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RE: st: repeated measures at two time points


From   "Nick Cox" <n.j.cox@durham.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: repeated measures at two time points
Date   Mon, 1 Sep 2003 17:48:16 +0100

Cornelia Zekweld

> >I hope someone can give me some pointers.  I have data on
> a few individuals
> >(n=12) and for each person I have two measurements.
> >
> >The first was made at the last time of exposure (the
> calendar date differs
> >for each person)
> >The second was made on the same calendar date.
> >
> >So the follow-up differs for each person, (mean (sd)
> follow-up 89 (108)
> >months).  So follow-up varies a lot.
> >
> >
> >I can graph these two-time points for all individuals:
> with the x-axis
> being
> >time since last(final) exposure and the actual measurement
> value on the
> >y-axis.
> >This produces a graph with 12 straight lines all starting
> at time 0 and
> >ending at different points.
> >
> >
> >Now my question is  - how can I summarise these 12
> "lines".  I need to get
> >one curve/line.

Ernest Berkhout

> What is your null hypothesis? Can't you just plot the
> _difference_ in
> measurement value against the _difference_ in days between
> measurement and
> follow-up? You get 12 points in which may seem to indicate some
> relationship between followup-time and
> measurement-difference. Although
> significance should be considered carefully with such a
> small sample, I guess.

Cornelia

> This is just descriptive work and I'm not testing a
> hypothesis - once I have
> this graph I hope to be able to get the half-life from the graph.

I will seize on the last specific detail; an interest in half-life
suggests, at least as a zeroth approximation, interest in exponential
decline such that

	y = y_0 exp(-kt).

Given two points y_1 and y_2 for times t_1 and t_2 you can get
12 estimates of k from

	ln y_1 - ln y_2
	---------------
	   t_2 - t_1

after which I would just look at those 12 estimates on a dot plot
or one-way plot. Half-life is proportional to 1 / k, so the
reciprocal might be better.

Nick
n.j.cox@durham.ac.uk

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