Question

Exhibit L.1 reports the multivariate odds ratios comparing each category to women who never had an induced abortion and had at least one pregnancy. Researchers were able to interview 845 out of 1,011 (83.5 percent) of the eligible cases and 961 out of 1,239 (78 per- cent) of the eligible controls. Of the cases, only 689 (81.5 percent) had complete information on abortion history, compared to 781 (81.3 per- cent) of the eligible controls.

Abortion History	Cases	Controls	Crude OR2	Multivariate OR (95% CI)3
Ever had abortion	210	201		1.5 (1.2–1.9)
1 abortion only	150	142		1.5 (1.1–2.0)
2+ abortions	60	59		1.6 (1.0–2.4)
Age at first abortion
<18	20	15		2.5 (1.1–5.7)
18–19	34	36		1.7 (1.0–3.0)
20–29	115	123		1.3 (1.0–1.7)
30+	41	27		2.1 (1.2–3.5)
Timing of first abortion
Before 1st birth	69	76		1.4 (1.0–2.0)
After 1st birth	74	63		1.5 (1.0–2.2)
Never gave birth	67	62		1.7 (1.2–2.6)
Never had abortion	479	580		––
Never had an abortion and at least one pregnancy1	466	564		––

Note: 1. Estimated from the data. 2. Multivariate OR adjusts for age, family history of breast cancer, religion, age at first pregnancy. 3. Both crude and multivariate odds ratio estimates risk relative to women with a least one pregnancy who never had an induced abortion. Source: Daling et al. (1994).

Calculate the crude odds ratios for each of the abortion history strata in Exhibit L.1. What is the overall increased risk of abortion after adjusting for several covariates?

Answer 1

Let us define a = Number of exposed cases · . b Number of exposed non-cases . cNumber of unexposed cases d = Number of unexposed non-cases a/c ad b/d bc OR = _ = (n) exposed cases/(n) unexposed cases (n)exposed non cases/(n) unexposed non cases OR (n) exposed cases x (n) unexposed noncases (n) exposed noncases x (n) unexposed cases In our problem, we have considered, Of the cases, only 689 (81.5 percent) had complete information on abortion history, compared to 781 (81.3 per- cent) of the eligible controls. And thus number of Cases 689 number of Controls -781 Let us take the first one

Let us take the first one ControlsCrude OR2 Abortion History Cases 210 1.27 Ever had abortion 201 We got answer Crude OR2-1.27. How to arrive at this value? . aNumber of exposed cases 210 b Number of exposed non-cases 689-210-479 · c = Number of unexposed cases = 201 Number of unexposed non-cases-781-201-580 ad 210 580 1.27 Thus Crude OR2= _- bc 479 201

Abortion History Cases Controls Crude OR2 1.25 1 abortion only We got answer Crude OR2 -1.25 150 142 How to arrive at this value? . a Numbe r of exposed cases= 1 50 . b Number of exposed non-cases 689-150-539 . C Number of unexposed cases 142 d Number of unexposed non-cases-781-142-639 Thus Crude OR2- And so on ad 150*639 bc 539.142 1.25

Control Cases 781 689 Multivariate OR 95% CI)3 es Controls Crude OR2 Abortion History Ever had abortion 1 abortion onl 2+ abortions Age at first abortion 18 18-19 20-29 30+ Timing of first abortion Before 1st birth After 1st birth Never gave birth Never had abortion 1.27 1.5 (1.2-1.9 1.25 1.5 (1.1-2.0 1.171.6 (1.0-2.4 201 142 59 210 150 60 1.532.5 (1.1-5.7 1.07 1.7 (1.0-3.0 1.07 1.3 (1.0-1.7 1.772.1 (1.2-3.5 15 36 123 27 20 34 115 41 1.03 1.4 (1.0-2.0 1.37 1.5 (1.0-2.2 1.25 1.7 (1.2-2.6 0.79 0.80 76 63 62 580 69 74 67 479 Never had an abortion and at least one pregnancy1 466 564