Convergence
Convergence rates for the random slopes model were generally high (range: 99.1% to 100%). However, for certain mean trajectories, a large proportion of datasets analysed using the random slopes model gave estimates of the correlation between the random intercepts and slopes that are very close to the boundaries. This is not automatically flagged by mixed but could still indicate some issues with convergence. For example, out of the 4991 observational studies with an early decline trajectory in which the random slopes model converged, 3796 (76%) had a correlation of > 0.99 (Table A4.1, For the 5-year trials with lower residual variance, the early and late decline trajectories have particularly high percentages of correlations of magnitude > 0.99 (32% to 67%; Table A4.2, For the scenarios with In practice, an analyst is likely to notice if the model estimate has ended on a boundary when analysing the observational study and explore alternative models. As a sensitivity analysis, we therefore summarised our results from the lower residual error scenarios for the early and late decline trajectories for those observational studies which gave a correlation of magnitude For some scenarios, the convergence rate using only the default Newton Raphson algorithm was low, and the use of alternative algorithms improved the convergence rate (see section A4, 