## Description

1. Determine the survival and density functions for a continuous survival time variable

with hazard function

h(x) = 2x

(1 + x

2

)

.

Hint: consider the derivative of log(1 + x

2

).

2. For the following data

1, 2, 2, 4+, 5+, 6, 7+, 8+, 9+, 10+,

where + denotes a right censored observation. Write out the data table and calculate

the following by hand.

(a) Find the Kaplan-Meier estimate of the survival function;

(b) Find the Nelson-Aalen estimate of the cumulative hazard function;

(c) Find the Fleming-Harrington estimate of the survival function.

3. Use the tongue data in the R package KMsurv. For each tumor type (aneuploidy

and diploid), plot the Kaplan-Meier curve of survival function and its pointwise 95%

confidence intervals (using the log transformation). What are the estimated 1-year

survival rate and 95% CI?

1