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- ?
Stata:
. cci 96 104 109 666 , cornfield
Proportion
| Exposed Unexposed | Total Exposed
-----------------+------------------------+----------------------
Cases | 96 104 | 200 0.4800
Controls | 109 666 | 775 0.1406
-----------------+------------------------+----------------------
Total 205 770 | 975 0.2103
| Point estimate | [95% Conf. Interval]
|------------------------+----------------------
Odds ratio | 5.640085 | 4.003217 7.94673
(Cornfield)
Odds ratio | 5.640085 | 4.000589 7.95147 (Woolf)
Odds ratio | 5.640085 | 3.937435 8.06179 (exact)
+-----------------------------------------------
Breslow & Day:
The CLs given by B&D are: 3.94 - 8.07 (Cornfield),
4.00 - 7.95 (Woolf).
Dupont & Plummer:
Those given by -exactcci- are:
| Point estimate | [95% Conf. Interval]
|------------------------+----------------------
| | Cornfield's limits
Odds ratio | 5.640085 | 3.942972 8.071281 Adjusted
| | 3.937435 8.061794
Unadjusted
| | Exact limits
| | 3.937467 8.061784
Woolf's limits
Odds ratio | 5.640085 | 4.000589 7.951467 (Woolf)
All 3 sources agree on Woolf.
However, Stata's -cci- is much too close to Woolf's CI and much too far
from the "exact CI".
Is there an error?
As to the difference between -exactcc- and -cc- regarding exact limits,
-cc- calls "exact" what -exactcci- terms "Unadjusted Cornfield's limits",
while B&D and D&P seem to agree on Cornfield's "adjusted" CLs. Why does
Stata's -cc- results seem ... "odd"?
What am I missing? (... other than a proper statistical training!)
Michel Camus, epidemiologist
Health Canada
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