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). Participants who contribute some period of time that does not end in an event are said to be ‘censored’. The values of ratio measures of intervention effect (such as the odds ratio, risk ratio, rate ratio and hazard ratio) usually undergo log transformations before being analysed, and they may occasionally be referred to in terms of their log transformed values (e.g. Note that the methods in (2) are applicable both to correlation coefficients obtained using (1) and to correlation coefficients obtained in other ways (for example, by reasoned argument). 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. Time-to-event data can sometimes be analysed as dichotomous data. If a 95% confidence interval is available for the MD, then the same SE can be calculated as: as long as the trial is large. Assuming the correlation coefficients from the two intervention groups are reasonably similar to each other, a simple average can be taken as a reasonable measure of the similarity of baseline and final measurements across all individuals in the study (in the example, the average of 0.78 and 0.82 is 0.80). An important principle in randomized trials is that the analysis must take into account the level at which randomization occurred. JJD received support from the NIHR Birmingham Biomedical Research Centre at the University Hospitals Birmingham NHS Foundation Trust and the University of Birmingham. The latter is especially appropriate if an established, defensible cut-point is available. To extract counts as time-to-event data, guidance in Section 6.8.2 should be followed. Chapter 6: Choosing effect measures and computing estimates of effect.
Analyses then proceed as for any other type of continuous outcome variable. Deeks J. Systematic Reviews in Health Care: Meta-analysis in Context.
Colantuoni E, Scharfstein DO, Wang C, Hashem MD, Leroux A, Needham DM, Girard TD. However, there are numerous variations on this design. For example, in subfertility studies, women may undergo multiple cycles, and authors might erroneously use cycles as the denominator rather than women. Editors: Julian PT Higgins, Tianjing Li, Jonathan J Deeks. Furukawa TA, Barbui C, Cipriani A, Brambilla P, Watanabe N. Imputing missing standard deviations in meta-analyses can provide accurate results. BMC Medical Research Methodology 2008; 8: 32. 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). Tierney JF, Stewart LA, Ghersi D, Burdett S, Sydes MR.
An approximate SE of the log rate ratio is given by: A correction of 0.5 may be added to each count in the case of zero events. The effect of interest in any particular analysis of a randomized trial is usually either the effect of assignment to intervention (the ‘intention-to-treat’ effect) or the effect of adhering to intervention (the ‘per-protocol’ effect). The confidence interval for a mean can also be used to calculate the SD. Using the correlation coefficient calculated in step 1 above of 0.80, we can impute the change-from-baseline SD in the comparator group as: Missing mean values sometimes occur for continuous outcome data. This means that for common events large values of risk ratio are impossible. International Journal of Statistics in Medical Research 2015; 4: 57–64. Table 6.5.a Formulae for combining summary statistics across two groups: Group 1 (with sample size = N1, mean = M1 and SD = SD1) and Group 2 (with sample size = N2, mean = M2 and SD = SD2). In the example, where MD=3.8 and t=2.78, the SE of the MD is obtained by dividing 3.8 by 2.78, which gives 1.37. Some studies will report both; others will report only change scores or only post-intervention values. Note that the SE refers to the log of the ratio measure. This boundary applies only for increases in risk, and can cause problems when the results of an analysis are extrapolated to a different population in which the comparator group risks are above those observed in the study. It can be used as a summary statistic in meta-analysis when outcome measurements in all studies are made on the same scale. Cochrane News 1997b; 11: 11–12. By definition this outcome excludes participants who do not achieve an interim state (clinical pregnancy), so the comparison is not of all participants randomized.
In research, risk is commonly expressed as a decimal number between 0 and 1, although it is occasionally converted into a percentage. Some study outcomes may only be applicable to a proportion of participants. 3 October 2019 the risk ratio (RR; also called the relative risk); the risk difference (RD; also called the absolute risk reduction); and.
The second approach is to estimate the hazard ratio approximately using statistics computed during a log-rank analysis. Statistical methods to compare functional outcomes in randomized controlled trials with high mortality. A final problem with extracting information on change from baseline measures is that often baseline and post-intervention measurements may have been reported for different numbers of participants due to missed visits and study withdrawals. and similarly for the comparator intervention.
patient-months, woman-years, etc) is irrelevant since it is cancelled out of the rate ratio and does not figure in the SE.
If several candidate SDs are available, review authors should decide whether to use their average, the highest, a ‘reasonably high’ value, or some other strategy. BMC Medical Research Methodology 2012; 12: 9. It may be preferable, or necessary, to address the number of times these events occur rather than simply whether each person experienced an event or not (that is, rather than treating them as dichotomous data). Parmar MKB, Torri V, Stewart L. Extracting summary statistics to perform meta-analyses of the published literature for survival endpoints. A particularly misleading error is to misinterpret a SE as a SD. Safety, immunogenicity, and induction of immunologic memory by a serogroup C meningococcal conjugate vaccine in infants: a randomized controlled trial. Updated guidance for trusted systematic reviews: a new edition of the Cochrane Handbook for Systematic Reviews of Interventions .
We can use other data in this study to calculate two correlation coefficients, one for each intervention group. Review authors should plan to extract count data in the form in which they are reported. 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 ratio of means method as an alternative to mean differences for analyzing continuous outcome variables in meta-analysis: a simulation study.
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