Mixed and Indirect Comparisons

Definition

A direct comparison of two interventions occurs when they are compared within the same randomized controlled trial (RCT). An indirect comparison is any method of comparing two interventions without the use of direct comparisons between the two. It can be used in meta-analysis of RCTs when a reviewer wishes to compare two interventions and no direct comparisons exist. It can also be used in conjunction with direct evidence to strengthen results.

Methods

There are two possible methods of performing indirect comparisons. One method is to take all [Page 770]evidence regarding the effects of two interventions from various sources and compare the two interventions as if they came from the same trial. This method has been referred to as unadjusted indirect comparison or the naive method. This method should be avoided since it violates the inherent randomization that occurs within the trials and is known to produce misleading results.

All further references to indirect comparisons in this entry refer to adjusted indirect comparisons. In this method, two interventions are compared indirectly by using their direct comparisons with a third common intervention.

This method is most easily demonstrated with an example. Suppose a reviewer wishes to assess the difference in efficacy between two drugs, A and B. While there are no RCTs directly comparing the two interventions, there are trials comparing each drug with a placebo (i.e., A vs. P and B vs. P). If efficacy is measured in terms of a mean difference, then two separate meta-analyses can be performed: one comparing Drug A with the placebo, resulting in a mean difference of dAP, and one comparing Drug B with the placebo, resulting in a mean difference of dBP. The mean difference between A and B (dAB) can be expressed as a “difference of differences”—that is,

Using the standard formula for the variance of a difference of independent variables, one can compute the variance of this difference as

The variance of an estimated quantity can be defined generally as the uncertainty one has as to the estimate. The uncertainty increases with an indirect estimate as the variance will be higher than either of the direct estimates.

With this information, one can compute a standard estimate with a confidence interval for the mean difference between the two drugs. If the efficacy is measured by a risk ratio or an odds ratio, the procedure is the same, but the ratios must be converted to the log scale first and then exponentiated to obtain the final results. This will result in a “ratio of ratios.”

This estimate will be unbiased as long as there is no interaction between the magnitude of the treatment effect and the covariates that define the subgroups in the corresponding studies—that is to say that the effects are transitive and the populations exchangeable. While this assumption is difficult to verify, it should be noted that it is the same assumption that is made in a standard meta-analysis of direct comparisons.

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