Clinical event sequences consist of hundreds of clinical events that represent records of patient care in time. Developing accurate predictive models of such sequences is of a great importance for supporting a variety of models for interpreting/classifying the current patient condition, or predicting adverse clinical events and outcomes, all aimed to improve patient care. One important challenge of learning predictive models of clinical sequences is their patient-specific variability. Based on underlying clinical conditions, each patient's sequence may consist of different sets of clinical events (observations, lab results, medications, procedures). Hence, simple population-wide models learned from event sequences for many different patients may not accurately predict patient-specific dynamics of event sequences and their differences. To address the problem, we propose and investigate multiple new event sequence prediction models and methods that let us better adjust the prediction for individual patients and their specific conditions. The methods developed in this work pursue refinement of population-wide models to subpopulations, self-adaptation, and a meta-level model switching that is able to adaptively select the model with the best chance to support the immediate prediction. We analyze and test the performance of these models on clinical event sequences of patients in MIMIC-III database.