A frequentist one-step model for a simple network meta-analysis of time-to-event data in presence of an effect modifier

Introduction
Individual patient data (IPD) present particular advantages in network meta-analysis (NMA) because interactions may lead an aggregated data (AD)-based model to wrong a treatment effect (TE) estimation. However, fewer works have been conducted for IPD with time-to-event contrary to binary outcomes. We aimed to develop a general frequentist one-step model for evaluating TE in the presence of interaction in a three-node NMA for time-to-event data.

Methods
One-step, frequentist, IPD-based Cox and Poisson generalized linear mixed models were proposed. We simulated a three-node network with or without a closed loop with (1) no interaction, (2) covariate-treatment interaction, and (3) covariate distribution heterogeneity and covariate-treatment interaction. These models were applied to the NMA (Meta-analyses of Chemotherapy in Head and Neck Cancer [MACH-NC] and Radiotherapy in Carcinomas of Head and Neck [MARCH]), which compared the addition of chemotherapy or modified radiotherapy (mRT) to loco-regional treatment with two direct comparisons. AD-based (contrast and meta-regression) models were used as reference.

Results
In the simulated study, no IPD models failed to converge. IPD-based models performed well in all scenarios and configurations with small bias. There were few variations across different scenarios. In contrast, AD-based models performed well when there were no interactions, but demonstrated some bias when interaction existed and a larger one when the modifier was not distributed evenly. While meta-regression performed better than contrast-based only, it demonstrated a large variability in estimated TE. In the real data example, Cox and Poisson IPD-based models gave similar estimations of the model parameters. Interaction decomposition permitted by IPD explained the ecological bias observed in the meta-regression.

Conclusion
The proposed general one-step frequentist Cox and Poisson models had small bias in the evaluation of a three-node network with interactions. They performed as well or better than AD-based models and should also be undertaken whenever possible.