Fisher information matrix computation for joint longitudinal and survival models to support clinical study design and covariate effect assessment

Joint modelling of longitudinal data using non-linear mixed effects models and time-to-event outcomes provides a suitable framework to account for informative censoring when estimating biomarker dynamics and quantifying event risk using covariates and longitudinal trajectories. Their usefulness in clinical research depends on data collection design, particularly to precisely estimate the association (link) parameter between longitudinal and survival processes. However, optimal design strategies have so far been addressed separately for longitudinal and survival endpoints and remain unexplored for joint models. We propose two Fisher Information Matrix (FIM) computation methods for joint models, relying on Monte-Carlo integration over observations combined with either Markov Chains Monte-Carlo or Adaptive Gaussian Quadrature to integrate random effects. Their accuracy is assessed against clinical trial simulations in an oncological example based on the HORIZON III study with a tumour-growth-survival model including discrete and continuous covariates. We apply these methods to quantify the impact of follow-up duration, sampling richness, sample size, and covariate distribution on parameter uncertainty and test power. In our example, longitudinal-parameter uncertainty is barely affected by follow-up duration or sampling richness, whereas survival-parameter uncertainty decreases substantially from 1-year to 2-year follow-up. The number of subjects needed (NSN) to achieve <15\% uncertainty on the link parameter is comparable for a 2-year rich design and a 3-year sparse design. Optimal covariate distributions are stable across designs and systematically improve test power, outperforming longer and richer but non-optimised designs. These FIM-based methods accurately predict uncertainty and test powers, enabling design evaluation and NSN computation for joint-model-based clinical studies.