Three's a Crowd: How to Deal with More than Two Arms in a Meta-Analysis

It is not uncommon to come across the following scenario: when conducting a meta-analysis between two arms (e.g., an active therapy vs. a placebo), the meta-analyst includes a study that actually included two active arms (e.g., two different doses of the same experimental drug vs. placebo, two different routes of administration, etc.) Let's say that both of these arms were relevant to the clinical question. How should meta-analysis be undertaken in this case? A new tutorial article published in Cochrane Evidence Synthesis and Methods gives a primer on how to approach this common conundrum. 

Including the study twice in the forest plot – for instance, with one dose versus placebo and the other versus the same placebo group – is statistically problematic. It leads to a "unit of analysis" error by essentially "double-counting" the participants in the control group and violating the assumption that every individual participant is only counted twice. (Aside: this is also a common error in meta-analyses combining multiple similar outcomes – e.g., including the handgrip strength of both the dominant and non-dominant hand in the same forest plot – and risks committing the same violation unless advanced multi-level statistical techniques are used to account for this). 

This leaves two basic options for including the data from more than two study arms into the same forest plot: combining interventions that are similar, and splitting the control group in half. For instance, if the three groups in question are as such (assuming a dichotomous outcome):

• Experimental group A: 50 participants, 45 of whom had the event.
• Experimental group B: 50 participants, 41 of whom had the event.
• Control group: 50 participants, 22 of whom had the event.

These two experimental groups can either be combined (100 participants, 89 of whom had the event) and compared to the control group as-is, or they can be split out and compared (on separate lines of the forest plot) to half of the control group on each line:

• Experimental group A (45 out of 50) versus control (11 out of 25)
• Experimental group B (41 out of 50) versus control (11 out of 25).

Both approaches will yield very similar pooled results.

In the case of a continuous outcome, the same general approaches can be applied. However, if pooling two or more arms together, a pooled mean and SD will need to be calculated using the following equations from the Cochrane Handbook:

Reference: Axon, E., Dwan, K., & Richardson, R. (2023) Multiarm studies and how to handle them in a meta-analysis: A tutorial. Cochrane Evidence Synthesis and Methods. Available at publisher's website here.

Review of Time-to-Event Outcomes Analyzed in 50 Systematic Reviews Indicates Lack of Rigorous Reporting

Commonly used in the fields of oncology, cardiology, and others, time-to-event (TTE) outcomes assess not only the occurrence of an event but the amount of time that has lapsed leading up to its occurrence. For individuals in which the event did not occur, their time under observation is included.

TTE outcomes can provide useful insight into, for instance, into how long individuals survive when taking a new drug for advanced cancer. Statistical methods of calculating TTE outcomes include the use of curves and probabilities (Kaplan-Meier curves) and hazard ratios (HRs). 

In addition to being more statistically complex than a simple risk ratio, TTE outcomes are often not reported adequately enough in trials to be used in a meta-analysis without some amount of imputation or exclusion of data, which can introduce error.

In an article published in the July 2023 issue of Journal of Clinical Epidemiology, Goldkuhle and colleagues more closely examined the use of TTE outcomes in meta-analyses included in both Cochrane and non-Cochrane systematic reviews between 2017 and 2020. In the 50 included reviews, a median two TTE outcomes were included in meta-analyses, the most common being comparing the use of biologics and drugs in the treatment of neoplasms. 

However, a lack of clear reporting in the 235 trials informing these systematic reviews could easily lead to incomplete data. For instance, only 82% of the trials included a measure of follow-up duration. Information about missing data was only reported for each trial arm in 134 (57%) of the trials, and about one-third of trials reported no information at all in this respect. 

The authors conclude that trial authors using TTE outcomes should more stridently follow the Consolidated Standards of Reporting Trials (CONSORT) extension to trial outcomes, while specific guidance is needed for the reporting of meta-analysis of TTE outcomes. 

Goldkuhle, M. et al. (2023). Meta-epidemiological review identified variable reporting and handling of time-to-event analyses in publications of trials included in meta-analyses of systematic reviews. J Clin Epidemiol 159: 174-189.

The full-text publication can be accessed here.