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Cite this chapter as: Higgins JPT, Li T, Deeks JJ (editors). Chapter 6: Choosing effect measures and computing estimates of effect. In: Higgins JPT, Thomas J, Chandler J, Cumpston M, Li T, Page MJ, Welch VA (editors). Cochrane Handbook for Systematic Reviews of Interventions version 6.3 (updated February 2022). Cochrane, 2022. Available from www.training.cochrane.org/handbook.

The ways in which the effect of an intervention can be assessed depend on the nature of the data being collected. In this chapter, for each of the above types of data, we review definitions, properties and interpretation of standard measures of intervention effect, and provide tips on how effect estimates may be computed from data likely to be reported in sources such as journal articles. Formulae to estimate effects (and their standard errors) for the commonly used effect measures are provided in a supplementary document Statistical algorithms in Review Manager, as well as other standard textbooks (Deeks et al 2001). Chapter 10 discusses issues in the selection of one of these measures for a particular meta-analysis.

The true effects of interventions are never known with certainty, and can only be estimated by the studies available. Every estimate should always be expressed with a measure of that uncertainty, such as a confidence interval or standard error (SE).

Cluster-randomized studies, crossover studies, studies involving measurements on multiple body parts, and other designs need to be addressed specifically, since a naive analysis might underestimate or overestimate the precision of the study. Failure to account for clustering is likely to overestimate the precision of the study, that is, to give it confidence intervals that are too narrow and a weight that is too large. Failure to account for correlation is likely to underestimate the precision of the study, that is, to give it confidence intervals that are too wide and a weight that is too small.

In studies of long duration, results may be presented for several periods of follow-up (for example, at 6 months, 1 year and 2 years). Results from more than one time point for each study cannot be combined in a standard meta-analysis without a unit-of-analysis error. Some options in selecting and computing effect estimates are as follows:

An estimate of effect may be presented along with a confidence interval or a P value. It is usually necessary to obtain a SE from these numbers, since software procedures for performing meta-analyses using generic inverse-variance weighted averages mostly take input data in the form of an effect estimate and its SE from each study (see Chapter 10, Section 10.3). The procedure for obtaining a SE depends on whether the effect measure is an absolute measure (e.g. mean difference, standardized mean difference, risk difference) or a ratio measure (e.g. odds ratio, risk ratio, hazard ratio, rate ratio). We describe these procedures in Sections 6.3.1 and 6.3.2, respectively. However, for continuous outcome data, the special cases of extracting results for a mean from one intervention arm, and extracting results for the difference between two means, are addressed in Section 6.5.2.

A limitation of this approach is that estimates and SEs of the same effect measure must be calculated for all the other studies in the same meta-analysis, even if they provide the summary data by intervention group. For example, when numbers in each outcome category by intervention group are known for some studies, but only ORs are available for other studies, then ORs would need to be calculated for the first set of studies to enable meta-analysis with the second set of studies. Statistical software such as RevMan may be used to calculate these ORs (in this example, by first analysing them as dichotomous data), and the confidence intervals calculated may be transformed to SEs using the methods in Section 6.3.2.

Where exact P values are quoted alongside estimates of intervention effect, it is possible to derive SEs. While all tests of statistical significance produce P values, different tests use different mathematical approaches. The method here assumes P values have been obtained through a particularly simple approach of dividing the effect estimate by its SE and comparing the result (denoted Z) with a standard normal distribution (statisticians often refer to this as a Wald test).

As an example, suppose a conference abstract presents an estimate of a risk difference of 0.03 (P = 0.008). The Z value that corresponds to a P value of 0.008 is Z = 2.652. This can be obtained from a table of the standard normal distribution or a computer program (for example, by entering =abs(normsinv(0.008/2)) into any cell in a Microsoft Excel spreadsheet). The SE of the risk difference is obtained by dividing the risk difference (0.03) by the Z value (2.652), which gives 0.011.

Where significance tests have used other mathematical approaches, the estimated SEs may not coincide exactly with the true SEs. For P values that are obtained from t-tests for continuous outcome data, refer instead to Section 6.5.2.3.

Measures of relative effect express the expected outcome in one group relative to that in the other. The risk ratio (RR, or relative risk) is the ratio of the risk of an event in the two groups, whereas the odds ratio (OR) is the ratio of the odds of an event (see Box 6.4.a). For both measures a value of 1 indicates that the estimated effects are the same for both interventions.

Since risk and odds are different when events are common, the risk ratio and the odds ratio also differ when events are common. This non-equivalence does not indicate that either is wrong: both are entirely valid ways of describing an intervention effect. Problems may arise, however, if the odds ratio is misinterpreted as a risk ratio. For interventions that increase the chances of events, the odds ratio will be larger than the risk ratio, so the misinterpretation will tend to overestimate the intervention effect, especially when events are common (with, say, risks of events more than 20%). For interventions that reduce the chances of events, the odds ratio will be smaller than the risk ratio, so that, again, misinterpretation overestimates the effect of the intervention. This error in interpretation is unfortunately quite common in published reports of individual studies and systematic reviews.

The risk difference is the difference between the observed risks (proportions of individuals with the outcome of interest) in the two groups (see Box 6.4.a). The risk difference can be calculated for any study, even when there are no events in either group. The risk difference is straightforward to interpret: it describes the difference in the observed risk of events between experimental and comparator interventions; for an individual it describes the estimated difference in the probability of experiencing the event. However, the clinical importance of a risk difference may depend on the underlying risk of events in the population. For example, a risk difference of 0.02 (or 2%) may represent a small, clinically insignificant change from a risk of 58% to 60% or a proportionally much larger and potentially important change from 1% to 3%. Although the risk difference provides more directly relevant information than relative measures (Laupacis et al 1988, Sackett et al 1997), it is still important to be aware of the underlying risk of events, and consequences of the events, when interpreting a risk difference. Absolute measures, such as the risk difference, are particularly useful when considering trade-offs between likely benefits and likely harms of an intervention.

Sometimes the numbers of participants and numbers of events are not available, but an effect estimate such as an odds ratio or risk ratio may be reported. Such data may be included in meta-analyses (using the generic inverse variance method) only when they are accompanied by measures of uncertainty such as a SE, 95% confidence interval or an exact P value (see Section 6.3).

To overcome problems associated with estimating SDs within small studies, and with real differences across studies in between-person variability, it may sometimes be desirable to standardize using an external estimate of SD. External estimates might be derived, for example, from a cross-sectional analysis of many individuals assessed using the same continuous outcome measure (the sample of individuals might be derived from a large cohort study). Typically the external estimate would be assumed to be known without error, which is likely to be reasonable if it is based on a large number of individuals. Under this assumption, the statistical methods used for MDs would be used, with both the MD and its SE divided by the externally derived SD.

The ratio of means (RoM) is a less commonly used statistic that measures the relative difference between the mean value in two groups of a randomized trial (Friedrich et al 2008). It estimates the amount by which the average value of the outcome is multiplied for participants on the experimental intervention compared with the comparator intervention. For example, a RoM of 2 for an intervention implies that the mean score in the participants receiving the experimental intervention is on average twice as high as that of the group without intervention. It can be used as a summary statistic in meta-analysis when outcome measurements can only be positive. Thus it is suitable for single (post-intervention) assessments but not for change-from-baseline measures (which can be negative).

When needed, missing information and clarification about the statistics presented should always be sought from the authors. However, for several measures of variation there is an approximate or direct algebraic relationship with the SD, so it may be possible to obtain the required statistic even when it is not published in a paper, as explained in Sections 6.5.2.1 to 6.5.2.6. More details and examples are available elsewhere (Deeks 1997a, Deeks 1997b). Section 6.5.2.7 discusses options whenever SDs remain missing after attempts to obtain them. 153554b96e

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