OBJECTIVES: In studies with time-to-event data, outcomes may be reported as hazard ratios (HR) or binomial counts/proportions at a specific time point. If the intent is to synthesise evidence by performing a meta-analysis or network meta-analysis (NMA) using the HR as the measure of treatment effect, studies that only report binomial data cannot be included in the network. Our objective was to define an appropriate statistical method for converting binomial counts to HRs and obtaining the associated variance for inclusion in evidence syntheses.

METHODS: Existing methods for converting binomial data to HR were reviewed, and a new method was proposed. The performance of the new method was assessed using simulations and data from a published NMA of multiple sclerosis treatments.

RESULTS: Estimating the log HR is relatively straightforward under the assumptions of proportional hazards and minimal censoring at the binomial data time point. To estimate the standard error of the log HR, a simple method based on using a Taylor series expansion to approximate the variance is proposed. Thus, we have two easy-to-calculate equations for the log HR and variance. In the simulation, our binomial method produced very similar HRs to those from survival analysis when censoring rates were low, and also when censoring rates were high but the event rate was low. In all situations, it outperformed using relative risk to approximate the HR. In the NMA, results were consistent between reported HRs and HRs derived from binomial data for studies that reported both types of data.

CONCLUSIONS: This method may be useful for easily incorporating trials reporting binomial data into an evidence synthesis of HR data, under certain assumptions.