I have some data here that I am at a loss on how to analyze.
The following data set represents a subset of some data I have where a number of subjects (4 here, about fifty in the actual set) underwent a single treatment over a period of days (unequally spaced, for reasons I can't get into, and much longer than twenty days), and I'm interested in proving the hypotheses that a) the response for each subject is not significantly different from 20,000 (from theoretical considerations) over the time elapsed; and b) the subjects' responses to the treatment are not significantly different from each other.
Days Subject 1 Subject 2 Subject 3 Subject 4 0 18978.32 19820.70 19820.73 19865.00 1 19773.49 20986.11 20659.65 20706.34 5 22150.53 20323.14 19966.60 19966.56 10 21131.95 20815.21 20634.20 20769.92 18 21041.41 19336.45 19627.55 20 19178.02 19264.49 19178.03
I had the initial thought of using repeated measures ANOVA, but it is my understanding that that procedure is unable to cope with missing data. (That is, a number of subjects dropped out before the full period elapsed, but I figure I still want to account for these drop-outs in my analysis.)
I've heard a mixed linear model might be suited for this task, but I'm not sure how to go about it.
Any assistance would be appreciated. How to do this analysis in, say, R, would be welcome.
I had the idea of doing a stationarity test for each subject (probably with augmented Dickey-Fuller) to test if the trend is essentially constant, but I don't know how to incorporate a way to test if the "constant trend" thus hypothesized is equal to the theoretical value of 20,000. I could also try doing a pairwise comparison of means, but I'm not sure the assumptions for that test would be fitting.