I would like to thank Stephen Senn and Trevor McMullan for their responses
to my recent query.  Their suggestions are given below

_________________________

>From Stephen Senn:

My comments.

> Recently a researcher at Salisbury approached me for advice.  A paper he
> had submitted for publication in a journal had been rejected on
> statistical grounds.  The researcher had performed repeated paired t-tests
> and the referee had suggested that a repeated measures ANOVA would
> be more appropriate.  I have little knowledge of mixed models and am not
> sure as to how such an analysis could be applied to his data set.  I would
> be grateful for any comments you might have.

Personally I hate repeated measures ANOVA and share the view of two
eminent statisticians: Yates and Finney, that the split plot approach
is not adequate for analysing repeated measures over time. I suspect
that the referee doesn't know what (s)he is talking about.

> The researcher had conducted a retrospective study of stroke and MS
> patients (n=111 and n=21 respectively) with a dropped foot who had
> been treated using the Odstock Drop Foot Stimulator (ODFS).  This
> device had been fitted to the patients’ leg with Functional Electrical
> Stimulation (FES) being used to stimulate the muscles as the patient
> walked.  The patients were allowed to take the ODFS devices home to
> use as desired.  Patients were routinely assessed at their initial visit,
> at 6 weeks, 4½ months and every 6 months thereafter whilst they
> continued to use the stimulator.  At each assessment the patients’ PCI
> (Physiological Cost Index) and walking speed were measured.
> PCI (beats/m) = change in heart rate from rest to walking (beats/min) /
> walking speed (m/min).
>
> At each assessment patients were asked to walk briskly over a 10 metre
> course six times with approx. 10 seconds rest between walks.  During three
> of the six walks the stimulator was activated.  The order of the
stimulated
> (S) / non-stimulated (NS) walks was varied to compensate for fatigue.  The
> following order was set:  NS  S  S  NS  NS  S.  The mean walking speed and
> PCI for the NS and S runs were calculated.  Some patients were not able to
> complete all six runs and their mean readings were therefore based on
> fewer runs. All data were obtained from patient notes.  Data for each
> individual run were recorded in the notes, but only the patient means
> have been recorded on the database and there is no way of knowing the
> number of observations on which each mean was based.

I would have preferred a randomised order. This sounds like  a
series of repeated n-of-1 trials. As such the data are interesting
and valuable and worth analysing used random effect models. Are you
and this researcher interested in a collaboration?

> For the paper in question only the initial and 4½ month assessments were
> considered.  The ability to walk at least 10 metres was defined as an
> inclusion criterion, as was the availability of data at both time points.
>
> The researcher had reported the results of repeated paired t-tests on the
> mean values as follows
>
> NS3 – NS1 (non-stimulated (3rd visit (at 4½ months)) – non-stimulated (1st
> visit))
> S3 – S1
> S1 – NS1
> S3 – NS3
> S3 – NS1
>
> The results were reported separately for stroke and MS patients.  No
> formal comparisons were made between the two patient groups.
>
That seems not unreasonable.

> As you can see it’s a bit of a mess.  I have reservations about performing
> an analysis treating mean values as individual observations, especially
> when the means in question are based on varying numbers of individual
> runs.  Also, the runs themselves cannot be considered independent.  The
> systematic way in which the order of runs was determined also raises
> concerns.  Even if it were acceptable to treat the means as individual
> observations, how could a mixed model be applied?  Note that S1, S3,
> NS1 and NS3 are all recorded on the same patient.
>
> All comments gratefully received - even if they’re to say that you don’t
> think that there is any appropriate analysis for this data set without the
> raw values.
>
> Regards
>
> Kate
>
> P.S. Other studies have reported that, if the ODFS is used periodically,
> the patients' ability to walk without the ODFS can also improve, hence
> the non-stimulated readings at each follow up assessment.
>
> *************************************************
Regards

Stephen
--------------------------------------------------
Professor Stephen Senn
Department of Statistical Science &
Department of Epidemiology and Public Health

University College London
Room 316, 1-19 Torrington Place
LONDON WC1E 6BT

Tel: +44 (0) 171 391 1698
Fax: +44 (0) 171 813 0280
Email: [log in to unmask]
webpage: http://www.ucl.ac.uk/~ucaksjs/
-------------------------------------------------



Whilst I am quite definitely no expert it does appear to be a split-plot in
time model that is being suggested. Another technique is Ante
Dependent Analysis. One name you might want to check out is Ron
Kennett, I think of Oxford who is due to have a book published on the
subject. I assume the editor was thinking that you might create a factor
type variable for your index, as ANOVA tends to be a designed
experiment with factors; how you would use a covariate in this context,
I am not sure.

I'd be interested in your replies.

Trevor
________________
Trevor McMullan
Statistician
Quintiles Toxicology Pathology Services
Tel:     +44 (0)1531 634121
Fax:     +44 (0)1531 634753
email:   [log in to unmask]









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