Dear allstat,
                 Thank you for the answers and the support. Here is a list
of the responses.

1.I would do a factorial repeated measures, month by vessel. If the month by
vessel interaction is not significant, then just look at the mean difference
between vessels. If the month by vessel interaction is significant, then you
have a different problem. You could do simple main effects, vessel within
month, or apply contrasts to the moth variable, such as a polynomial. The
question is whether the data will meet the assumptions. this could be doen
as a mixed model or, if the distributions are bad, a generalized estimating
equation.

2.The way you analyse these data depends on what interest you have in
repeating measures. If you think that there is no natural evolution during
time, you are simply taking multiple measures to improve precision in an
otherwise largely variable assessment. In this case you could simply
average all measures taken on an individual and use these averages as
estimates of the individual performance. The analysis variable is the
between-vessel difference at each measure, and the test is a paired t-test.

However this could not to be your case, as placenta suggests pregnancy
which you do not expect to be without evolution during time. In this case
you probably take repeated measures as you are interested in showing that
there is a different trend in time in blood flow in the two vessels. You
could therefore try to model the time trend of blood flow: in the luckyest
case a linear regression model will be suitable. Again your variable is the
between-vessel difference, and you will model the time trend of difference
between the two vessels. The usual test for significance of the regression
coefficient (again a t-test) should suit your needs.

Hope it helps

3.Check this out
Repeated measures in clinical trials: analysis using mean summary statistics
and its implications for design by L. Frison and S.J. Pocock, Statistics in
Medicine 1992; 12: 1685-1704
which is summarised on pp 3133-3135 Statistics in Medicine 2000; 19: in a
letter by Steven A. Julious

4.DATA
You have longitudianl data that looks like, for example:

id vessel time flow
1 1 1 73
1 2 1 34
1 1 2 75
1 2 2 35
1 1 3 76
1 2 3 33
1 1 4 76
1 2 4 36
2...

where time=1 is week 20, 2 is w24 3 is w28, 4 is w32. id=1,...,10 fo rteh
ten patients.

METHOD
Possible methods:
1. Multilevel model
2. GEE marginal model

I recommend these methods because the can allow for the correlation between
readings subject to specifiying the correct hierarchal data structure.

I would use a multilevel model in this instance because the sample size is
small, and I am more interested in modelling the mean progress of each
patient.

MODEL STRUCTURE
The hierarchal structure consists of: Patient[i], Vessel type[j], and
Time[k]; so a 3 level structure should be allowed for in the multilevel
model.

MODEL SPECIFICATION
(a)If you're interested in comparing the FLOW CHANGE SINCE WEEK 20 between
the 2 vessels, then I would fit a baseline (week 20) adjusted model:

y[ijk]= cons + a.y[ij1] + b.vessel[j] + c.time[k] + random effects

where y is flow; time is modelled as a linear effect, but may take
non-linear specifications, eg time^2, log(time); a,b,c are just regression
coeffs.

(b)If you're interested in comparing the flow between the 2 vessels at all
time points, then fit without adjusting for week 20:

y[ijk]= cons + b.vessel[j] + c.time[k] + random effects

MULTIPLE TESTING
There is no need to make any multiple testing adjustment as the hyposthesis
test for coeff 'b' is:

PRIMARY ANALYSIS
H0: There is no difference between vessels 1 and 2 over the whole time
period.
H1: There is a difference between vessels 1 and 2 at at-least one time point
over the observation period.

SECONDARY ANALYSIS
If you get a significant result for 'b', then you can look further at the
model to see WHEN they are different by evaluating the difference
y[i1k]-y[i2k] and testing when H0: diff=0. This would be a secondary
analysis, so no need to adjust for multiple testing.

DISTRIBUTION OF DATA
This will determine the model you can fit. Obviously, it is most simple when
the data can be assumed to be drawn from a Normal distribution.



5.I don't think we can answer this without knowing why you are doing it.
In general, however, I would go for a summary statistic, as described by

Matthews, J.N.S., Altman, D.G., Campbell, M.J., and Royston, P. (1990)
Analysis of serial measurements in medical research. British Medical
Journal vol 300, p 230-35.

i would avoid repeated measures anova, far too difficult to interpret.

Best Wishes
Ian