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?
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