Which measure for dichotomous outcomes?

Summary statistics for dichotomous data are described in Section 9.2.2. The effect of intervention can be expressed as either a relative or an absolute effect. The risk ratio (relative risk) and odds ratio are relative measures, while the risk difference and number needed to treat are absolute measures. A further complication is that there are in fact two risk ratios. We can calculate the risk ratio of an event occurring or the risk ratio of no event occurring. These give different pooled results in a meta-analysis, sometimes dramatically so.


The selection of a summary statistic for use in meta-analysis depends on balancing three criteria (Deeks 2002). First, we desire a summary statistic that gives values that are similar for all the studies in the meta-analysis and subdivisions of the population to which the interventions will be applied. The more consistent the summary statistic the greater is the justification for expressing the intervention effect as a single summary number. Second, the summary statistic must have the mathematical properties required for performing a valid meta-analysis. Third, the summary statistic should be easily understood and applied by those using the review. It should present a summary of the effect of the intervention in a way that helps readers to interpret and apply the results appropriately. Among effect measures for dichotomous data, no single measure is uniformly best, so the choice inevitably involves a compromise.


Consistency: Empirical evidence suggests that relative effect measures are, on average, more consistent than absolute measures (Engels 2000, Deeks 2002). For this reason it is wise to avoid performing meta-analyses of risk differences, unless there is a clear reason to suspect that risk differences will be consistent in a particular clinical situation. On average there is little difference between the odds ratio and risk ratio in terms of consistency (Deeks 2002). When the study aims to reduce the incidence of an adverse outcome (see Section there is empirical evidence that risk ratios of the adverse outcome are more consistent than risk ratios of the non-event (Deeks 2002). Selecting an effect measure on the basis of what is the most consistent in a particular situation is not a generally recommended strategy, since it may lead to a selection that spuriously maximizes the precision of a meta-analysis estimate.


Mathematical properties: The most important mathematical criterion is the availability of a reliable variance estimate. The number needed to treat does not have a simple variance estimator and cannot easily be used directly in meta-analysis, although it can be computed from the other summary statistics (see Chapter 12, Section 12.5). There is no consensus as to the importance of two other often cited mathematical properties: the fact that the behaviour of the odds ratio and the risk difference do not rely on which of the two outcome states is coded as the event, and the odds ratio being the only statistic which is unbounded (see Section 9.2.2).


Ease of interpretation: The odds ratio is the hardest summary statistic to understand and to apply in practice, and many practising clinicians report difficulties in using them. There are many published examples where authors have misinterpreted odds ratios from meta-analyses as if they were risk ratios. There must be some concern that routine presentation of the results of systematic reviews as odds ratios will lead to frequent overestimation of the benefits and harms of treatments when the results are applied in clinical practice. Absolute measures of effect are also thought to be more easily interpreted by clinicians than relative effects (Sinclair 1994), and allow trade-offs to be made between likely benefits and likely harms of interventions. However, they are less likely to be generalizable.


It seems important to avoid using summary statistics for which there is empirical evidence that they are unlikely to give consistent estimates of intervention effects (the risk difference) and it is impossible to use statistics for which meta-analysis cannot be performed (the number needed to treat). Thus it is generally recommended that analysis proceeds using risk ratios (taking care to make a sensible choice over which category of outcome is classified as the event) or odds ratios. It may be wise to plan to undertake a sensitivity analysis to investigate whether choice of summary statistic (and selection of the event category) is critical to the conclusions of the meta-analysis (see Section 9.7).


It is often sensible to use one statistic for meta-analysis and re-express the results using a second, more easily interpretable statistic. For example, meta-analysis may often be best performed using relative effect measures (risk ratios or odds ratio) and the results re-expressed using absolute effect measures (risk differences or numbers needed to treat – see Chapter 12, Section 12.5). This is one of the key motivations for ‘Summary of findings’ tables in Cochrane reviews: see Chapter 11 (Section 11.5). If odds ratios are used for meta-analysis they can also be re-expressed as risk ratios (see Chapter 12, Section 12.5.4). In all cases the same formulae can be used to convert upper and lower confidence limits. However, it is important to note that all of these transformations require specification of a value of baseline risk indicating the likely risk of the outcome in the ‘control’ population to which the experimental intervention will be applied. Where the chosen value for this assumed control risk is close to the typical observed control group risks across the studies, similar estimates of absolute effect will be obtained regardless of whether odds ratios or risk ratios are used for meta-analysis. Where the assumed control risk differs from the typical observed control group risk, the predictions of absolute benefit will differ according to which summary statistic was used for meta-analysis.