STA 5179 Spring 2015
E. Slate
STA 5179: Solution 2
1. KM exercise 3.6. For subject i, let Xi be the time to relapse, let Yi be the time to death
following relapse, and let Ci be the censoring time. (In this study, even though there are two
outcomes per su
STA 5179 Spring 2015
E. Slate
STA 5179: Solution 4
1.0
1. KM exercise 8.2. Figure 1 shows the Kaplan-Meier survival curves for the routine and
chlorhexidine cleansing groups. It appears chlorhexidine cleansing is an improvement in that
time to infections
STA 5179 Spring 2015
E. Slate
STA 5179: Solution 5
1. KM exercise 9.4. An appropriate model is
h(t | group, A(t), C(t) = h0 (t)
exp cfw_L I(AML-low) + H I(AML-high) + A A(t) + C C(t) + AC A(t)C(t) ,
where group represents the disease group (ALL, AML-low o
STA 5179 Spring 2015
E. Slate
STA 5179: Solution 3
1. KM exercise 4.4. We model (nonparametrically) the time to infection for the two catheter
placement groups. Figure 1 shows the Kaplan-Meier curves (S, for the two groups, together
with 95% pointwise con
STA 5179 Spring 2015
E. Slate
STA 5179: Exam 1 Due Thursday March 5 in class.
May be submitted by hand to Dr. Slate or by email to [email protected] If you use email, I will
reply conrming I received your exam. If you do not receive the conrmation, please c
STA 5179 Spring 2015
E. Slate
STA 5179: Homework 1 Solution
1.
(i) The likelihood of the n iid observations here (with = 3) is
n
L()
3n
xi .
expcfw_
i=1
Hence the derivative of the log-likelihood function is () = 3n1 n, which implies
x
= 3/. We also nd
STA 5179 Spring 2015
E. Slate
STA 5179: Exam 2
Due Friday April 24 by 5:00pm
May be submitted by hand to Dr. Slate or by email to [email protected] If you use email, I will
reply conrming I received your exam. If you do not receive the conrmation, please co
STA 5179 Spring 2015
E. Slate
STA 5179: Exam 2 Sketch solutions
1. A study recruited 250 women with primary node positive breast cancer and followed them
from diagnosis to recurrence or death (or censoring). The data contain the following variables:
Varia
STA 5179 Spring 2015
E. Slate
STA 5179: Counting Process Useful Facts
Let X be the survival time of interest (right censored and possibly left truncated). Dene
hazard
h(t) = limdt0
1
dt
Pr(t X < t + dt | X t)
t
0 h(s) ds
cumulative hazard
H(t) =
at risk
Y
The time-to-event variable, X
Let X be the time to event. X is a r.v., X 0.
To model X , we might specify the cdf , F (x) = Pr(X x).
Advantage: same for X discrete and continuous
F () is nondecreasing, right continuous
F () = 0, F () = 1
Equivalently, spe
Recurrent Events
Recurrent infections among people with AIDS
Recurrent heart attacks, strokes, skin cancer, colon polyps
Recurrent hospitalization
Recurrent crimes, jobs
Recurrent part failures, software bugs, hack attacks
Recurrent Events: Bladder Cancer
Multivariate Survival Data
Suppose the subjects in our time-to-event study naturally cluster:
families
clinics
litters
laboratories
Survival times for subjects within a cluster are not independent.
But clusters are still independent.
One approach: shared
STA 5179 Spring 2015
E. Slate
STA 5179: Nonparametric likelihood for Survival
Nonparametric estimation for survival data begins with estimation of the survival function, S(t) =
Pr(T > t) where T is the time to the event of interest. (We have used X instea