Understanding the association of risk factors with longitudinal change in biomarker measurements is an essential theme in epidemiological and clinical research. In this talk, we consider semiparametric models of marker trajectories on a clinically meaningful time interval between an initiating event and a failure event. In real applications, subjects can enter a study with or without experiencing the initiating event, and may not encounter the failure event during the follow-up period; moreover, the markers are usually intermittently observed at baseline and follow-up visits. As a result, analytical challenges includes late-entry bias and irregular observations of the marker on the time scale of interest. To tackle these problems, we propose estimating equations where nuisance parameters are eliminated using local estimates of representative samples of the underlying population. We establish the large-sample properties of the proposed estimators. Simulation studies and a data example are presented to illustrate the proposed methodology.