Background: The characterizing symptom of Alzheimer disease (AD) is cognitive deterioration. While much recent work has focused on defining AD as a biological construct, most patients are still diagnosed, staged, and treated based on their cognitive symptoms. But the cognitive capability of a patient at any time throughout this deterioration reflects not only the disease state, but also the effect of the cognitive decline on the patient's pre-disease cognitive capability. Patients with high pre-disease cognitive capabilities tend to score better on cognitive tests that are sensitive early in disease relative to patients with low pre-disease cognitive capabilities at a similar disease stage. Thus, a single assessment with a cognitive test is often not adequate for determining the stage of an AD patient. Repeated evaluation of patients' cognition over time may improve the ability to stage AD patients, and such longitudinal assessments in combinations with biomarker assessments can help elucidate the time dynamics of biomarkers. In turn, this can potentially lead to identification of markers that are predictive of disease stage and future cognitive decline, possibly before any cognitive deficit is measurable. Methods and Findings: This article presents a class of statistical disease progression models and applies them to longitudinal cognitive scores. These non-linear mixed-effects disease progression models explicitly model disease stage, baseline cognition, and the patients' individual changes in cognitive ability as latent variables. Maximum-likelihood estimation in these models induces a data-driven criterion for separating disease progression and baseline cognition. Applied to data from the Alzheimer's Disease Neuroimaging Initiative, the model estimated a timeline of cognitive decline that spans ~15 years from the earliest subjective cognitive deficits to severe AD dementia. Subsequent analyses demonstrated how direct modeling of latent factors that modify the observed data patterns provides a scaffold for understanding disease progression, biomarkers, and treatment effects along the continuous time progression of disease. Conclusions: The presented framework enables direct interpretations of factors that modify cognitive decline. The results give new insights to the value of biomarkers for staging patients and suggest alternative explanations for previous findings related to accelerated cognitive decline among highly educated patients and patients on symptomatic treatments.