Methods and formulas for distribution characteristics in Nonparametric Distribution Analysis (Right Censoring)

Log-rank test

Minitab uses the log-rank test, along with the Wilcoxon test, to assess whether the survival functions significantly differ. The log-rank test compares the actual and expected number of failures between the survival curves at each failure time.

Formula

The chi-square statistic is calculated by squaring the log-rank statistic and dividing by the estimated variance. A p-value < α indicates that the survival curves are significantly different.

Notation

TermDescription
nj the number at risk at time j
d1 j the number of failures in group 1 at time j
e1 j the expected number of events in group 1 at time j
r the total of all unique times in all groups

Wilcoxon test

Minitab uses the Wilcoxon test, along with the log-rank test, to assess whether the survival functions significantly differ. The Wilcoxon test is a log-rank test that is weighted by the number of items that still survive at each point in time. Because the Wilcoxon test weights early failure times more heavily, the test is less sensitive than the log-rank test to differences that occur later.

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