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Logrank test (Some extensions of the logrank test (Weighted logrank test…
Logrank test
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Types of tests
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Omnibus test:not specific to one type of difference, tends to has some power against some or all types of difference.
How to choose from these two tests: a. prior expectations of the likely difference; b. properties of various tests for a variety of settings; c. practical consequences of a false negative result.
Basic logrank test
Construction: order distinct event times --> construct 2 X 2 table for each distinct event time (event number for one group follows hypergeometric distribution given the margins) --> calculate the expected value and variance of number of events for each event time table --> calculate the normal (or chi-squre) test statistic
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In constructing the test statistic, we assume the contributions from each time are independent
The construction of the test statistic is very similar to that of the chi-square test for contingency table
For 2 X 2 table, as long as the number of at risk of one group become 0, the construction of tables should stop since the observed and expected values become same.
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