Oral Contraceptive Use and Ovarian Cancer - Library

CDC-EIS: OCs and Ovarian Cancer (811-X11) - Participant’s Guide page 7
The investigators used the data in Table 1 and
the formulas shown below to calculate an odds
ratio and 95% test-based confidence limits.
They also calculated a Mantel-Haenszel Chi as a
test of statistical significance to evaluate the
likelihood that any difference between the
observed (calculated) OR and the OR under the
null hypothesis could be due to chance.
Measure Formula Calculation from Table 1
Odds Ratio (OR)
ad
(93)(683)
OR =
= 0.77
bc
(959)(86)
Expected Value of Cell ‘a’
(E(a))
H 1V
E(a)=
T
1
(1052)(179)
= 103.41
1821
Mantel-Haenszel (MH)
Variance
H 1 H 0V
1V
MH variance=
2
T (T -1)
0
(1052)(769)(179)(1642)
= 39.40
2
(1821 ) (1821-1)
Mantel-Haenszel Chi*
a - E(a)
93 -103.41
X MH =
= -1.66
MH variance
39.40
Test-based Confidence
Limits
(Note: Z values for 2-sided
confidence limits are:
90% = 1.645,
95% = 1.96,
99% = 2.58.)
(1-(Z/
X MH ))
LOWER CL= OR
(1 X ))
UPPER CL = OR
+(Z/ MH
0.77
(1(1.96 / 1.66))
= 0.57
(1
0. (1.96 / 1.66
77
)) 1.05
* The chi is the square root of the more commonly used chi-square. The Mantel-Haenszel chi with one
degree of freedom (X MH ) is equivalent to a Z-score and can be used to find the 2-tailed p-value from a
table of areas in two tails of the standard normal curve. In this case, p = 0.097.