ERASMUS

Survival Analysis

Exercises for Tuesday (Day 2)

Introduction to Cox Regression:

1. On the class web page is data from a study of 268 children with acute lymphoblastic leukemia (ALL) that was considered in Exercise #1.

(a) Use Cox regression to estimate the increase (decrease) in the risk of relapse associated with treatment. Provide an estimate of the hazard ratio, a confidence interval, and summarize these estimates in language appropriate for a general scientific audience.

(b) Use Cox regression to estimate the increase (decrease) in the risk of relapse associated with treatment controlling for the white blood cell count (WBC) and age. Provide an estimate of the treatment hazard ratio, a confidence interval, and summarize these estimates in language appropriate for a general scientific audience. Comment on the relapse risk associated with WBC. Justify the model choices that you have made (e.g. using categories of WBC and/or a linear or non-linear form).

(c) The investigators wanted to know if the treatment was particularly beneficial (harmful) for subsets of the patient population. In particular, the investigators sought to determine whether treatment effect differed for subjects with a white blood cell count of less than 5,000/(mm^3) (i.e. wbc < 50), or greater than 20,000/(mm^3) (i.e. wbc > 200). Summarize the results of your analysis to address this question.

(d) Use Cox regression to estimate the increase (decrease) in the risk of relapse associated with treatment controlling for the white blood cell count (WBC), age, and the recruitment site (institution). Provide an estimate of the treatment hazard ratio, a confidence interval, and summarize these estimates in language appropriate for a general scientific audience. Justify the model choices that you have made (e.g. the method by which you control for site).

Estimating Survival Distributions:

2. Please answer the following questions regarding the ALL data.

(a) Based on the regression model that you have used in 1(b) please display estimates of the relapse-free survival curves for:

subject with treatment, and WBC = 45, age = 5

subject with no treatment, and WBC = 45, age = 5

subject with treatment, and WBC = 210, age = 5

subject with no treatment, and WBC = 210, age = 5