Situation:
Question: Gene X is suspected to have an general effect on growth (has an effect on growth of all cell types).
Knockdown cell lines (=strongly reduced expression of the gene) of different cell types were generated. Growth curves were established for the KD and control cell lines by seeding 10 wells on day 1 (stemming from the same cell mixture) and counting 2 wells each day for the following 5 days (day1: seeding; day2 - 6: counting cells). This experiment was performed 5 times.
For each experiment, for each day, the mean of the cell counts was calculated, Ln transformed and plotted against time. A linear fit was used to determine the linear part of the growth curve. To find the linear part I tried to obtain the highest R2 value with a minimum of 3 data points (sometimes 3 points gave the highest R2, sometimes 5 points gave the highest R2). I then used the mean cell count from the first and last point of the linear part to calculate the doubling time (which is often used in literature to represent growth rate of cells).
Formula used:
First image
I’m however not sure if I should calculate the doubling time using this formula (using the cell counts), or whether I should calculate the doubling time from the equation of the linear fit.
To calculate the error of the doubling time the following formula was used:
Second image
At this point I have 5 normalized doubling times and their error (normalized to the control, so the doubling time of the knockdown divided by the doubling time of the corresponding control).
I now want to assess whether there is a significant difference in doubling times (= significant difference in growth rate) between knockdown and control. Someone in my lab suggested a T-test and I agree, yet I have a few problems with this=
· I don't know how to test normality of my data since I (currently) only have 3 data points (I will have 5 in the end)
· I don't know how to test equality of variance with only 3 (in the end 5) data points.
· I don't know if this is the best method to accurately determine whether there is a significant difference in growth or not. (For example, maybe there’s a way to immediately compare the growth curves, I suspect that such a test would be more accurate, but also more complicated to such a degree that I myself might not be able to apply it)
I work in a lab where no one really has any expertise in this (or statistics in general), so I have to figure it out on my own. I have a lot of doubts on whether or not what I’m doing is correct or not, not helped by the fact that my understanding of statistics is very basic.
If you see any other mistakes, please do tell.
Dear Michael, The classic work on this problem was done by C. R. Rao and is cited in the link below. There are also some other less mathematical treatments given: https://www.google.com/search?q=Growth+curve+comparison+of+2+statistically&oq=Growth+curve+comparison+of+2+statistically&aqs=chrome..69i57j33.49231j0j4&sourceid=chrome&ie=UTF-8
You are extremely fortunate in your choice of University. You have an excellent Statistics group. I have attached a directory:
https://wis.kuleuven.be/statdatascience/members
I know both Peter and Mia personally though it was years ago. I suggest that you contact one or the other and ask for advice. If they can't help (i would be very surprised) ask them whom you might contact at your university. I hope this helps.
Best wishes, David Booth
Two pairs test between treated distribution and untreated distribution
https://www.istat.it/it/files//2018/07/2004_19.pdf
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