## Presenting results relative or absolute measures

We have emphasized the importance of providing estimates of treatment effect to aid the clinical interpretation of data (see also Chapter 9). However, in many situations, there will be more than one way to present estimates of treatment effect. One distinction, introduced in Chapter 5, is between absolute and relative measures. In general, absolute measures use differences while relative measures employ ratios. Many outcome measures can be expressed in both absolute and relative terms. With respect to survival data, the difference in the proportions surviving to a given time point in two treatment arms gives an estimate of the absolute difference in survival. For example, if the 5-year survival rate for one treatment is 40 per cent and for the other is 50 per cent, the absolute difference in survival is 10 per cent. The hazard ratio on the other hand is a measure of the relative treatment effect; a survival hazard ratio of 0.76 implies that the relative risk of death at any given time is 24 per cent less in one treatment group than the other. This may sound like a more impressive difference than an absolute difference of 10 per cent. In fact, under the assumption of proportional hazards, an absolute increase from 40 per cent to 50 per cent is equivalent to a hazard ratio of 0.76. In general, relative measures will sound 'bigger' than absolute measures. A small absolute increase in a very rare event (for example the risk of a second, treatment-related cancer) may generate dramatically large relative risks, which can cause an unnecessary degree of alarm. It is therefore important to provide actual event rates in addition when using relative measures. It has been argued that absolute measures of treatment effect are most relevant at an individual patient level, and relative measures of more relevance at the population level.

A further measure which has gained popularity in the setting of a binary treatment outcome is the 'number needed to treat (NNT) [4]'. This is intended to describe the number of patients who must be treated with a new intervention for one patient to benefit, or for one adverse outcome to be avoided. For binary data, this is obtained as the reciprocal of the absolute difference in the proportion of patients with the outcome of interest. For example, if 40 per cent of patients respond on standard therapy and 50 per cent respond on a new therapy, the absolute difference is 10 per cent and the NNT is 1/0.1 = 10, i.e. ten patients need to be treated for one patient to benefit. The NNT can provide a useful measure which can be compared in many different settings, particularly useful perhaps for those comparing the cost of introducing different treatments. Confidence intervals can (and should) be calculated for the NNT [5]; it is a measure which is all too easily taken simply at face value forgetting the uncertainty in the data from which it was generated. Furthemore, caution must be applied to the use of NNT for time-to-event data, for which there is debate about its role. Essentially, there is no single NNT for such data, since it will depend on the time point chosen and the number of patients at risk at that time [6]. In general the NNT will fall as the time from start of treatment increases. Furthermore, when a relative measure of treatment effect is the appropriate summary statistic, the absolute difference and hence the NNT is dependent on the baseline risk of the population to which it is applied [7] (see also Chapter 11). The NNT remains a controversial statistic, as a paper by Hutton and subsequent discussion illustrates [8].

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