Accounting for random observation time in risk prediction with longitudinal markers: An imputation approach

Longitudinally measured biomarkers are useful to predict the risk of clinical endpoints, since subject-specific marker trajectory contains additional information on pathology and critical windows. The work is motivated by the Scandinavian Fetal Growth Study, aiming at predicting pregnancy outcomes with repeated ultrasound measurements during pregnancy. While the observation time of markers often varies across individuals, it is not well understood how the variations affect risk prediction. Existing methods of longitudinal risk prediction, such as shared random effects model and pattern mixture model, construct a prediction implicitly as a function of the biomarkers and their observation time. Methods that ignore the longitudinal structure, such as sufficient dimension reduction and logistic regression, have better interpretability regarding how a biomarker measured at specific time window contributes to the disease risk, but often have reduced accuracy because of ignoring the observation time information. We propose a novel imputation approach to handle the random observation time, while preserving the direct interpretation. Through extensive simulation studies and analyses of the Scandinavian Fetal Growth Study data, we systematically compared the discrimination and calibration performance of different risk prediction methods, and found that the imputation method has comparable performance to longitudinal methods with an advantage of better interpretability.