158The Essentials of Biostatistics for Physicians, Nurses, and Clinicians,
First Edition. Michael R. Chernick.
© 2011 John Wiley & Sons, Inc. Published 2011 by John Wiley & Sons, Inc.
CHAPTER 10
10. Survival Analysis
Survival analysis is based on data where patients are followed over
time until the occurrence of a particular event such as death, relapse,
recurrence, or some other event that is of interest in to the investigator.
Of particular interest is the construction of an estimate of a survival
curve which is illustrated in Figure 10.1. Survival probability at t rep-
resents the probability that an event does not occur by time t.
In the fi gure, the x - axis shows time in years and the y - axis survival
probability. In this case, the function S ( t ) is a Weibull curve with
S ( t ) = exp( − ( λ t ) β^ ) and λ = 0.4 and β = 2.0. In a clinical study, S ( t )
represents the probability that the time from initiation in the study
( t = 0) until the occurrence of the event for an arbitrary patient is
greater than a specifi ed value t. The curve represents the value for this
probability as a function of t. Data on the observed time to the event
for each patient is the information to use to estimate the survival curve
for all t in (0, ∞ ). See Section 10.4.2 for more details on the Weibull
family of survival curves.
The survival curve or the comparison of two or more survival
curves is often important in determining the effectiveness of a new
treatment. It can be used for effi cacy as in the case of showing that an
anticoagulant is effective at reducing stroke for patients with atrial
fi brillation. More often, it is used as a safety parameter, such as in the