In a survival experiment, I'd like to test if there is a difference not only between the two treatments and the two respective controls, but also if there is a difference between the (statistically significant) two differences. So my Nullhypothesis would go something like this:
There is no difference between the survival of Treatment A compared to Control A and Treatment B compared to Control B.
Which test applies to this situation?
I hope I've managed to describe my problem clearly enough without adding too much confusion.
Thanks a lot,
Arne
If the sample sizes are sufficiently large, by the central limit theorem, each difference follows a normal distribution. Therefore the difference of difference also follows a normal distribution being a linear combination of normally distributed random variables. Therefore the Z distribution is applicable. Then the z-test is used. If the samples are small in size, the t-test is applicable.
Not sure how you modeled the survival, but there are ways to include covariates to survival models, just as it can be donoe for linear models. In your case you would consider two factors as covariates, one for the treatment (yes/no) and one for the group (you said you have two groups, like A/B). The model will include the two main effects and the interaction between teartment and group, and this is precisely what you want to find.
http://data.princeton.edu/pop509/ParametricSurvival.pdf
My Arne B.
I compatabile with answer my collegue Jochen, you can use ANOVA to test differnces between main factors and multiple comaparison between factore levels.
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