Survival Analysis

INTRODUCTION TO SURVIVAL ANALYSIS
What is Survival Analysis? 

Survival Analysis is referred to statistical methods for analyzing survival data 

Survival data could be derived from laboratory studies of animals or from clinical and epidemiologic studies 

Survival data could relate to outcomes for studying acute or chronic diseases 

What is Survival Time? 

Survival time refers to a variable which measures the time from a particular starting time (e.g., time initiated the treatment) to a particular endpoint of interest (e.g., attaining certain functional abilities) 

It is important to note that for some subjects in the study a complete survival time may not be available due to censoring 

Censored Data 

Some patients may still be alive or in remission at the end of the study period 

The exact survival times of these subjects are unknown 

These are called censored observation or censored times and can also occur when individuals are lost to follow-up after a period of study 

Random Right Censoring 
Suppose 4 patients with acute leukemia enter a clinical study for three years 
Remission times of the four patients are recorded as 10, 15+, 35 and 40 months 
15+ indicate that for one patient the remission time is greater than 15 months but the actual value is unknown .

Important Areas of Application 
•Clinical Trials (e.g., Recovery Time after heart surgery) 
•Longitudinal or Cohort Studies (e.g., Time to observing the event of interest) 
•Life Insurance (e.g., Time to file a claim) 
•Quality Control & Reliability in Manufacturing (e.g., The amount of force needed to damage a part such that it is not useable) 
Survival Function or Curve 
Let T denote the survival time
S(t) = P(surviving longer than time t )
= P(T > t) 
The function S(t) is also known as the cumulative survival function. 0£ S( t ) £ 1 
Ŝ(t)=number of patients surviving longer than t 
The Logrank Test 
SPSS, SAS, S-Plus and many other statistical software packages have the capability of analyzing survival data 
Logrank Test can be used to compare two survival curves 
A p-value of less than 0.05 based on the Logrank test indicate a difference between the two survival curves 
Hazard Function 
The hazard function h(t) of survival time T gives the conditional failure rate 

The hazard function is also known as the instantaneous failure rate, force of mortality, and age-specific failure rate 
The hazard function gives the risk of failure per unit time during the aging process 
Multivariate Analysis: (CPHM) Cox's Proportional Hazards Model 
CPHM is a technique for investigating the relationship between survival time and independent variables 
A PHM possesses the property that different individuals have hazard functions that are proportional to one another 
Comparing the survival curves by Age Groups after Adjusting Cellularity using CPHM 
Comparing the survival curves by Cellularity Groups after Adjusting Age using CPHM