The main theme of the research is to develop new methodologies for resolving statistical issues emerging from our team's collaborations in cohort studies of underrepresented and overall US aging populations with a particular interest in Alzheimer's disease (AD). We focus on making appropriate statistical inference for censored survival data with partially known risk sets, developing methods for assessing prediction precision for recurrent events survival data including time-dependent ROC and extension of the C-index, and developing new conditional modeling strategies that best model life history processes during the lifespan. We also plan to develop publicly available statistical software with the goal of dissemination and generalization. The proposed methods of estimating time-dependent ROC and C-index for recurrent events extend those for a single survival time by taking into account different models for recurrent events, producing novel predictive models for recurrent events when there are possible missing events. Such predictive models are useful in estimating the partially observed risk sets which would lead to appropriate parameter estimation in regression analysis for censored survival data, in particular, time of AD onset, using the proposed weighted estimating approaches. In AD research, death as a terminal event occurs frequently in aging cohorts. The proposed conditional modeling strategy allows us to investigate AD events during the entire lifespan, which provides a clearer picture of the relationships among AD onset, death, other life evens, and risk factors, thus a better understanding of AD etiology and prevention. The method also provides a straightforward thus more precise estimation of AD prevalence that is potentially impactful to health care policy making. These methods are motivated from and will be applied to a wide range of datasets, including the Indian Health Service – a unique source for studying the disproportionate burden of AD among Native American populations, the Aging, Demographics and Memory Study – a subset of the Health and Retirement Study representing an ideal observation cohort study for studying the epidemiology of AD in the Black and Latinx communities, the National Alzheimer's Coordinating Center uniform data sets collected by more than ADRCs in the US from their longitudinal cohorts, the 90+ study that focuses on aging and dementia of the oldest old population, and the CMS Limited Data Set that is a random sample of Medicare/Medicaid claims data accessible for research purposes – the most representative data of the US aging population. The methods will be widely applicable to problems in many other fields of biomedical research.