Meta-analysis of change scores

In some circumstances an analysis based on changes from baseline will be more efficient and powerful than comparison of final values, as it removes a component of between-person variability from the analysis. However, calculation of a change score requires measurement of the outcome twice and in practice may be less efficient for outcomes which are unstable or difficult to measure precisely, where the measurement error may be larger than true between-person baseline variability. Change-from-baseline outcomes may also be preferred if they have a less skewed distribution than final measurement outcomes. Although sometimes used as a device to ‘correct’ for unlucky randomization, this practice is not recommended.


The preferred statistical approach to accounting for baseline measurements of the outcome variable is to include the baseline outcome measurements as a covariate in a regression model or analysis of covariance (ANCOVA). These analyses produce an ‘adjusted’ estimate of the treatment effect together with its standard error. These analyses are the least frequently encountered, but as they give the most precise and least biased estimates of treatment effects they should be included in the analysis when they are available. However, they can only be included in a meta-analysis using the generic inverse-variance method, since means and standard deviations are not available for each intervention group separately.


In practice an author is likely to discover that the studies included in a review may include a mixture of change-from-baseline and final value scores. However, mixing of outcomes is not a problem when it comes to meta-analysis of mean differences. There is no statistical reason why studies with change-from-baseline outcomes should not be combined in a meta-analysis with studies with final measurement outcomes when using the (unstandardized) mean difference method in RevMan. In a randomized trial, mean differences based on changes from baseline can usually be assumed to be addressing exactly the same underlying intervention effects as analyses based on final measurements. That is to say, the difference in mean final values will on average be the same as the difference in mean change scores. If the use of change scores does increase precision, the studies presenting change scores will appropriately be given higher weights in the analysis than they would have received if final values had been used, as they will have smaller standard deviations.


When combining the data authors must be careful to use the appropriate means and standard deviations (either of final measurements or of changes from baseline) for each study. Since the mean values and standard deviations for the two types of outcome may differ substantially it may be advisable to place them in separate subgroups to avoid confusion for the reader, but the results of the subgroups can legitimately be pooled together.


However, final value and change scores should not be combined together as standardized mean differences, since the difference in standard deviation reflects not differences in measurement scale, but differences in the reliability of the measurements.


A common practical problem associated with including change-from-baseline measures is that the standard deviation of changes is not reported. Imputations of standard deviations is discussed in Chapter 16 (Section 16.1.3).