Ratio of Means - appropriate test for single or multiple comparisons? Fieller's CI?

#1
I would really appreciate any suggestions with the following data analysis issue. Please read till the end as the problem at first may appear trivial, but after much researching, I assure you it is not. The situation is a little complicated because I want to compare the ratios of means:

For example, in one experiment I have collected data (Electric current levels, a continuous variable) from 7-8 cells (replicates) which express a particular ion channel gene (Gene1). This gives me a mean current level for Gene1. I have then measured current levels from a different set of 7-8 replicate cells which also express Gene1 PLUS an activator gene (the "treatment"). Now I have a mean current value for Gene1+activator.

I repeat the two measurements for Gene2 (a different ion channel gene), again recording mean current values from 7-8 cell replicates for Gene2 alone and then for Gene2+activator.

The quantity I am interested in comparing is the %activation or fold activation caused by the activator for Gene1 versus Gene2. So, I would obtain a ratio by dividing the mean current for Gene1+activator by the mean current for Gene1 alone. This would give me the fold activation for Gene1. I would compare this to a similar ratio obtained for Gene2.

I have done some research on this and using Fieller's intervals to compute the error bars or confidence intervals seems promising. However, I don't know how to convert that to hypothesis/comparison test and get an appropriate p-value for the comparison of means being same/different. Furthermore, the best solution would also allow multiple comparisons and allow me to compare "fold-activations" for Gene1 and Gene2 and Gene3 and Gene4 at the same time.

Fieller's intervals seem like the perfect tool to compute 95% confidence intervals etc around each fold-activation but this does not lend itself to calculation of a p-value. As of now, I am reduced to insisting the lack of CI overlap clearly signals a significant difference but I know that lack of 95%CI overlap is an overly stringent comparison test which represents an alpha<0.05. I would truly appreciate any suggestions to the appropriate comparison test (single or multiple comparison, either at this point will be helpful) which would test at alpha=0.05 and yield a p-value. Thanks in advance.
 

rogojel

TS Contributor
#4
Re: Ratio of Means - appropriate test for single or multiple comparisons? Fieller's C

hi,
it seems to me that this would be the perfect candidate for a boostrap.

regards
 
#5
Re: Ratio of Means - appropriate test for single or multiple comparisons? Fieller's C

I've been spending a long time considering the use of statistics in laboratory based experiments. All the guides and talks I read discuss either epidemiological studies, or experiments on people who are allocated to groups - both of which are susceptible to a lot of interference due to the huge number of variables affecting them. Laboratory based experiments are completely different as you have complete control, and your two groups will differ only in the variables you choose to change. The current practice in the studies I look at is to use a simple T-test to compare the groups. My question would be why that can't be done in this case?

One thing I can see in this case is that the experimenter uses 7-8 cells per sample, whilst the research I've been doing has used cell cultures of 100,000+ cells. Also, its whether the conversion to ratios means that assumptions allowing parametric testing are violated, but wouldn't an answer to that be to use a non-parametric such as Mann-Whitney?

Cheers

G
 

hlsmith

Less is more. Stay pure. Stay poor.
#6
Re: Ratio of Means - appropriate test for single or multiple comparisons? Fieller's C

Were new cells used each time all of which came from the same donor and were the same age?
 
#7
Re: Ratio of Means - appropriate test for single or multiple comparisons? Fieller's C

Hi hlsmith

In short, although it was new cells each time they were from the same donor and of the same age.

They were from a tumour cell line established about 15 years ago, and experiments carried out over 2-3 months. The cells had been taken out of deep freeze so there was some difference in the time they had been growing (rather than hibernating) but this cell line is popular because it has been found not to change over time and has a consistent growth and function profile over prolonged periods.

This isn't true for many cell culture experiments which use freshly isolated cells.

Cheers

Gareth
 

rogojel

TS Contributor
#8
Re: Ratio of Means - appropriate test for single or multiple comparisons? Fieller's C

pp
The current practice in the studies I look at is to use a simple T-test to compare the groups. My question would be why that can't be done in this case?

One thing I can see in this case is that the experimenter uses 7-8 cells per sample, whilst the research I've been doing has used cell cultures of 100,000+ cells. Also, its whether the conversion to ratios means that assumptions allowing parametric testing are violated, but wouldn't an answer to that be to use a non-parametric such as Mann-Whitney?

Cheers

G
hi,
The T-rest assumes that the values tested have a more or less normal distribution. Simulation experiments show that this is not a strict condition, t-tests are pretty robust vs. deviations from normality - if the variance of the groups is not very different then a t-test will deliver a good result even if the distribution is quite non-normal.

The number of cells plays a role here through the Central Limit Theorem - averages over large samples tend to be closer to the normal distribution then averages over small samples if the individual values have the same distribution ( which can be quite different from normal).

If you build ratios, these will be definitely non- normal ( Cauchy dustribution if both values are normally distributed, for example) so if possible I would use the t-test or a non-parametric variant and not the ratios.

A non-parametric test is always an option, you might just lose some information ( or power) . So, the decision should be based on the power of the test and the availability of samples ( to detect a small effect one needs more samples if the test has a low power.)

I hope this helps a bit
 
#9
Re: Ratio of Means - appropriate test for single or multiple comparisons? Fieller's C

rogojel

Thanks for the reply - it does help.

Now off to spend some time with SPSS.....

Cheers

G