Implications of analysing time-to-event outcomes as binary in meta-analysis: empirical evidence from the Cochrane Database of Systematic Reviews

Background

Systematic reviews and meta-analysis of time-to-event outcomes are frequently published within the Cochrane Database of Systematic Reviews (CDSR). However, these outcomes are handled differently across meta-analyses. They can be analysed on the hazard ratio (HR) scale or can be dichotomized and analysed as binary outcomes using effect measures such as odds ratios (OR) or risk ratios (RR). We investigated the impact of reanalysing meta-analyses from the CDSR that used these different effect measures.

Methods

We extracted two types of meta-analysis data from the CDSR: either recorded in a binary form only (“binary”), or in binary form together with observed minus expected and variance statistics (“OEV”). We explored how results for time-to-event outcomes originally analysed as “binary” change when analysed using the complementary log–log (clog-log) link on a HR scale. For the data originally analysed as HRs (“OEV”), we compared these results to analysing them as binary on a HR scale using the clog-log link or using a logit link on an OR scale.

Results

The pooled HR estimates were closer to 1 than the OR estimates in the majority of meta-analyses. Important differences in between-study heterogeneity between the HR and OR analyses were also observed. These changes led to discrepant conclusions between the OR and HR scales in some meta-analyses. Situations under which the clog-log link performed better than logit link and vice versa were apparent, indicating that the correct choice of the method does matter. Differences between scales arise mainly when event probability is high and may occur via differences in between-study heterogeneity or via increased within-study standard error in the OR relative to the HR analyses.

Conclusions

We identified that dichotomising time-to-event outcomes may be adequate for low event probabilities but not for high event probabilities. In meta-analyses where only binary data are available, the complementary log–log link may be a useful alternative when analysing time-to-event outcomes as binary, however the exact conditions need further exploration. These findings provide guidance on the appropriate methodology that should be used when conducting such meta-analyses.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12874-022-01541-9.

Evidence synthesis from aggregate recurrent event data for clinical trial design and analysis

Information from historical trials is important for the design, interim monitoring, analysis, and interpretation of clinical trials. Meta-analytic models can be used to synthesize the evidence from historical data, which are often only available in aggregate form. We consider evidence synthesis methods for trials with recurrent event endpoints, which are common in many therapeutic areas. Such endpoints are typically analyzed by negative binomial regression. However, the individual patient data necessary to fit such a model are usually unavailable for historical trials reported in the medical literature. We describe approaches for back-calculating model parameter estimates and their standard errors from available summary statistics with various techniques, including approximate Bayesian computation. We propose to use a quadratic approximation to the log-likelihood for each historical trial based on 2 independent terms for the log mean rate and the log of the dispersion parameter. A Bayesian hierarchical meta-analysis model then provides the posterior predictive distribution for these parameters. Simulations show this approach with back-calculated parameter estimates results in very similar inference as using parameter estimates from individual patient data as an input. We illustrate how to design and analyze a new randomized placebo-controlled exacerbation trial in severe eosinophilic asthma using data from 11 historical trials.