the outcome chosen indicates benefit or harm. For infection rates, a...