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Re: Analysis of a case control study (was st: more cases thancontrols)


From   Dario Consonni <dario.consonni@unimi.it>
To   statalist@hsphsun2.harvard.edu
Subject   Re: Analysis of a case control study (was st: more cases thancontrols)
Date   Wed, 24 Mar 2004 10:57:10 +0100

I agree with Phil, in fact this is the reason why usually case-control
studies are analyzed using logistic regression: you get OR - the
relationship of risk of disease with increasing levels of exposure (the
serum levels) - a measure much more informative than a simple t-test .
Dario


----- Original Message ----- 
From: "Philip Ryan" <philip.ryan@adelaide.edu.au>
To: <statalist@hsphsun2.harvard.edu>
Sent: Wednesday, March 24, 2004 8:10 AM
Subject: Analysis of a case control study (was st: more cases than controls)


> Ricardo
>
> I do not mean to imply that the studies (of which I know nothing!) are
> *incorrectly* analysed.
>
> Indeed, Hosmer and Lemeshow (Applied Logistic Regression, Wiley 1989)
state
> that, in the univariate case at least, the t test is equivalent to the
> simple logistic model.  They appeal to the analogous discriminant
> function.  This is somewhat qualified by their statements (p84 of first
> edition):
>
> 1. "the most desirable univariate analysis involves fitting a univariate
> logistic regression..."
> 2. there are assumptions of normality when using the t test that are not
> required in the logistic model (I note you appear to have taken care of
this)
>
> and
>
> 3. ".. the t test should be useful in determining if the variable should
be
> included in the model....", by which they mean a logistic model.  That is
> to say, they certainly don't push the t test as being the test of choice
> for the c-c study *because the usual objective is to estimate risk* (or
> some related metric eg OR).
>
> There is no reference in Schlesselman's book "Case Control Studies" (nor
in
> Breslow and Day, nor in Rothman & Greenland's Modern Epidemiology) to the
> use of the t test in analysis of case control studies, possibly
> because  (i) as I have said before, it seems to reverse the sense of the
> study design and (ii) it doesn't deliver the risk estimate.
>
> So, I don't think you have analysed _incorrectly_, as long as your
analyses
> are univariate.  My own preference (prejudice, practice and pedagogy) is
to
> put predictors on the right and outcomes on the left.
>
> Phil
>
>
>
> At 08:01 PM 23/03/2004 -0800, you wrote:
> >I am now very confused by your intuitive argument.
> >
> >This was a population-based Case­Control Study
> >comparing a specific enzyme in the serum of infected
> >patients (cases) to that in healthy non-infected
> >controls. We compared these levels using a t-test
> >after log-tranforming the data. Is this
> >incorrect?There are many similar studies in the
> >literature. Am I to understand that they are all
> >incorrectly analyzed?
> >
> >Am sorry but I do not get it.
> >
> >Ricardo.
> >
> >
> >--- Philip Ryan <philip.ryan@adelaide.edu.au> wrote:
> > > Ricardo
> > >
> > > Leaving aside the question of relative numbers of
> > > cases and controls, I
> > > wonder if the reviewers remarked on your choice of
> > > analysis.  That is to
> > > say, in a case control study the outcome is the case
> > > control status, not
> > > the antecedent exposure (in your study the biomarker
> > > level).  A t-test
> > > reverses this sense of the study design, as the
> > > exposure is now the outcome
> > > and the case control status is (I was taught) forced
> > > unnaturally to be the
> > > "predictor".  In modelling terms, keep the outcome
> > > defined by the study
> > > design on the left hand side.  I would choose a
> > > logistic model, either
> > > keeping the biomarker level continuous if you
> > > believe there is a linear
> > > dose response with the log odds or perhaps with
> > > dummies of ordered
> > > categories of the biomarker if you wish to explore
> > > the functional nature of
> > > the relationship.
> > >
> > > Phil
> > >
> > >
> > >
> > >
> > > At 05:32 AM 23/03/2004 -0800, you wrote:
> > > >Thank you Michel,
> > > >
> > > >I would like to clarify two points:
> > > >
> > > >1. We had more cases than controls because of
> > > >budgetary constrains. It was easier and less
> > > expensive
> > > >to enroll cases than controls.
> > > >
> > > >2. The main outcome of interest was a serum
> > > biomarker
> > > >measured on a continuous scale and log transformed
> > > for
> > > >the analysis. A t-test was used to compare cases
> > > and
> > > >controls and therefore no OR computed.
> > > >
> > > >Best,
> > > >Ricardo.
> > > >
> > > >
> > > >
> > > >--- Michel Camus <mcamus@videotron.ca> wrote:
> > > > > Ricardo Ovaldia wrote:
> > > > >
> > > > > >(...) We recently submitted a manuscript for
> > > > > publication to
> > > > > >a major medical journal. It was a case-control
> > > > > study
> > > > > >with 329 cases and 126 controls. One of the
> > > > > reviewers
> > > > > >wrote that "to have such a larger number of
> > > cases
> > > > > was
> > > > > >statistically atypical" and asked if the
> > > "authors
> > > > > find
> > > > > >that the use of the same control for multiple
> > > > > patients
> > > > > >significantly limits results"?
> > > > > >
> > > > > >I never heard of any biases or other problems
> > > cause
> > > > > by
> > > > > >having more cases than controls in a study. We
> > > had
> > > > > >sufficient power and the difference for our
> > > main
> > > > > >outcome was highly significant (less than
> > > 0.00001).
> > > > > Am
> > > > > >I missing something or is it that this reviewer
> > > > > does
> > > > > >not understand the case-control designed? By
> > > the
> > > > > way
> > > > > >this was not a matched study design.
> > > > > >Thank you,
> > > > > >Ricardo.
> > > > > >
> > > > > >
> > > > > Dear Ricardo,
> > > > > There is no problem per se with having less
> > > controls
> > > > > than cases, though
> > > > > it should raise some eyebrows.
> > > > > The critique of using "the same control for
> > > multiple
> > > > > patients" suggests
> > > > > the reviewer's misunderstanding of an unmatched
> > > > > design.
> > > > > A smaller number of controls for a single group
> > > of
> > > > > cases is "atypical"
> > > > > still.
> > > > > One usually chooses an equal or larger group of
> > > > > controls to increase
> > > > > power to be able to detect even a small odds
> > > ratio
> > > > > when exposure is
> > > > > relatively rare.
> > > > > A smaller number of controls than cases suggests
> > > > > that the investigators
> > > > > had more cases than needed given an expected a
> > > > > priori a large relative
> > > > > risk (>5) and a high prevalence of exposure
> > > (>75%)
> > > > > among controls (cf.
> > > > > Schlesselmann, 1982, p.155). Could it not then
> > > be
> > > > > construed that the
> > > > > investigators knew enough beforehand not to do a
> > > > > study?...
> > > > > With respect to the outcome measure, I do not
> > > > > understand how you can say
> > > > > from a case-control study that "the difference
> > > for
> > > > > our main outcome was
> > > > > highly significant (less than 0.00001)".
> > > Usually
> > > > > the measure of effect
> > > > > in a case-control study is an odds ratio, not a
> > > > > difference (in rates?).
> > > > >
> > > > > Michel
> > > > >
> > > > > ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
> > > ~ ~
> > > > > ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
> > > > > ~ ~ ~ ~ ~
> > > > >
> > > > > Michel Camus, Ph.D.
> > > > >
> > > > > Épidémiologue, Div. Biostatistique et
> > > épidémiologie,
> > > > > DGSESC, Santé Canada
> > > > >
> > > > > Epidemiologist, Biostatistics and Epidemiology
> > > Div.,
> > > > > HECSB, Health Canada
> > > > >
> > > > > Courriel / e-mail : mcamus@videotron.ca
> > > > > <mailto:mcamus@videotron.ca>
> > > > >
> > > > > Téléphone / phone     :    (514) 850-0157
> > > > >
> > > > > Télécopieur / fax        :    (514) 850-0836
> > > > >
> > > > > ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
> > > ~ ~
> > > > > ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
> > > > > ~ ~ ~ ~ ~
> > > > > ==============================
> > > > >
> > > > >
> > > > >
> > > > >
> > > > > *
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> > > >
> > > >
> > > >__________________________________
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> > > Philip Ryan
> > > Associate Professor,
> > > Department of Public Health
> > > Associate Dean (Information Technology)
> > > Faculty of Health Sciences
> > > University of Adelaide 5005
> > > South Australia
> > > tel 61 8 8303 3570
> > > fax 61 8 8223 4075
> > > http://www.public-health.adelaide.edu.au/
> > > CRICOS Provider Number 00123M
> > >
> >=== message truncated ===
> >
> >
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>
> Philip Ryan
> Associate Professor,
> Department of Public Health
> Associate Dean (Information Technology)
> Faculty of Health Sciences
> University of Adelaide 5005
> South Australia
> tel 61 8 8303 3570
> fax 61 8 8223 4075
> http://www.public-health.adelaide.edu.au/
> CRICOS Provider Number 00123M
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