# One-step parametric network meta-analysis models using the exact likelihood that allow for time-varying treatment effects

## TL;DR

This paper introduces a new Bayesian method for network meta-analysis that allows for time-varying treatment effects and uses exact likelihoods for more accurate results in oncology trials.

## Contribution

A one-step Bayesian parametric NMA model is proposed that uses exact likelihoods and allows time-varying treatment effects without relying on discrete hazards.

## Key findings

- The one-step model allows straightforward selection among various survival distributions including gamma and generalized gamma.
- Generalized gamma provides flexibility to model U-shaped hazards and simplifies to other standard distributions in special cases.
- The proposed method was compared with two-step approaches using real-world melanoma trials and simulations.

## Abstract

The importance of network meta-analysis (NMA) methods for time-to-event (TTE) that do not rely on the proportional hazard (PH) assumption is increasingly recognized in oncology, where clinical trials evaluating new interventions versus standard comparators often violate this assumption. However, existing NMA methods that allow for time-varying treatment effects do not directly leverage individual events and censor times that can be reconstructed from Kaplan–Meier curves, which may be more accurate than discrete hazards. They are also challenging to implement given reparameterizations that rely on discrete hazards. Additionally, two-step methods require assumptions regarding within-study normality and variance. We propose a one-step fully Bayesian parametric individual patient data (IPD)-NMA model that fits TTE data with the exact likelihood and allows for time-varying treatment effects. We define fixed or random effects with the following distributions: Weibull, Gompertz, log-normal, log-logistic, gamma, or generalized gamma distributions. We apply the one-step model to a network of randomized controlled trials (RCTs) evaluating multiple interventions for advanced melanoma and compare results with those obtained with the two-step approach. Additionally, a simulation study was performed to compare the proposed one-step method to the two-step method. The one-step method allows for straightforward model selection among the “standard” distributions, now including gamma and generalized gamma, with treatment effects on either the scale alone or with multivariate treatment effects. Generalized gamma offers flexibility to model U-shaped hazards within a network of RCTs, with accessible interpretation of parameters that simplifies to exponential, Weibull, log-normal, or gamma in special cases.