Dear Robin,
My first remark here is about the score itself, not the questionnaire, and
how it is constructed. let me exlian my point of view: For each subject, the
full data the questionaire is providing is Y = (Y1,Y2,...., Y12) where each
Yj represents the answer to item j (j= 1,2,...12) with values in 1,2,3,4,5.
This data vector can be reduced without signifivant loss to a vector n =
(n1,n2,n3,n4,n5) where ni = the number of items (among the 12 items) where
the answer was equal to i. For example n = (2,4,5,1,0) means that two
items were answered by 1; 4 items wrere answred by 2; 5 items were answred
by 3; 1 item was answred by 1 and no items with answer 5 was recorded. So
the sum of ni shouls equal 12. The score you are calculating (called here
Oxford hip score) If I well understood it is equal to :
n1+2*n2+3*n3+4*n4+5*n5. Example; if n = (12,0,0,0,0) the score will be 12.
If n = (10,1,1,0,0) the score will be 1*10 + 2*1 + 3*1 + 4*0+5*0 = 15 etc
... The problem with this score is that it doesn't preserve the ordering for
some monontonic function of the initial coding (1,2,3,4,5). In other way, if
you decide to change the coding of items from 1,2,3,4,5 to 11,13,14,15,20
(which is legitimate since these are just coding or ordinal categories) then
you may find 2 subjects such that: According to coding 1, subject1 is better
than subject2 but according to coding 2 it is the opposite. This is not
consistent I think because using this score one is trying trying to create a
quantitative measure from a set of qualitative measures. Normally we do it
in the opposite sense. I think it better to analyse the vector n =
(n1,n2,n3,n4,n5) instead of using this score. The vector n may be analysed
using a sort of multivariate binomial distributions.
I hope this helps,
Abderrahim
Dr Abderrahim Oulhaj, M.S.c. PhD
Senior Research Statistician
The Oxford Project to Investigate Memory and Ageing (OPTIMA)
Nuffield Department of Clinical Medicine (NDM)
University of Oxford
UK
----- Original Message -----
From: "G Robin Henderson" <[log in to unmask]>
To: <[log in to unmask]>
Sent: Tuesday, January 18, 2011 12:42 PM
Subject: Analysis of Oxford Hip Score data
> Dear AllStat
>
> I've had some conversations recently with colleagues in orthopaedics who
> are interested in analysing Oxford hip score data for patients who have
> undergone hip arthroplasty. The Oxford hip score questionnaire contains
> 12 items each of which has five categories of response. Each item is
> scored from 1 to 5, from least to most difficulty or severity. The scores
> are then added to produce a single figure with a range from 12 (least
> difficulties) to 60 (most difficulties). They've been following the
> advice given by Vickers and Altman in "Analysing controlled trials with
> baseline and follow up measurements" (BMJ. 2001 November 10; 323(7321):
> 1123–1124) and fitted at an analysis of covariance model of the form: -
> Post-op score=Constant+a×Pre-op score+b×Type. Type is a dummy variable
> indicating which of two arthroplasty procedures was used. However
> concerns arise due to the discrete nature of the scores and the fact that
> a fifth of patients have post-op scores of 12, the lowest posssible.
>
> One suggestion that has been made is to categorise outcome and use
> logistic regression. They'd be grateful for any other thoughts or
> references.
>
> Best Wishes
>
> Robin
>
> G Robin Henderson
> Stroke Audit Coordinator
> Royal Infirmary of Edinburgh
>
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