Why is the survival curve important in radiation therapy?
This ensures that the effect of the radiation dose can be separated from the other factors. Surviving Fraction versus Dose: The Cell Survival Curve A plot of the surviving fraction of cells as a function of the radiation dose is called the cell survival curve.
What happens to the survival curve as time goes to infinity?
As time goes to infinity, the survival curve goes to 0. – In theory, the survival function is smooth. In practice, we observe events on a discrete time scale (days, weeks, etc.). • The hazard function, h(t), is the instantaneous rate at which events occur, given no previous events.
What is a cell survival curve?
Common mathematical models used in analyzing cell survival curves and the key parameters associated with each model Clinically important radiosensitizers and radioprotectors Introduction A cell survival curve is a plot of the number of cells that survive to form colonies as a function of radiation dose.
What is Kaplan-Meier survival curve?
The Kaplan-Meier survival curve is defined as the probability of surviving in a given length of time while considering time in many small intervals.[3] There are three assumptions used in this analysis.
Why is median survival undefined?
The median survival time is defined to be the time at which the survival curve crosses 50% survival. If the curve doesn't cross 50% (because survival is greater than 50% at the last time point), then median survival is simply undefined. More precisely, it is greater than the last time point on your survival curve.
What does a survival curve tell you?
The visual representation of this function is usually called the Kaplan-Meier curve, and it shows what the probability of an event (for example, survival) is at a certain time interval. If the sample size is large enough, the curve should approach the true survival function for the population under investigation.
What makes a valid survival function?
– The survival function gives the probability that a subject will survive past time t. – As t ranges from 0 to ∞, the survival function has the following properties ∗ It is non-increasing ∗ At time t = 0, S(t)=1. In other words, the probability of surviving past time 0 is 1. ∗ At time t = ∞, S(t) = S(∞)=0.
What method can be used to estimate the survival curve?
The Kaplan–Meier estimator, also known as the product limit estimator, is a non-parametric statistic used to estimate the survival function from lifetime data. In medical research, it is often used to measure the fraction of patients living for a certain amount of time after treatment.
How do you analyze a survival plot?
Survival analysis is used in several ways:To describe the survival times of members of a group. Life tables. Kaplan–Meier curves. ... To compare the survival times of two or more groups. Log-rank test.To describe the effect of categorical or quantitative variables on survival. Cox proportional hazards regression.
What are the assumptions of survival analysis?
Survival analysis techniques make use of this information in the estimate of the probability of event. An important assumption is made to make appropriate use of the censored data. Specifically, we assume that censoring is independent or unrelated to the likelihood of developing the event of interest.
What is failure time in survival analysis?
Failure time analysis (Ff A), or survival analysis, addresses data of the form "time until an event occurs." The survival times of medical patients or industrial products have been the usual subjects ofFf A, but data from a wide variety of ecological studies may be cast in these terms, including survival times of ...
What is left censoring in survival analysis?
Left-censored In contrast to right-censoring, left censoring occurs when the person's true survival time is less than or equal to the observed survival time. An example of a situation could be for virus testing.
What is survival analysis explain clearly with an example?
Survival analysis is a model for time until a certain “event.” The event is sometimes, but not always, death. For example, you can use survival analysis to model many different events, including: Time the average person lives, from birth. Time after cancer treatment until death.
What does censoring mean in Kaplan-Meier?
Censoring has an effect on the survival rates. Censored observations that coincide with an event are usually considered to fall immediately after the event. Censoring removes the subject from the denominator, i.e., individuals still at risk.
How do you explain Kaplan Meier curve?
The Kaplan Meier Curve is the visual representation of this function that shows the probability of an event at a respective time interval. The curve should approach the true survival function for the population under investigation, provided the sample size is large enough.
When do you use Kaplan-Meier vs Cox regression?
KM Survival Analysis cannot use multiple predictors, whereas Cox Regression can. KM Survival Analysis can run only on a single binary predictor, whereas Cox Regression can use both continuous and binary predictors. KM is a non-parametric procedure, whereas Cox Regression is a semi-parametric procedure.
Radiation Toxicology, Ionizing and Nonionizing
Cell-survival curves are used to describe the relationship between radiation dose and the proportion of cells that survive. Usually mathematical models are used to describe cell survival data. Survival of normal cells is an important consideration in radiation therapy.
Radiobiology of Lung Cancer
Jose G. Bazan, ... Daniel Zips, in IASLC Thoracic Oncology (Second Edition), 2018
Radiation Therapy Physics and Treatment Optimization
Cell survival curves often have a shoulder in the dose region around 2 Gy, which is the normal clinical dose per fraction. At high doses, the clonogenic survival of a homogeneous cell population approaches a stochastic process with a fixed inactivation cross section.
Physical and Biologic Basis of Radiation Therapy
Eric J. Hall, James D. Cox, in Radiation Oncology (Ninth Edition), 2010
Radiation Therapy Physics and Treatment Optimization
When looking at the cell survival curves for photons and ions, it becomes clear that RBE is determined by the changing slope of the survival curves of photons, while the slope of the survival curve for heavy ions of a given LET is nearly constant and increasing with higher LET values (i.e., steeper survival curves).
Fractionation Effects in Clinical Practice
Søren M. Bentzen PhD, DSc, in Leibel and Phillips Textbook of Radiation Oncology (Third Edition), 2010
Basics of Radiation Therapy
Elaine M. Zeman, ... Joel E. Tepper, in Abeloff's Clinical Oncology (Fifth Edition), 2014
What is survival analysis?
Survival analysis is a statistical method aimed at determining the expected duration of time until an event occurs. In this instance, the event is an employee exiting the business.
What is the challenge of predicting employee turnover?
The challenge with predicting employee turnover is that for anyone that is still employed at the time of observation, their future behaviour is uncertain. They might resign the next day, continue for another ten years, or anything in between. This uncertainty is called "right-censoring". Each line segment below represents the career of an employee from start to finish date. Survival analytics converts these career lengths to tenures to calculate the probability of reaching each milestone.
Is turnover a factor in tenure?
Turnover and tenure have a complex relationship. A business with a high turnover will logically have a lower average tenure, and at the same time tenure is an important factor in the decision to exit. It follows that any analysis of attrition in isolation from tenure will smooth over important insight.
How to estimate survival function?
There are several different ways to estimate a survival function or a survival curve. There are a number of popular parametric methods that are used to model survival data, and they differ in terms of the assumptions that are made about the distribution of survival times in the population. Some popular distributions include the exponential, Weibull, Gompertz and log-normal distributions. 2 Perhaps the most popular is the exponential distribution, which assumes that a participant's likelihood of suffering the event of interest is independent of how long that person has been event-free. Other distributions make different assumptions about the probability of an individual developing an event (i.e., it may increase, decrease or change over time). More details on parametric methods for survival analysis can be found in Hosmer and Lemeshow and Lee and Wang 1,3.
Why is it important to analyze survival data?
Because of the unique features of survival data, most specifically the presence of censoring, special statistical procedures are necessary to analyze these data. In survival analysis applications, it is often of interest to estimate the survival function, or survival probabilities over time.
What is the survival probability of a population of 9 years?
Notice that the survival probability is 100% for 2 years and then drops to 90%. The median survival is 9 years (i.e., 50% of the population survive 9 years; see dashed lines).
What is the term for the time when a participant drops out of a study?
True survival time (sometimes called failure time) is not known because the study ends or because a participant drops out of the study before experiencing the event. What we know is that the participants survival time is greater than their last observed follow-up time. These times are called censored times.
What is the median survival?
The median survival is approximately 11 years. A flat survival curve (i.e. one that stays close to 1.0) suggests very good survival, whereas a survival curve that drops sharply toward 0 suggests poor survival. The figure above shows the survival function as a smooth curve.
How long is a prospective study?
A small prospective study is run and follows ten participants for the development of myocardial infarction (MI, or heart attack) over a period of 10 years. Participants are recruited into the study over a period of two years and are followed for up to 10 years. The graphic below indicates when they enrolled and what subsequently happened to them during the observation period.
Why is it important to record the time of entry in a clinical trial?
Thus, it is important to record the entry time so that the follow up time is accurately measured.
What is median survival time?
The median survival time is defined to be the time at which the survival curve crosses 50% survival. If the curve doesn't cross 50% (because survival is greater than 50% at the last time point), then median survival is simply undefined. More precisely, it is greater than the last time point on your survival curve.
Can you extrapolate the median survival time?
Yes, unless you use a parametric approach and are willing to extrapolate. See SAS Lifereg. The median survival time is defined to be the time at which the survival curve crosses 50% survival. If the curve doesn't cross 50% (because survival is greater than 50% at the last time point), then median survival is simply undefined. ...
Introduction
Learning Objectives
- After completing this module, the student will be able to: 1. Identify applications with time to event outcomes 2. Construct a life table using the actuarial approach 3. Construct a life table using the Kaplan-Meier approach 4. Perform and interpret the log rank test 5. Compute and interpret a hazard ratio 6. Interpret coefficients in Cox proportional hazards regression analysis
Time to Event Variables
- There are unique features of time to event variables. First, times to event are always positive and their distributions are often skewed. For example, in a study assessing time to relapse in high risk patients, the majority of events (relapses) may occur early in the follow up with very few occurring later. On the other hand, in a study of time to death in a community based sample, the majority o…
Introduction to Survival Data
- Survival analysis focuses on two important pieces of information: 1. Whether or not a participant suffers the eventof interest during the study period (i.e., a dichotomous or indicator variable often coded as 1=event occurred or 0=event did not occur during the study observation period. 2. The follow up timefor each individual being followed.
The Survival Function
- In survival analysis, we use information on event status and follow up time to estimate a survival function. Consider a 20 year prospective study of patient survival following a myocardial infarction. In this study, the outcome is all-cause mortality and the survival function (or survival curve) might be as depicted in the figure below. Sample Survival Curve - Probability Of Surviving …
Estimating The Survival Function
- There are several different ways to estimate a survival function or a survival curve. There are a number of popular parametric methods that are used to model survival data, and they differ in terms of the assumptions that are made about the distribution of survival times in the population. Some popular distributions include the exponential, Weibull, Gompertz and log-normal distributi…
Comparing Survival Curves
- We are often interested in assessing whether there are differences in survival (or cumulative incidence of event) among different groups of participants. For example, in a clinical trial with a survival outcome, we might be interested in comparing survival between participants receiving a new drug as compared to a placebo (or standard therapy). In an observational study, we might b…
Cox Proportional Hazards Regression Analysis
- Survival analysis methods can also be extended to assess several risk factors simultaneously similar to multiple linear and multiple logistic regression analysis as described in the modules discussing Confounding, Effect Modification, Correlation, and Multivariable Methods. One of the most popular regression techniques for survival analysis is Cox proportional hazards regression…
Summary
- Time to event data, or survival data, are frequently measured in studies of important medical and public health issues. Because of the unique features of survival data, most specifically the presence of censoring, special statistical procedures are necessary to analyze these data. In survival analysis applications, it is often of interest to estimate the survival function, or survival p…
References
- Hosmer, DW and Lemeshow, S. Applied Survival Analysis: Regression Modeling of Time to Event Data. NewYork: John Wiley and Sons; 1999.
- Cox DR, Oakes D. Analysis of Survival Data, Chapman and Hall, 1984.
- Lee ET and Wang JW. Statistical Methods for Survival Data Analysis. 3rd edition. New York: John Wiley & Sons; 2003.
- Hosmer, DW and Lemeshow, S. Applied Survival Analysis: Regression Modeling of Time to Event Data. NewYork: John Wiley and Sons; 1999.
- Cox DR, Oakes D. Analysis of Survival Data, Chapman and Hall, 1984.
- Lee ET and Wang JW. Statistical Methods for Survival Data Analysis. 3rd edition. New York: John Wiley & Sons; 2003.
- SAS version 9.1© 2002-2003 by SAS Institute, Inc., Cary, NC.
