3
$\begingroup$

Depending on which statistics text you read you will get 2 different formulations of the log-rank test statistic. In some texts you will see it specified as:

$$ \frac{(O-E)^2}{E} $$ Example 1

Whilst in others you will see it as $$ \frac{(O-E)^2}{V} $$

Example 1
Example 2

My questions are:

  • Do these variants have specific names?
  • Do they have any differences in properties?
  • When should one be used over the other?
$\endgroup$
0
$\begingroup$

The first one is related to the chi-squared test. The second one is the log-rank test that I am aware of. The problem with running a chi-squared test in survival statistics is that the tests at various time points are not independent (i.e. to be considered for a later time point someone must survive an earlier time point), so I would not recommend using it. In general with survival analysis use the second variant (truly I think it is the primary methodology).

It can be shown that the second variant approaches a z-distribution (N(0,1)) and a chi-squared distribution with one degree of freedom when squaring the statistic as shown here.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.