# Thread: biostatistics: quantify association between two variable in survival time?

1. ## biostatistics: quantify association between two variable in survival time?

Hi mathematics boffins. This is my first time here, and i'm here on behalf of my very scientific and brainy girlfriend.

so she's doing stuff with mice. grafting skin to them, and seeing how long it takes them to reject the graft, and whether they do reject the graft.

So two groups of mice, one positive control, the other has been treated with something.

here are the results.
(a 1 means a mouse rejected the graft on that day. a 0 means no rejection)
(12 mice in each group)

+ve control

Days post graft rejection
90. 1.
90. 1.
103. 1.
112. 1.
125. 1.
150. 0.
150. 0.
150. 0.
150. 0.
150. 0.
150. 0.
150. 0.

anti CD4 after grafting
days post graft rejection
45. 1.
45. 1.
56. 1.
56. 1.
61. 1.
150. 0.
150. 0.
150. 0.
150. 0.
150. 0.
150. 0.
150. 0.

so as you can see, rejection was much faster in the second group.

so now, is the difference in the times taken to reject significant? I'm no scientist, but i remember 5% confidence intervals etcetra from doing intro to stats at uni.

How would you go about working out a time based problem like this? The best my girlfriend can come up with is calculations for the total amount of rejections, which is obviously not significant at all as the difference is only one mouse.

I hope this all made sense, and any help is greatly appreciated.

2. Originally Posted by bruxism
Hi mathematics boffins. This is my first time here, and i'm here on behalf of my very scientific and brainy girlfriend.

so she's doing stuff with mice. grafting skin to them, and seeing how long it takes them to reject the graft, and whether they do reject the graft.

So two groups of mice, one positive control, the other has been treated with something.

here are the results.
(a 1 means a mouse rejected the graft on that day. a 0 means no rejection)
(12 mice in each group)

+ve control

Days post graft rejection
90. 1.
90. 1.
103. 1.
112. 1.
125. 1.
150. 0.
150. 0.
150. 0.
150. 0.
150. 0.
150. 0.
150. 0.

anti CD4 after grafting
days post graft rejection
45. 1.
45. 1.
56. 1.
56. 1.
61. 1.
150. 0.
150. 0.
150. 0.
150. 0.
150. 0.
150. 0.
150. 0.

so as you can see, rejection was much faster in the second group.

so now, is the difference in the times taken to reject significant? I'm no scientist, but i remember 5% confidence intervals etcetra from doing intro to stats at uni.

How would you go about working out a time based problem like this? The best my girlfriend can come up with is calculations for the total amount of rejections, which is obviously not significant at all as the difference is only one mouse.

I hope this all made sense, and any help is greatly appreciated.
It looks to me as though you need a model to represent the survivals.

I would suggest that it be something like:

$\displaystyle p(d)=(1-p_1) p_2(d)$

where $\displaystyle p(d)$ represents the probability that a mouse rejects on day $\displaystyle d$, $\displaystyle p_1$ is the probability the graft survives the trial and $\displaystyle p_2$ is probaility that it rejects on day $\displaystyle d$ given it rejects. Then assume given it rejects that $\displaystyle d$ has a normal distribution (remember that the recorded day is rounded to the appropriate integer).

Now you have two things to test:
1.That the probability that the grafts survive are equal
2.That the mean times to graft rejection given rejection are equal.

RonL

I thought i was looking less at probability and more at something like a t test or chi square test or something similar.

the whole idea is that my girlfriend's trying to prove that the mice in the second group take significantly less time to reject the graft than the mice in the first group.

so, is there an easy way to show, with some kind of confidence interval (say 5% certain) that treating mice with the stuff she did for the second test decreases the time taken to reject the graft?

Bear in mind i'm entry level stats, and my girlfriend is an immunology graduate, so stats is something we've never been very good at. Thanks so much for your time so far!

4. although, reading your reply again, it's starting to make sense. Argh, i wish i'd listened more in Uni!! would i be able to get a little walk through or something?

5. Originally Posted by CaptainBlack
It looks to me as though you need a model to represent the survivals.

I would suggest that it be something like:

$\displaystyle p(d)=(1-p_1) p_2(d)$

where $\displaystyle p(d)$ represents the probability that a mouse rejects on day $\displaystyle d$, $\displaystyle p_1$ is the probability the graft survives the trial and $\displaystyle p_2$ is probaility that it rejects on day $\displaystyle d$ given it rejects. Then assume given it rejects that $\displaystyle d$ has a normal distribution (remember that the recorded day is rounded to the appropriate integer).

Now you have two things to test:
1.That the probability that the grafts survive are equal
2.That the mean times to graft rejection given rejection are equal.

RonL
Since there are the same number of rejections in the two groups, we can
assume that any test for 1. above would be passed.

That leaves the mean time to reject for those that do reject. If we assume
the the rejection times are normally distributed (and placed in 1 day wide
bins) we want a two sample t-test for equality of means, using only those
which do reject in our samples.

(do we have to correct for using binned data? I would have to look that up)

RonL