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

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)


Less is more. Stay pure. Stay poor.
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.