ERASMUS

Survival Analysis

Exercises for Monday (Day 1)

One Sample Summaries:

1. On the class web page is data from a study of 268 children with acute lymphoblastic leukemia (ALL). In this study the children were randomized to one of two maintenance regimes after disease remission. One group was assigned to chemotherapy with 6MP and Methotrexate (MTX) (``control group'') while another group also took dactinomycin (``treatment group''). Interest is in the time-until-relapse, and whether the additional treatment was beneficial. Secondary interest is in whether the treatment effect is different for specific subgroups of subjects.

Subjects were recruited into the study from a number of clinical centers.

In addition, the age of the child at entry, and their white blood cell count was recorded. Time is recorded as the time from remission to relapse.

(a) For the entire sample of children produce estimates of survival functions based on: a discretization of the data; using an Exponential model and a Weibull model; and using Kaplan-Meier. Based on these analyses do either of the parametric models appear adequate for the data?

(b) Plot Kaplan-Meier curves for each of the two treatment groups. What do these plots suggest about treatment? Based on these curves estimate the median time-until relapse for each treatment group.

(c) Does it appear that white blood cell (WBC) count predicts time-until-relapse? Provide survival summaries for categories of WBC, and interpret.

(d) Plot estimates of hazard functions for the treatment and the control groups.

Interpret what these curves suggest about the comparison between groups over time.

Testing Survival Distributions:

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

(a) Produce and interpret a test for the equality of survival curves comparing treatment and control groups. Justify the statistic that you use.

(b) Produce and interpret a test for the equality of survival comparing treatment and control groups while controlling for WBC category. Justify the statistic that you use.

(c) Produce and interpret a test for the equality of survival comparing treatment and control groups while controlling for WBC category and clinic.

(d) Children were randomized to either treatment or control. Is it necessary and/or useful to report the analyses in 2(b) and 2(c)? Please comment and justify your response.