I am a noob in AUC analyses and would like to get some help with a probably quite stupid problem:
Consider a population of cells, splitted to 5 plates. Each plate is treated with a different concentration (X) of some drug. The fraction Y of surviving cells is then modeled by log(Y) = aX² + bX + c. This experiment is reapeated n times with similar cell populations. That much is fixed and given, I can't change anythng on this setup or the model (e.g. I know that this kind of model is
For an AUC analysis, I see in principle 2 (or 3) ways:
0) [not really considered because I think this is clearly suboptimal, since it does not make any use of the specified model]: manual "brute-force": calulate the polygon area for each cell population, do the statistics (mean, confidence interval) using these n AUC values.
1) use the data from each cell population (experiment) individually, fit the model, calculate the AUCs. Similarily to 0) one ends up with n AUC values to do the statistics.
2) use all the data from all n experiments together, fit the model and get the (mean) AUC. I consider this the best way, but I don't know how to calulate for instance the conficence interval for the AUC from the standard errors of the model parameters a and b. To go one step further: How would I get a comparison of the AUCs of different groups (e.g. different cell types)?
Any suggestions?
Thanks, Jan, for your answer. As far as I understood, you add the point of calculating a mixed model that would allow to include estimates on differences between "individuals" (the cell populations). This may be advantagous in some cases, but here I think the correlation of data within individuals is is not a problem. But still: good idea, worth to keep in mind! What I still do not understand: for both, a fixed as well as a mixed model, I come up with some estimate for a and b, plus some standard errors for these parameters (for a mixed model I would additionally get some covariance matrix). Now having these estimates with errors, how do I calculate/derive an estimate for the AUC? I would simply use error propagation. Is this wise or nonsense? And if I do so, what would be the corresponding degree of freedom for the standard error of the AUC as derived from error-propagation? 5n-2?
Consider me a 'noob' too... but the above discussion seems to be about two different things?
Isn't the OP asking for Area Under the Concentration Curve for a pharmokinetic study of concentration vs effect. The responses seem to be about Area Under the Receiver Operating Characteristic Curve, but are correct per se.
The way to see which is which is to ask yourself, is their a binary reference variable (e.g. dead/alive, LD50 >/< k, etc). I think the OP is talking about cts variables and there is no exogenously known binary reference variable.
Just sayin'!
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