First of all this is a crosspost with Cross Validated. No answers so far and I think it might be more appropriate here since I have no idea what I'm doing statisticswise.
I'm using a plate reader to measure optical density of different bacterial strains so I can compare their responses (growth rates and changes in them over time) to stress conditions. The growth curves often don't follow any standard shape so I'm fitting them empirically with the loess
or locfit
functions in R, breaking the fits into intervals, and taking the derivatives to get growth rates. My plots look like this:
As you can see the fitted curves have confidence intervals, but I'm not sure how to transform them into a meaningful form (95% confidence or standard deviation for example). And assuming that's doable, how do I go on to calculate uncertainty in the rates?
I suppose I could just use the worstcase difference in slopes like this:
But that seems like a bad idea.
I could fit each well separately or split them into groupsthere are a few replicates for each strain and I could add more if neededand just use the standard deviation of the final calculated rates. Is that the best way? If so, how do I decide the optimal group size to balance accurate fits with a good number of replicates? I would also be open to using a different type of fit of course.
I've found a couple related questions, but neither one quite answers it:

This one seems to rely on the true relationship being linear, which my curves violate

This one may well be correct but my stats knowledge is too basic to understand the answer
EDIT: I'm using deg=1
for both types of fits because I expect growth during logphase to be linear on a logtransformed scale, but maybe higherdegree polynomials would be more accurate?
EDIT: This answer looks very promising and I'm off to read the suggested paper.
EDIT: Nope, also depends on having a known underlying physical model.