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Unformatted text preview: Chapter 7: Analysis of Censored Data 2. Permutation Tests for Two-Sample Censored Data • comparing two survival functions using permutation tests in studies in which censored observations occur • Censoring Mechanism – difficulty arises when the censoring mechanism depends on the treat- ments – Key Assumption: the censoring mechanism does not depends on the treatments ∗ drop out because of moving ∗ death for reasons unrelated to the treatments – If the distributions of survival times of the treatments are not the same, then one treatment tun out to have more censored observations than another even though the censoring mechanism does not depend on the treatments ⇒ Examine the experimental setup not just the data to determine what causes censoring • Notation and Assumptions – observations X i = min ( T i ,C i ) where T i is the survival time and C i is the censoring time of the ex- perimental unit i ( i = 1 ,...,n ). – data x i : uncensored x + i : censored – Random Censoring: assume that C i ∼ iid F C ( t ) and C i ’s and T i ’s are mutually independent – Fixed-Time Censoring (Type I censoring): all experimental units begin the study at the time and the study is terminated at a fixed time C i = C 1 • Examples of Tests Based on Medians and Ranks – Hypothesis H : R 1 ( t ) = R 2 ( t ) H a : R 1 ( t ) ≥ R 2 ( t ) H a : R 1 ( t ) ≤ R 2 ( t ) H a : R 1 ( t ) negationslash = R 2 ( t ) – comparing two treatment means is not possible because we will not have all the actual survival times – Permutation Tests Based on Medians and Ranks – Random censoring: permutation test based on median (a) Compute D obs : the median difference between two groups...
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- Spring '08
- Statistics, Statistical tests, Non-parametric statistics, Mann–Whitney U