ST332/ST409 Medical Statistics 2023-24: Practical 3
1. Consider the following data taken from a study taken from patients diagnosed with pancreatic cancer. The data are the survival times (in months) following diagnosis with a particular variant for 10 patients, where * indicates right censoring. Data; 3, 5, 11, 11, 12*, 20, 48, 48*, 57, 60*.
a. Write out the Kaplan-Meier life-table to estimate the survival function.
b. Write down the estimate of the survival function at t = 6 and t = 36 months.
c. Estimate the variance of the survival function at t = 6 and t = 36 months, using the simple approximation.
d. Estimate the variance of the survival function at t = 6 and t = 36 months, using Greenwood's formula.
e. Type the data into R and use the function survfit to verify that your Kaplan-Meier life-table is correct. Which formula does R use to estimate the standard error? [HINT: you will need a variable for times and a variable for death/censoring. To use survfit you will need the survival package in R].
f. Produce a Kaplan-Meier plot using the results of survfit.
g. Write out the actuarial life-table estimate using fixed intervals of 1 year duration.
h. What is the median survival time and 95% CI from survfit? What is the restricted mean survival time (with an upper limit of 50 months)? [Hint: look at the help for print and survfit]
2. Consider the following additional data taken from a different arm of the same pancreatic cancer study. In this arm, patients were given a new drug alongside the treatment given in Q.1. Data are; 1, 1, 1, 1, 1, 60*, 60*, 60*, 60*, 60*, 60*, 60*, 60*, 60*, 60*, 60*, 60*, 60*, 60*, 60*.
a. Perform. a log-rank test to determine if there is a statistically significant difference in survival between the two groups.
b. Type the additional data into R and use the survdiff function to verify the p-value produced by your hypothesis test is correct.
c. Produce two Kaplan-Meier curves on the same plot, showing the survival curves for the two arms of the trial.
d. Calculate the restricted mean survival time (with an upper limit of 50 months) for the new drug group, and calculate the difference in restricted mean survival time between the groups together with a 95% CI and perform a hypothesis test (with a null hypothesis of no difference).
e. What can you conclude about the effectiveness of the new drug?