Organization: Institut Armand Frappier
Newsgroups: bit.listserv.stat-l
Date:         Thu, 30 Jul 1992 08:52:21 EDT
Comments:     Adresse alternative de l'envoyeur: <IMR2027@UQUEBEC>
From:         Eduardo Franco <IMR2027@IAF.UQUEBEC.CA>
Subject:      logistic regression
X-To:         stat-l@vm1.mcgill.ca

Quoting from lawhiteside%UALR.EDU@VM1.MCGILL.CA...

LW> I have a variable that I think is a very good predictor of my good/bad
LW> outcome measure.  However, it is so good (and I have so few cases)
LW> that all of the good outcome cases measure in the "good" category
LW> of the predictor variable ... that is the situation is like
LW> this (where the numbers are the N in each cell) :
LW>
LW>
LW>                         Outcome Variable
LW>   Predictor var         bad            good
LW>        low            143               28
LW>        high            25                0
LW>
LW>
LW> What I really want is to compute odds ratio - but I don't know how to handl
LW> the 0 cell .....

Add 0.5 to each cell frequency in the above crude table (if I'm not
mistaken, this is known as Woolf's technique) if you must derive the OR
as measure of association.

LW> On a related issue, I have another variable in the same model that is
LW> "the number of people living in the home"  ... I want to be able to say
LW> something like:   "Living with 4 or more people puts a child at risk of xxx
LW> Is there a standard way to determine the cut point?  I know I could leave i
LW> continuous but in the first place I don't think it is linear and in the sec
LW> I want to know when the risk starts not just that more is worse....
LW>
LW> Thanks in advance,
LW> Leanne Whiteside
LW> LAWHITESIDE@UALR.EDU

Build your model using dummy covariates to represent contrasts. This method
comes in handy when calculating ORs. For instance, assume that your variable
for no. of people is named NUMP. The following set of dummy regressors would
be used in place of NUMP in your LR model: (assuming hypothetical values)

        Value for             Coding for dummy variables
          NUMP                NUMP2  NUMP3  NUMP4  NUMP5       Level
          0-1                   0      0      0      0           1
          2-3                   1      0      0      0           2
          4-5                   0      1      0      0           3
          6-7                   0      0      1      0           4
          >=8                   0      0      0      1           5

Observe that for j levels in your original variable you need to
specify j-1 dummy regressors.  The exponentiated regression coefficient
for NUMPi will denote the OR for level i contrasted with level 1, taken as
reference category.

By playing with the coding scheme you may be able to probe other interesting
relations.  For instance, the somewhat modified scheme shown below would
allow you to contrast adjacent levels (any j against j-1):

        Value for             Coding for dummy variables
          NUMP                NUMP2  NUMP3  NUMP4  NUMP5       Level
          0-1                   0      0      0      0           1
          2-3                   1      0      0      0           2
          4-5                   1      1      0      0           3
          6-7                   1      1      1      0           4
          >=8                   1      1      1      1           5

Now back to your question, the use of dummy regressors as shown above
would allow you to model non-linear trends in dose-response between your
predictor and the outcome. It would also allow you to spot sudden changes
in effect, such as a threshold, as you mention. In fact, with the latter
scheme you would use the Wald statistics for each coefficient to detect
a significant difference in two consecutive ORs.

E. Franco, Univ. Quebec (imr2027@iaf.uquebec.ca)

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