In many longitudinal clinical studies, the level and progression rate of repeatedly measured biomarkcrs on each subject quantify the severity of the disease and that subjects susceptibility to progression of the disease.It is of scientific and clinical interest to relate such quantities to a later time-to-event clinical endpoint such as patient survival.This is usually done with a shared parameter model.In such mod els, the longitudinal biomarker data and the survival outcome of each subject are assumed to be conditionally independeut given subject-level severity or susceptibil ity (also called frailty in statistical terms).In this paper, we study the case where the conditional distribution of longitudinal data is modeled by a linear mixed-effect model, and the conditional distribution of the survival data is given by a Cox propor tional hazard model.We allow unknown regression coefficients and time-dependent covariates in both models.The proposed estimators are maximizers of an exact correction to the joint log-likelihood with the frailties eliminated as nuisance param eters, an idea that originated from error correction in measurement error models.The corrected joint log likelihood is shown to be asymptotically concave and leads to consistent and asymptotically normal estimators.Unlike most published methods for joint modeling, the proposed estimation procedure does not rely on distributional assumptions of the frailties.The proposed method was studied in simulations and applied to a data set from the NIH-sponsored Hemodialysis (HEMO) Study.