Below, Dr. Nicholas Coombs introduces us to the concept of survival analysis and its utility within clinical research.
Understanding a patient’s response to healthcare treatment is fundamentally necessary to improve their health outcomes, quality of life, and overall survivorship. Typically, response to treatment is measured over a period of time with either continuous and/or categorical indicators. Thus, various forms of regression analysis are often used to measure these patient-centered outcomes. For instance, linear regression is often used to measure a continuous outcome, logistic regression is used to measure a dichotomous (yes/no) outcome, and Poisson regression is used to measure a count outcome. Survival analyses is another form of regression analysis that considers an outcome with more time-based precision, one that is both dichotomous and linear. It is a “time-to-event” that measures the duration of time that has lapsed before an outcome is (or is not) experienced.
The term “survival” is used because mortality is the most commonly used health outcome when considering time-to-event. However, any health outcome in clinical research may be used in survival analysis (e.g. incidence of re-hospitalization, suicide attempt, or an adverse side effect from treatment). Survival analysis may be used so long as both time and event are adequately captured from a patient population. It is perhaps the best tool to answer time-to-event questions in clinical research and sufficiently addresses censorship (when patients drop out of a study or are lost to follow-up).
Time-to-event studies typically employ a Kaplan-Meier (K-M) analysis. The statistical output for a K-M analysis offers a visual representation of predicted survival curves (i.e. from not experiencing the event of interest). It is not a smooth curve or line; rather, it has a distinctive monotonic (one-direction) stair-step appearance that represents the passage of time and occurrence of events (see the figure below). For any K-M estimator, the horizontal x-axis represents the variable of time expressed in a linear fashion (e.g. weeks, months, years, etc.), while the y-axis represents the percent of patients who “survive” or do not experience the event. For this reason, at a time-point of zero, all patients start at the top of the y-axis (1.0 or 100%), as this indicates that patients have not yet experienced the event. Each time a patient experiences an event, the K-M curve drops down and continues horizontally, indicating the percentage of surviving patients has reduced.
Here, we see a hypothetical K-M analysis comparing survival rates between Cohort A and Cohort B. Let’s assume the x-axis is a measure of months, and the outcome is mortality. Note that both cohorts had a survival rate of 100% at zero months. After two months, one patient in Cohort B died, which brought Cohort B’s survival probability to 80%. Cohort A did not experience a patient death until 3 months, which then brought Cohort A’s survival probability to 90%. This stairstep pattern continues when any death occurs in either group. After 12 months, we noted the survival probability for Cohort A is approximately 45%, whereas the survival probability of Cohort B is only 25%. This might suggest that whatever treatment that is unique to patients in Cohort A may account for their increased and extended likelihood survival as compared to patients in Cohort B.
The tick marks present in this K-M analysis indicate censored patients-indicating that a patient was followed for that duration and (for whatever reason) was not followed up beyond that point. Unlike a patient dying and changing the direction of the line, this tick mark denotes that the denominator is reduced by one. In clinical research, having a strong visual tool to examine a time-to-event with the ability to mark instances where patients were no longer followed up is a multi-purposeful and handy tool to have on hand. More details can be found in the paper below.
If this analysis is of interest to you, or you have additional questions, feel free to reach out to us at ContactUs@PiedmontResearch.org
Reference
*Dudley, W. N., Wickham, R., & *Coombs, N. (2016). An Introduction to Survival Statistics: Kaplan-Meier Analysis. Journal of the advanced practitioner in oncology, 7(1), 91–100. https://doi.org/10.6004/jadpro.2016.7.1.8
