Survival Analysis: An Application with Censored Head and Neck Cancer Data

Survival analysis is a branch of statistics focused on estimation for time to event data. Many specialized fields rely on survival analysis to gain insight into what factors impact the time to an event. Some notable examples include the fields of medicine, engineering, and biology. Using a dataset provided by McGill University containing 298 patients diagnosed with head and neck squamous cell carcinoma, we investigate what factors impact the survival prognosis of patients and determine the shape of their hazard rate. We employ non-parametric, semi-parametric, and parametric modeling techniques in our analysis. A Kaplan-Meier estimator indicates that survival prognosis differs by both hospital and primary site of cancer. However, a Cox proportional hazards model and a log normal model find no evidence of an effect of hospital on survival prognosis. Furthermore, the Cox and log normal models determine that locoregional failure and distant metastasis both negatively impact survival prognosis. The log normal model determines that increases in age negatively impact survival prognosis, while the Cox model indicates that having the oropharynx as the primary site of cancer positively impacts survival prognosis. Finally, the log normal model indicates that the patients’ hazard rate is hump shaped, meaning that their risk of death increases and then decreases during their time on study