Abstract

Objectives

Network meta-analysis (NMA) of time-to-event outcomes based on constant hazard ratios can result in biased findings when the proportional hazards (PHs) assumption does not hold in a subset of trials. We aimed to summarize the published non-PH NMA methods for time-to-event outcomes, demonstrate their application, and compare their results.

Methods

The following non-PH NMA methods were compared through an illustrative case study in oncology of 4 randomized controlled trials in terms of progression-free survival and overall survival: (1) 1-step or (2) 2-step multivariate NMAs based on traditional survival distributions or fractional polynomials, (3) NMAs with restricted cubic splines for baseline hazard, and (4) restricted mean survival NMA.

Results

For progression-free survival, the PH assumption did not hold across trials and non-PH NMA methods better reflected the relative treatment effects over time. The most flexible models (fractional polynomials and restricted cubic splines) fit better to the data than the other approaches. Estimated hazard ratios obtained with different non-PH NMA methods were similar at 5 years of follow-up but differed thereafter in the extrapolations. Although there was no strong evidence of PH violation for overall survival, non-PH NMA methods captured this uncertainty in the relative treatment effects over time.

Conclusions

When the PH assumption is questionable in a subset of the randomized controlled trials, we recommend assessing alternative non-PH NMA methods to estimate relative treatment effects for time-to-event outcomes. We propose a transparent and explicit stepwise model selection process considering model fit, external constraints, and clinical validity. Given inherent uncertainty, sensitivity analyses are suggested.