Multivariate meta-analysis of individual participant data helped externally validate the performance and implementation of a prediction model

Abstract

Objectives: Our aim was to improve meta-analysis methods for summarizing a prediction model's performance when individual participant data are available from multiple studies for external validation.

Study design and setting: We suggest multivariate meta-analysis for jointly synthesizing calibration and discrimination performance, while accounting for their correlation. The approach estimates a prediction model's average performance, the heterogeneity in performance across populations, and the probability of "good" performance in new populations. This allows different implementation strategies (e.g., recalibration) to be compared. Application is made to a diagnostic model for deep vein thrombosis (DVT) and a prognostic model for breast cancer mortality.

Results: In both examples, multivariate meta-analysis reveals that calibration performance is excellent on average but highly heterogeneous across populations unless the model's intercept (baseline hazard) is recalibrated. For the cancer model, the probability of "good" performance (defined by C statistic ≥0.7 and calibration slope between 0.9 and 1.1) in a new population was 0.67 with recalibration but 0.22 without recalibration. For the DVT model, even with recalibration, there was only a 0.03 probability of "good" performance.

Conclusion: Multivariate meta-analysis can be used to externally validate a prediction model's calibration and discrimination performance across multiple populations and to evaluate different implementation strategies.

Keywords: Calibration; Discrimination; External validation; Heterogeneity; Individual participant data (IPD); Model comparison; Multivariate meta-analysis; Prognostic model; Risk prediction.

Fig. 1

Forest plot showing the C statistic results from the trivariate random-effects meta-analysis result (Table 1) for the DVT prediction model implemented using strategy (2).

Fig. 2

Forest plot showing the calibration slope result from the trivariate random-effects meta-analysis (Table 1) for the DVT prediction model implemented using strategy (2).

Fig. 3

Summary of validation performance of the breast cancer model for each implementation strategy, with regard to the C statistic and the calibration slope results from the trivariate meta-analysis (Table 3).