A tutorial on dynamic risk prediction of a binary outcome based on a longitudinal biomarker

Abstract

Dynamic risk predictions based on all available information are useful in timely identification of high‐risk patients. However, in contrast with time to event outcomes, there is still a lack of studies that clearly demonstrate how to obtain and update predictions for a future binary outcome using a repeatedly measured biomarker. The aim of this study is to give an illustrative overview of four approaches to obtain such predictions: likelihood based two‐stage method (2SMLE), likelihood based joint model (JMMLE), Bayesian two‐stage method (2SB), and Bayesian joint model (JMB). We applied the approaches to provide weekly updated predictions of post–molar gestational trophoblastic neoplasia (GTN) based on age and repeated measurements of human chorionic gonadotropin (hCG). Discrimination and calibration measures were used to compare the accuracy of the weekly predictions. Internal validation of the models was conducted using bootstrapping. The four approaches resulted in the same predictive and discriminative performance in predicting GTN. A simulation study showed that the joint models outperform the two‐stage methods when we increase the within‐ and the between‐patients variability of the biomarker. The applicability of these models to produce dynamic predictions has been illustrated through a comprehensive explanation and accompanying syntax (R and SAS®).

Joint modeling versus discriminant analysis for dynamic prediction of a binary outcome based on longitudinal data: A simulation study

“…The joint model will not capture the differences in variability between the two groups since we only fit one mixed effects model for both groups, whereas in the LoDA the variability is better captured using a mixed model per outcome group. One way to improve the discrimination power of the joint model is to incorporate the within-subjects variability i.e., the subject-specific residual variance, 2 , as a predictor in the logistic submodel, similar to the work done by Parker et al (2019), where they jointly model the individual trajectories, within-individual variability and a later continuous outcome (12).…”

“…In our simulations, we implement the Bayesian framework to the JM-Bin approach. Since our prior knowledge is limited, we use proper but vague prior distributions which are commonly used for the model's location and dispersion parameters, see Dandis et al, 2019 for more details (2). We apply the MCMC technique, where two chains are initiated with 1,000 burn-in iterations and are run for 10,000 iterations.…”

“…In general, the hCG levels for the subjects who develop GTN (GTN patients) are higher and more stable compared to the hCG levels for the healthy subjects, which start at lower levels and decrease with time. These data have been analysed elsewhere (2,10,11).…”

“…In a previously published paper we presented a tutorial for using different SREM approaches to obtain dynamic prediction for a binary outcome (2). The presented SREM approaches consist of two sub-models.…”

“…1 ) , and ( ) represents a normal density distribution with mean 0 and variance2 . Likewise, ( ) is a bivariate normal density with mean zero and covariance matrix Σ.…”