Survival data analysis is a vital area of statistics that helps researchers understand outcomes such as time to disease onset, recovery after treatment, or mortality. This type of analysis provides health professionals with insights into how various factors, such as treatments or risk exposures, affect patient outcomes over time. However, current methods for analyzing survival data using semiparametric linear models often face limitations: they either involve significant computational challenges or rely on inaccurate approximations. This project addresses these gaps by developing new and more accurate statistical methodologies that are also computationally efficient. These tools will improve our ability to assess the impact of clinical and environmental factors on survival, ultimately supporting better disease prevention and treatment strategies. In doing so, the research promotes national health, enhances healthcare effectiveness, and contributes to overall societal well-being. Beyond its technical contributions, the project delivers broad societal benefits through its strong commitment to education, collaboration, and open science. The investigators will mentor graduate students and create new interdisciplinary coursework at the intersection of statistics and medicine. All developed software tools will be made openly available to encourage reproducibility and accessibility in scientific research. By fostering collaboration across statistics, medicine, and computer science,