# Timeline statistics - (Jan/16/2012 )

Hi Everyone, I am a PhD student with some difficulties about what test to choose to verify an experiment. Hope you can give me some help!

My experiment:

I am counting the number of a subset of cells in Drosophila overtime.

I have a mutant and a wild type control. I dissect the flies at different time points: just eclosed, 1 day after eclosion, 3 dae, 6 dae, 9 dae, 12 dae and 15 dae. For each time-point I have a n number of around 50.

The problem:

What happen with these cells is that in the wild type population the number of cells does not decrease overtime, while in the mutants it does. Moreover the wild type population has an average of 6 (in all the dissection days), while the mutant starts with 4 and goes down to 2. Maybe if they were the same amount initially I could have used an anova test with a posthoc test (like tukey) to show the difference between wild type and control for each day, but in this case an anova would tell me only that all the wild type are different from the mutants (even at eclosion!) because of the basic difference they have, or that for example mutant dae15 is different from mutant dae0,1,3. Moreover, what I would like to test against is not that the wild type is different from the mutant at a particular timepoint, but that the mutant numbers decrease faster than the control numbers.

Possible solutions:

I was thinking that one possibility would be to do an anova on a normalized sample: I could divide every number (and I mean the single numbers, not the average) I get for the average of the eclosion day, and do an anova on that ratio (So I would have liked normalized the two populations to the eclosion day and it would not matter anymore that their raw number are different), but something tells me I would mess up all the statistics: I am not sure if this approach is statistically correct.

Another possibility I was thinking is to use some kind of correlation or regression analysis, but in the example I found I never found this approach on my kind of experiment, so i am not sure how to work this out. In the various handbook it always show this kind of approach to smaller experiments, like comparing blood pressure and coffee assumption, and with much less numbers.

If you have any idea how this problem could be solved, I would be grateful!

First it would be interesting what question(s) you want to answer with your experiment?

Anyway perhaps survival analysis with estimators such as Kaplan–Meier might work.

The question to answer with the experiment would be: is the mutant involved in the survival of this cell type?

I had a look at the Kaplan-Meier test, but it does not seem to apply to my experiment. The problem I see with the Kaplan-Meier is that it is counting either an alive or death state, while for me each sample has a different number that can range from 0 to 9. Also in the kaplan-Meier statistic are used the same exact patient all the time (even if yes, it allows for drop out etc), while the cell I count are different all the time (that is because when I take these cells out of a fly, I kill the fly in the process). I think that possibly some kind of logrank could work, now I will see if I can find any that can work with my experiment!

Then you need something like the log-rank test, as it has the null hypothesis that the survival is by chance independent from group and that if not then in one group the deaths are delayed. Anyway here's also the problem that it works with the same individuals throughout the timeline.

What you also might try is to use more or less simple curve parameters such as slope or area under the curve to get more the curve progress in focus. These characteristics you then can analyse e.g. with non-parametric tests.