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Re: st: more cases than controls

From   Michel Camus <[email protected]>
To   [email protected]
Subject   Re: st: more cases than controls
Date   Wed, 24 Mar 2004 22:34:23 -0500

Dear Ricardo,
Following up on my previous posting and those of Philip Ryan and Ronan Conraoy, in a case-control study, you are sampling on the basis of outcome variable, thus you cannot state that the level of enzymes is your "outcome" variable; the outcome is the disease that defines cases.
Indeed, ....
1) If the enzyme level is an effect of the disease, then you do not have a case-control study but a cohort or cross-sectional study.
2) If the enzyme level is a diagnostic marker of the disease, then you rather have a cross-sectional study.
3) If the enzyme level is a risk factor for or a "determinent" of the outcome, you do have a case-control study, but then you are testing for the difference in a "determinant" of the disease. You cannot call the enzyme variable your "outcome variable" like you did in your postings.

Like Philip Ryan states, the logistic approach and the t-test approach provide a similar test statistic in a univariate analysis. So your analysis may not be wrong statistically in a univariate context, but it is unnecessarily awkward and limited. You should use a logistic regression approach because first, in addtion to the test statistic, it can provide an eiologically meaningful estimate of how much the risk of disease increases as a function of enzyme level. Second, you remain clear as to what is a determinant and what is an effect. Third, you may and probably should adjust for confounders (e.g. age is often a determinant of enzyme levels). Finally, your results will be expressed in a consistent manner with cohort studies.

Finally, I would not rely on how other previous studies have analysed the data per se. Habits and traditions often have the inconvenience of incomplete and intuitive thought processes. For comparison, you may report the same analysis, but you should add the better and more coherent approach.


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Michel Camus, Ph.D.
Epidemiologist, Biostatistics and Epidemiology Div., HECSB, Health Canada

Courriel / e-mail : [email protected] <mailto:[email protected]>

Téléphone / phone : (514) 850-0157

Télécopieur / fax : (514) 850-0836

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Ronán Conroy wrote:

on 24/03/2004 04:01, Ricardo Ovaldia at [email protected] wrote:

This was a population-based Case–Control 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?

There is a difference of model involved.

When you do a t-test, your are asking whether the presence of a condition
affects the mean value of a variable of interest. Do patients with
Parkinson's disease have poorer performance on complex problem solving
tasks? (Yes, they do.)

When you do a logistic regression, you are asking whether a variable changes
the odds of having a disease or condition. Does being a women change the
odds of having depression (yes it does). Note that you cannot turn this
example around. It makes no sense to ask if depression affects your chances
of being a woman.
Some case control studies can meaningfully be analysed either way. People
who have recently had a heart attack are more depressed than people who have
not. But there is evidence that depression is not just a consequence of
serious physical illness, but actually a risk factor for heart disease. And,
of course, a case-control study cannot differentiate depression as a cause
of heart disease from depression as a sequel.

So you don't know the right statistical procedure until you know the
scientific model you are testing.

Ronan M Conroy ([email protected])
Lecturer in Biostatistics
Royal College of Surgeons
Dublin 2, Ireland
+353 1 402 2431 (fax 2764)

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