4.1
4. Proportional Hazard Model
In medical study, it is often to not only measure the lifetime of the
subject but some additional characteristics that may aect the lifetime
demographic variables: Age, gender, socio-economic status, education
behaviora
3.1
Hypothesis Testing
One sample test
A censored sample of size n from some population
Want to test the hypothesis that the population hazard
rate is h0(t) for all t , i.e.,
H0 : h(t) = h0(t), 0 < t
Typically, take to be the largest of the observed
2.1
Likelihood Construction for Censored Data
Likelihood function:
If x1, x2, . . . , xn are the values of a sample from a population with parameter , the likelihood function of the sample
is given by
L() = f (x1, x2, . . . , xn; )
for the values of with
1.1
1 Introductory Notes and Concepts
1.1. What is survival analysis?
Analysis of failure time
Failure time = Time to a point event occurs
Examples:
Lifetime of machine components
Time from diagnosis to death in a clinical trial
duration of an industri
Inference for Exponential Distribution
f (t) = exp (t)
1
t
= exp
(1)
where = 1/ = E (T ) which is the mean lifetime
1. Complete Sample
Let t1, t2, . . . , tn be a random sample of size n from exponential
distribution with density function (1)
Then the