Comparison of Joint Modelling and Landmarking Approaches for Dynamic Prediction Using Bootstrap Simulation

Abstract Prediction models for clinical outcomes can greatly help clinicians with early diagnosis, cost-effective management and primary prevention of many medical conditions. In conventional prediction models, predictors are typically measured at a fixed time point, either at baseline or at other time point of interest such as biomarker values measured at the most recent follow-up. Dynamic prediction has emerged as a more appealing prediction technique that takes account of longitudinal history of biomarkers for making predictions. We compared prediction performance of two well-known approaches for dynamic prediction, namely joint modelling and landmarking, using bootstrap simulation based on the Alzheimer’s Disease Neuroimaging Initiative (ADNI) data with repeat Mini-Mental State Examination (MMSE) scores as the longitudinal biomarker and time-to-Alzheimer’s disease (AD) as the survival outcome. We assessed the performance of both approaches in terms of extended definitions of discrimination and calibration , namely dynamic area under the receiver operating characteristic curve (dynAUC) and expected prediction error (PE). We focused on real data-based bootstrap simulation in an attempt to be as impartial as possible to both methods as landmarking is a pragmatic approach which does not specify a statistical model for the longitudinal markers, and therefore any comparison based on model based data simulation may potentially be more advantageous to joint modelling approach. The dynAUC and PE were compared at landmarks $$ t_{s}=1.0, 1.5, 2.0\,\text{ and }\,2.5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>t</mml:mi> <mml:mi>s</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>1.0</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1.5</mml:mn> <mml:mo>,</mml:mo> <mml:mn>2.0</mml:mn> <mml:mspace /> <mml:mspace /> <mml:mtext>and</mml:mtext> <mml:mspace /> <mml:mspace /> <mml:mn>2.5</mml:mn> </mml:mrow> </mml:math> years and within a 2-year window from the landmark time points. The optimism corrected estimates of dynAUC for joint modelling were slightly higher (1.26, 3.22, 2.76 and 0.12% higher at the four landmark time points) than that of landmarking approach. Apart from the final landmark point (at 2.5 years), dynamic prediction based on joint models has also performed slightly better in terms of calibration. The expected prediction errors (PE) for joint models were 0.70, 2.56 and 2.04% lower at the first three landmark time points, respectively, compared to the landmarking approach. In general, joint modelling approach has performed better than the landmarking approach in terms of both discrimination (dynAUC) and calibration (PE), although the margin of gain in performance by using joint models over landmarking was relatively small indicating that landmarking approach was close enough, despite not having a precise statistical model characterising the evolution of the longitudinal markers. Future comparative studies should consider extended versions of joint modelling and landmarking approaches which may overcome some of the limitations of the standard methods.