Predicting personalised absolute treatment effects in individual participant data meta-analysis: an introduction to splines

Belias M, Rovers MM, Hoogland J, Reitsma JB, Debray TPA, IntHout J

Background: Modelling non-linear associations between an outcome and continuous patient characteristics, whilst investigating heterogeneous treatment effects, is one of the opportunities offered by individual participant data meta-analysis (IPD-MA). Splines offer great flexibility, but guidance is lacking.

Objective: To introduce modelling of nonlinear associations using restricted cubic splines (RCS), natural B-splines, P-splines, and smoothing splines in IPD-MA to estimate absolute treatment effects.

Methods: We describe the pooling of spline-based models using pointwise and multivariate meta-analysis (two-stage methods) and one-stage generalised additive mixed effects models (GAMMs). We illustrate their performance on three IPD-MA scenarios of five studies each: one where only the associations differ across studies, one where only the ranges of the effect modifier differ and one where both differ. We also evaluated the approaches in an empirical example, modelling the risk of fever and/or ear pain in children with acute otitis media conditional on age.

Results: In the first scenario, all pooling methods showed similar results. In the second and third scenario, pointwise meta-analysis was flexible but showed non-smooth results and wide confidence intervals; multivariate meta-analysis failed to converge with RCS, but was efficient with natural B-splines. GAMMs produced smooth pooled regression curves in all settings. In the empirical example, results were similar to the second and third scenario, except for multivariate meta-analysis with RCS, which now converged.

Conclusion: We provide guidance on the use of splines in IPD-MA, to capture heterogeneous treatment effects in presence of non-linear associations, thereby facilitating estimation of absolute treatment effects to enhance personalized healthcare.