BMTRY 722 (Summer 2015): Homework 2
1. Below is a set of relapse times in patients in a pancreatic cancer clinical trial:
c(5, 7+, 10, 12, 12, 20, 24, 24+, 29+)
For a-g do all the calculations by hand or with a calculator (i.e. not on the computer).
(a) Write the data in tabular form with columns for time, number of events at time t, number of
censored subjects at time t, and the risk set at time t
(b) Calculate the estimated survival, S(t), for each time using the Kaplan-Meier approach
(c) Calculate the estimated survival using the Nelson-Aalen approach
(d) Plot the survival curves for the estimate in b and c
(e) Calculate the 90% pointwise confidence intervals for each time t
(f) Report the median survival and calculate the 90% confidence interval for median survival using
the Brookmeyer-Crowley approach
(g) Calculate and plot 90% confidence bands for the Kaplan-Meier survival curves using the whole
range of t. Comment on the impact on the confidence bands if you decrease the range of t.
Note: Chose one method for calculating confidence intervals and bands for the KM estimate (just be
sure to note which one you used and why).
3. Do problem 4.7 in K & M. Write an R function to calculate the risk set and survival function in the
event of left-truncated and right censored data to verify your results for the truncated analysis.
2. Using the Klein and Moeschberger data in problem 4.9 and treating thymic lymphoma as the event of
interest:
(a) Use a non-competing risks approach to estimate the risk of thymic lymphoma as a function of
time
(b) Use a competing risks approach and repeat (a) accounting for other risks and censoring
(c) Summarize what you learned comparing the results of (a) and (b)
4. Find the variance estimate of log(-log(S(t))) and show how you would construct a confidence interval
for this estimate of the original S(t) scale.