The main theme of the research is to develop new methodologies for resolving statistical issues emerging from our team’s long-term collaborations in cohort studies of aging populations and patients with kidney disease. We focus on developing robust and efficient estimating procedures for regression parameters from data with delayed entry in prevalent cohort studies, making appropriate and efficient statistical inference when covariates are subject to censoring and measurement error, and developing new strategies that best model the effects of terminal events on longitudinal measurements. We also plan to develop publicly available statistical software with the goal of dissemination and generalization. The proposed approach for delayed entry is based on an augmented conditional likelihood constructed from truncation times without specifying the truncation distribution, which leads to a more efficient estimator. The proposed approach for regression models for longitudinal data with censored covariates addresses some serious issues with the common nonparametric and parametric methods. For example, the nonparametric methods cannot recover any tail information for the censored covariates due to limit of detection, while the parametric methods may yield biased results due to model misspecification. Our method will facilitate investigation of covariates subject to limit of detection together with measurement error, reflecting the reality of many lab measures. The proposed statistical models for longitudinal data with the occurrence of a terminal event reflect the reality that the relationship between a response variable and covariates is approximately the same as the usual marginal model (without considering terminal event) when data are observed far from the terminal event, but becomes heavily dependent on the terminal event time when data collecting time is close to the terminal event. These methods are motivated from and will be applied to a wide range of datasets, including the kidney disease progression data, the kidney transplant registry data, the women’s health longitudinal data collected from the Michigan Bone Health and Metabolism Study and the Study of Women's Health Across the Nation, and the longitudinal end stage renal disease medical cost data. The methods will be widely applicable to problems in many other fields of biomedical research.