Editing Survival analysis (section)

====Log-rank test: Testing for differences in survival in the aml data====

The [[log-rank test]] compares the survival times of two or more groups. This example uses a log-rank test for a difference in survival in the maintained versus non-maintained treatment groups in the aml data. The graph shows KM plots for the aml data broken out by treatment group, which is indicated by the variable "x" in the data.

[[File:Kaplan-Meier by treatment in AML.svg|thumb|320px|Kaplan–Meier graph by treatment group in aml]]

The null hypothesis for a log-rank test is that the groups have the same survival. The expected number of subjects surviving at each time point in each is adjusted for the number of subjects at risk in the groups at each event time. The log-rank test determines if the observed number of events in each group is significantly different from the expected number. The formal test is based on a chi-squared statistic. When the log-rank statistic is large, it is evidence for a difference in the survival times between the groups. The log-rank statistic approximately has a [[Chi-squared distribution]] with one degree of freedom, and the [[p-value]] is calculated using the [[Chi-squared test]].

For the example data, the log-rank test for difference in survival gives a p-value of p=0.0653, indicating that the treatment groups do not differ significantly in survival, assuming an alpha level of 0.05. The sample size of 23 subjects is modest, so there is little [[Power of a test|power]] to detect differences between the treatment groups. The chi-squared test is based on asymptotic approximation, so the p-value should be regarded with caution for small [[Sample size determination|sample sizes]].