Consider calculating the rate of a biological process (e.g.clearance rates in a suspension):
rate = ln(B0/Bt) - ln(B0c/Btc)
where B0 and Bt is the biomass at the beginning and end of the experiment under treatment conditions, respectively, and
B0c and Btc is the biomass at the beginning and end of the experiment under control conditions, respectively.
Now, every measure of B stems from single biological replicates and hence consists of a mean and its variance. I want to calculate the mean rate and its variance, but I am unsure how this is done in a statistically rigorous way.
I was suggested to just use the mean from the controls (B0c and Btc) but this feels like I am disregarding a portion of the variation in my experiment.
Instead, my biologist's (certainly non-statistician) brain whispers to me that perhaps one could make a bootstrap-calculation (i.e. calculating the rate iteratively n times, where n is the number of all possible pairwise combinations of replicates)? Is this statistically correct? If so, how do you this efficiently (e.g. using R)?
Thanks! Any hint is appreciated!
Hello Ramsy Agha
I think you need to look at the literature where similar problems were solved. However, resampling technics are always good. You can calculate the mean using both methods (why not?).
Some examples in R:
https://cran.r-project.org/web/packages/broom/vignettes/bootstrapping.html
https://cran.r-project.org/web/packages/bayesboot/readme/README.html
https://www.statmethods.net/advstats/bootstrapping.html
https://uoftcoders.github.io/studyGroup/lessons/r/resampling/lesson/
http://www.di.fc.ul.pt/~jpn/r/bootstrap/resamplings.html
Python:
https://machinelearningmastery.com/a-gentle-introduction-to-the-bootstrap-method/
https://gist.github.com/johnb30/4166016
P.S.
roscoff-culture-collection.org/file/55058/download?token=vAxJ8D8H - search result " clearance rates ". The authors used the package "frair". May be it's help you.
I hope I understood correctly what you want to do, but here's my take:
If I get it right, B0 and Bt (and B0c and Btc, respectively) are measured on the same observational unit, but on different units for control and treatment groups. If these groups are independent of each other, this basically means you are looking for the standard error of the difference between the averages of treat = log( B0 / Bt ) and cont = ln(B0c / Btc ) calculated for each observational unit.
If the observations are independent and things are normal, the standard error of a difference is the square root of the sum of the squared standard errors of each mean. This is just what the t.test function in R does internally, so you can use this function to get a fast confidence interval for your rate by plugging in treat and cont (you can disregard the rest of the output because you likely know a priori that the rate is not 0).
If I wanted to get a more robust resampling based estimate for the confidence intervals of your rate, I'd likely just do something like this:
# logs of ratios for each observation
treat
That´s exactly what I was looking for! Thanks a lot, Roman! Kudos to you! :)