Introducing Survival Analysis

Survival analysis is a branch of statistics that deals with modeling of time-to-event. In the context of “survival,” the most common event studied is death; however, any other important biological event could be analyzed in a similar fashion (e.g., spreading of the primary tumor or occurrence/relapse of disease). The significant event should be well-defined and occur at a specific time.As the primary outcome event is typically unfavorable (e.g., death, metastasis, relapse, etc.), the event is called a “hazard.” Survival analysis tries to answer questions such as: What is the proportion of a population who will survive past a certain time (i.e., what is the 5-year survival rate)? What is the rate at which the event occurs? Do particular characteristics have an impact on survival rates (e.g., are certain genes associated with survival)? Is the 5-year survival rate improved in patients treated by a new drug? Cox regression and Kaplan-Meier analysis are two techniques which are commonly used to assess survival analysis. 

In survival analysis, the event should be well-defined with two levels and occur at a specific time. Because the primary outcome of the event is typically unfavorable (e.g., death, metastasis, relapse, etc.), the event is called a “hazard.” The hazard ratio is an effect size measure used to assess the direction and magnitude of the effect of a predictor variable on the relative likelihood of the event occurring at any given point in time, while controlling for other predictors in the model. For continuous predictors, such as gene expression values and tumor size, co-predictors (co-variables/co-factors) if added to the model. In other words the hazard ratio is the predicted change in the hazard for a unit increase in the predictorhow rapidly an event is experienced and is a comparison of the hazard between groups. A hazard ratio greater than 1 indicates that the predictor is associated with a shorter time-to-event, a hazard ratio less than 1 indicates that the predictor is associated with a greater time-to-event, and a hazard ratio of 1 indicates that the predictor has no effect on time-to-event. For categorical predictorsexample, if the hazard ratio is relative 2 then there is twice a chance of occurrence compared to the reference categoryother group. 

An important feature aspect of survival analysis is the presence of “censored” data. Censored data refers to subjects that have not experienced the event being studied. For example, medical studies often focus on survival of patients after treatment so the survival times are recorded during the study period. At the end of the study period, some patients are dead, some patients are alive, and the status of some patients is unknown because they dropped out of the study. Censored data refers to the latter two groups. The patients who survived until the end of the study or those who dropped out of the study have not experienced the study event "death" and are listed as "censored". 

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Cox Regression

Cox regression (Cox proportional-hazards model) tests the effects of factors (predictors) on survival time. Predictors that lower the probability of survival at a given time are called risk factors; predictors that increase the probability of survival at a given time are called protective factors. The Cox proportional-hazards model are similar to a multiple logistic regression that considers time-to-event rather than simply whether an event occurred or not. Cox regression should not be used for a small sample size (n < 40) because the events could accidently concentrate into one of the cohorts leading to an infinite hazard ratio which will not produce meaningful results (Xu R, Shaw PA, Mehrotra DV. Hazard ratio estimation in small samples. Stat Biopharm Res. https://shawstat.org/wp-content/uploads/2021/03/Hazard-ratio-estimation-in-small-samples.pdf)

Configuring the Cox Regression Dialogue 

• Open the Cox Regression task in the task menu under Statistics. 

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