Help on one sample repeated measures (>2 data points per subject)

#1
Dear members of Talk Stats forum:

I come to you in the hope that you can point me in the right direction to explore. I am trying to find the appropriate statistical test for a one sample, repeated measure experiment.

Basically, I am measuring variable A on each participant at seven time points. (FYI: I am giving the participant a treatment before measuring variable A every time.) However, there is no control group [Don't shoot the messenger, I didn't design the experiment. I inherited it.].

Had there been a control, it would be simple to run a 2 way (1 within [time], 1 between [exp group vs control group]) repeated measures ANOVA. However, as I only have one group, can I run a statistical test to see if variable A is significantly different from 0?

Any help would be very appreciated!

What I have considered:

Data from different time points from a single subject have some innate correlation to each other, which violates the assumption of independence for non-repeat-measure tests.

Had this been a single time point study, I could have used a single sample t-test of difference. But alas, it is not.

What I am playing around with:
Hotelling's T-squared test (one sample variant)
 

hlsmith

Less is more. Stay pure. Stay poor.
#3
So the outcome (dependent variable) is continuous and gradually goes down as more time goes by and doses administered (assuming this is related to intervention)?

Perhaps a trend test may be of interest, though off hand I am unsure how to incorporate the same person correlations.