I would like to compare the cell proliferation rate (as measured by MTT assay over time) with two different conditions given to the same cell line (plated seperately). As far as I can tell statistical comparisons of proliferation rates vary between t-test comparisons at individual time points to Kruskal-Wallis stats on regression lines. And everything in between. Can someone tell me how this is done- it must be a common enough analysis?
Suppose you have measurements on prolif rates y_it, where i indexes the conditions, t indexes time.
You specify that y_it = alpha + X_i* beta + t*gamma + epsilon_it, where gamma is the to-be-estimated parameter for the secular trend for the cell line regardless of condition, X_i is an indicator for the condition, and the disturbance is almost certainly serially correlated. You assume that it's a first order auto-regressive dynamic: epsilon_it = rho*epsilon_it-1 + eta_it.
You're trying, I think, to estimate beta, after accounting for secular trends and serially correlated disturbances, and have some hypothesis that it's not zero.
If this is what you want, it seems that a time series cross-sectional regression with more time observations than units, and with accommodation for serial correlation over time in the disturbance is what you need.
STATA will do this with on a time-set dataset. Good luck!
ASAIK the MTT assay measures cellular metabolic activity. This measure is proportional to the number of viable cells ONLY if the metabolic rate and redox potential is constant. I hope you checked that this is the case for your treatment. Also consider that growing and dividing cells will have a different metabolic rate than non-growing cells.
Apart from this, you should model the response (absorbance, OD) by time and condition (treatment). The interaction of time and treatment is what you are interested in. I would guess that an exponential or logistic model might be appropriate.
I don't think that the above mentioned autocorrelation will play a major role in your data.
Using t-test to compare rates at particular time points is particularily stupid. You throw away the majority of data and run into a multiple testing problem.
PS: I assume you compare OD values [cell numbers] and not rates [change in cell number per unit time]
Dear Jochen,
Your response is crystal-clear (I have understood it!).
Dear Marco,
"In contrast", I understood nothing to yours ...
Dear Sebastian,
Folowing the remarks of Jochen that I fully share, here attached is an article that could may be of help with respect to certain problems occuring with the MTT assay.
Best regards,
Robert
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