Question

Suppose all women with at least one birth in a recent study are classified as either having breast cancer or not and with age at first birth either s 29 or 2 30. The results áre displayed in the following contingency table: Age at first births 29 Age at first birth 230 Breast Cancer 1498 683 No Breast Cancer 8747 2537 a) Calculate the odds ratio for the sample data. Be sure to present the fo mula, values substituted, and odds ratio value (10 points) b) Construct a 95% confidence interval for the odds ratio. You need only provide the last two steps of the calculation process: show the values substituted into O Re^(-w) and OR*e(w) then report the final interval values. For example, your answer to part b should appear as follows: (10 points) 1.23*e^(-4.56) and 1.23*e^(4.56) (1.23.4.56)

Answer 1

Odds ratio basically tells about the presence or absence of property A has an effect on the presence or absence of property B.

Formula for Ofds Ratio

OR = a*d / b*c, where:

• a is the number of times both A and B are present,
• b is the number of times A is present, but B is absent,
• c is the number of times A is absent, but B is present, and
• d is the number of times both A and B are negative.

Let A be the property that Age at For Birth <=29 and B be the property that Breast Cancer is present.

Therefore,

a = 1498

b = 8747

c = 683

d = 2537

Substitute values in the formula

OR = (1498)(2537)/(8747)(683)

OR = 0.6361

$\omega = z_{\frac{\alpha}{2}} \times \sqrt{\frac{1}{a}+\frac{1}{b}+\frac{1}{c }+\frac{1}{d}}$

Z value for 95%CI = 1.96

Substituting the values we get

$\omega =$ 0.10071

CI upper limit = 0.6361 x e ^ 0.10071 = 0.7035

CI lower limit = 0.6361 x e^ -0.10071 = 0.5752

Confidence Interval = (0.5752, 0.7035)

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