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.

BACKGROUND: Adequate field triage of trauma patients is crucial to transport patients to the right hospital. Mistriage and subsequent interhospital transfers should be minimized to reduce avoidable mortality, life-long disabilities, and costs. Availability of a prehospital triage tool may help to identify patients in need of specialized trauma care and to determine the optimal transportation destination.

METHODS: The GOAT (Gradient Boosted Trauma Triage) study is a prospective, multi-site, cross-sectional diagnostic study. Patients transported by at least five ground Emergency Medical Services to any receiving hospital within the Netherlands are eligible for inclusion. The reference standards for the need of specialized trauma care are an Injury Severity Score ≥ 16 and early critical resource use, which will both be assessed by trauma registrars after the final diagnosis is made. Variable selection will be based on ease of use in practice and clinical expertise. A gradient boosting decision tree algorithm will be used to develop the prediction model. Model accuracy will be assessed in terms of discrimination (c-statistic) and calibration (intercept, slope, and plot) on individual participant's data from each participating cluster (i.e., Emergency Medical Service) through internal-external cross-validation. A reference model will be externally validated on each cluster as well. The resulting model statistics will be investigated, compared, and summarized through an individual participant's data meta-analysis.

DISCUSSION: The GOAT study protocol describes the development of a new prediction model for identifying patients in need of specialized trauma care. The aim is to attain acceptable undertriage rates and to minimize mortality rates and life-long disabilities.