BIOS 280
                           Survival Analysis
                               Homework 1


Do not present any computer output unless it was explicitly requested.
Just describe what you did, if necessary, and copy whatever numbers you
think are relevant.
Example files: LIFETST1.SAS LIFETST2.SAS PBC06.S PBC07.S
               WEIBULL3.SAS  

1.

Verify that for the case of no censoring the Kaplan-Meier estimator
reduces to the empirical cumulative distribution function and that
Greenwood's formula reduces to the usual binomial variance formula.



2.
Find out what formula the S+ software uses to compute confidence
intervals for S(t).



3.
(Files: PBC312.DAT and PBC.DOC. Also appendix of F&H).

Use graphical methods to explore the distribution of survival times in
the placebo group (z1=2, n=154) and comment on the feasability of some
of the common parametric forms.

Fit an exponential model and overlay on the same graph the Kaplan-Meier
estimate of S(t) with that based on assuming an exponential
distribution.  Present the graph.  Comment.


4.
Obtain a Kaplan-Meier estimate of S(t) for the treatment group (z1=1,
n1=158) and the placebo group (z1=2, n2=154).  Overlay the two graphs.
Comment.



5.
Suppose that T > 0 has a continuous distribution function F with
cumulative hazard H. What is the distribution of H(T)?



6.
Suppose that T > 0 has a continuous distribution function F with
cumulative hazard H. Let c > 0 be a constant and X=min(T, c).  Show that
E[H(X)] = F(c).



K+P problem 17
K+P problem 18