BUILT-IN MATHEMATICA SYMBOL
LogRankTest
LogRankTest[{data1, data2, ...}]
tests for equal hazard rates among the 
using a log-rank type test.
LogRankTest[{data1, data2, ...}, wspec]
performs a weighted log-rank test with weights wspec.
LogRankTest[{data1, ...}, wspec, "property"]
returns the value of 
.
- LogRankTest performs a hypothesis test on the
with null hypothesis 
that the true hazard rates of the populations are equal 
for all 
and alternative hypothesis 
that at least one 
is different for some value of 
.
- The number
is generally taken to be the largest event time in the 
.
- By default, a probability value or
-value is returned.
- A small
-value suggests that it is unlikely that 
is true.
- The
must be univariate 
.
- The
can be a SparseArray or EventData object.
- LogRankTest is effectively based on
where 
, 
, and 
are the observed number of events, the expected number of events based on the pooled sample, and some weights, respectively.
- For named weight methods, the weight at time
, 
, is generally based on the number at risk 
, the number of events 
, the product limit estimator 
of the pooled sample, or a similar estimator 
of the pooled sample.
- The following weight specifications wspec can be given:
-
|  | Fleming-Harrington weights with  |
| {, } | fully specified Fleming-Harrington weights |
| "name" | use a named weight method |
- The values of and can be any non-negative numbers.
- Specifying and yields Fleming-Harrington weights of the form
.
- Possible named weight specifications include:
-
| "AndersenPeto" |  |
| "Equal" |  |
| "Gehan" |  |
| "Peto" |  |
| "TaroneWare" |  |
- For interval-censored data the Zhao-Zhao-Sun-Kim generalized log-rank test is used.
- LogRankTest[{data1, ...}, wspec, "HypothesisTestData"] returns a HypothesisTestData object htd that can be used to extract additional test results and properties using the form htd["property"].
- LogRankTest[{data1, ...}, wspec, "property"] can be used to directly give the value of
.
- Properties related to the reporting of test results include:
-
| "AllTests" | list of all applicable tests |
| "AutomaticTest" | test chosen if Automatic is used |
| "DegreesOfFreedom" | the degrees of freedom used in a test |
| "EventTimes" | list of time points used in the test |
| "EventWeights" | a list of weights used at each event time |
| "PValue" | list of  -values |
| "PValueTable" | formatted table of  -values |
| "ShortTestConclusion" | a short description of the conclusion of a test |
| "TestConclusion" | a description of the conclusion of a test |
| "TestData" | list of pairs of test statistics and  -values |
| "TestDataTable" | formatted table of  -values and test statistics |
| "TestStatistic" | list of test statistics |
| "TestStatisticTable" | formatted table of test statistics |
- The following options can be given:
-
Compare hazard rates using some sample data:
| Out[2]= |  |
Create a HypothesisTestData object for repeated property extraction:
| Out[3]= |  |
| Out[4]= |  |
Test some censored data:
A significant difference is detected at the 5% level:
| Out[2]= |  |
Perform a weighted log-rank test:
Use a named weight scheme:
| Out[2]= |  |
Use Fleming-Harrington weights:
| Out[4]= |  |
Test for equal hazard rates with many samples:
A visual comparison of the survival rates:
| Out[2]= |  |
A significant difference is not detected:
| Out[3]= |  |
New in 9
-values
