Analysis of time to event outcomes in randomized controlled trials by generalized additive models

Randomized Controlled Trials almost invariably utilize the hazard ratio calculated with a Cox proportional hazard model as a treatment efficacy measure. Despite the widespread adoption of HRs, these provide a limited understanding of the treatment effect and may even provide a biased estimate when the assumption of proportional hazards in the Cox model is not verified by the trial data. Additional treatment effect measures on the survival probability or the time scale may be used to supplement HRs but a framework for the simultaneous generation of these measures is lacking.

By splitting follow-up time at the nodes of a Gauss Lobatto numerical quadrature rule, techniques for Poisson Generalized Additive Models (PGAM) can be adopted for flexible hazard modeling. Straightforward simulation post-estimation transforms PGAM estimates for the log hazard into estimates of the survival function. These in turn were used to calculate relative and absolute risks or even differences in restricted mean survival time between treatment arms. We illustrate our approach with extensive simulations and in two trials: IPASS (in which the proportionality of hazards was violated) and HEMO a long duration study conducted under evolving standards of care on a heterogeneous patient population.

PGAM can generate estimates of the survival function and the hazard ratio that are essentially identical to those obtained by Kaplan Meier curve analysis and the Cox model. PGAMs can simultaneously provide multiple measures of treatment efficacy after a single data pass. Furthermore, supported unadjusted (overall treatment effect) but also subgroup and adjusted analyses, while incorporating multiple time scales and accounting for non-proportional hazards in survival data.

By augmenting the HR conventionally reported, PGAMs have the potential to support the inferential goals of multiple stakeholders involved in the evaluation and appraisal of clinical trial results under proportional and non-proportional hazards.