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st: Re: Cornfield and Woolf confused? -cc- vs -exactcc- vs Breslow&Day


From   Weihua Guan <wguan@stata.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: Re: Cornfield and Woolf confused? -cc- vs -exactcc- vs Breslow&Day
Date   Mon, 02 Dec 2002 14:11:10 -0600

--Michel Camus <Michel_Camus@hc-sc.gc.ca>

> Stata's -cc- and Dupont & Plummer's -exactcc- do not provide the same
> Cornfield confidence intervals for ORs.
> Moreover, Stata's -cci- does not provide the same results as those by
> Breslow & Day (Stat.Methods in Cancer Research-Vol.1, p.124, 135-6)
> neither. Why is it so? Is their a mistake in Stata's -cci- ?
> [...]

First, let's clarify what -cci- produces.  In Stata 7, -cci- calculates the
exact confidence intervals by default, and calculates the unadjusted Cornfield
confidence intervals when -cornfield- is specified.  Now we can compare the
results from -cci- and -exactcci- using Michel's example:

1) exact confidence intervals:  

. cci 96 104 109 666
[...]
      Odds ratio |         5.640085       |  3.937435    8.061794  (exact)
[...]

. exactcci 96 104 109 666, exact
[...]
                 |                        | Exact limits
                 |                        |  3.937467    8.061784
[...]

These two commands actually apply the same algorithm in computing the upper
and lower limits.  The slight difference is due to computational precision.
If both program stored the intermediate results as double precision or
scalars, they would return identical results.

2) Cornfield confidence intervals:

. cci 96 104 109 666, cornfield
[...]
      Odds ratio |         5.640085       |  4.003217     7.94673  (Cornfield)
[...]

. exactcci 96 104 109 666, exact
[...]            
                 |                        | Cornfield's limits
      Odds ratio |         5.640085       |  3.942972    8.071281  Adjusted
                 |                        |  3.937435    8.061794  Unadjusted
[...]

The diffenence is due to the change of -cci-'s behavior.  In Stata 6, -cci-
computes (unadjusted) Cornfield confidence intervals by default, but switch
the default to the exact CI in Stata 7.  Since -exactcci- calls -cci- to grab
the unadjusted CI, it in fact gets the exact CI while expecting Cornfield.  If
we run this command in Stata 6, the correct values will be returned:

. exactcci 96 104 109 666, exact
[...]
                 |                        | Cornfield's limits
      Odds ratio |         5.640085       |  3.942972    8.071281  Adjusted
                 |                        |  4.003217     7.94673  Unadjusted
[...]


The adjusted Cornfield CI should be calculated correctly in -exactcci-.  The
difference between "adjusted" and "unadjusted" Cornfield CIs is a term +/-0.5
in the iterative process.  The formula for adjusted CI is given in
Schlesselman's "Case-Control Studies" (1982) p.177 (7.10).


Weihua Guan <wguan@stata.com>
Stata Corp.

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