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The log rank test is usually taken as the
default method. It is appropriate when the relative mortality does not change with time.
This is known as the "proportional hazard" (PH) assumption. The figure on the left illustrates the
survival functions, S(t), when PH assumption is true. In the figure on the right, suppose the blue line represents the survival of patients who have received a drug treatment,
and the red line patients who have received a surgical treatment.
Immediately after surgery there is a chance of infection and complication so the relative
mortality is high initially. So the S(t) drops sharply. Gradually surgical patients may
have a lower relative mortality; and the survival curve becomes less steep. This violates
the PH assumption. The log rank test would tend to conclude that there is no difference.
The Breslow test (Wilcoxon test) gives more emphasis to early deaths and is
preferred in this situation.
Breslow NE. A generalized Kruskal-Wallis test for
comparing k samples subject to unequal patterns of censorship. Biometrika 1970; 57:
579-594. |
