Question

7. A prospective study was conducted many years ago on a sample of young women in Nebraska, to determine if there was an association between cigarette smoking during pregnancy and the incidence of miscarriages. Of the 385 mothers, 50 reported smoking cigarettes during pregnancy, and 10 of these had miscarriages. A total of 25 miscarriages occurred altogether. Assuming that the smoking and non-smoking subgroups were similar with regard to other factors and study was not biased, the relative risk (RR) of miscarriages in this population is 4.47. Determine if RR was statistically significant and determine its 95% confidence interval. Interpret your results.

Answer 1

2 Way table is,

smoking cigarettes	miscarriages	No miscarriages	Total
Yes	10 (A)	40 (B)	50
No	15 (C)	320 (D)	335
Total	25	360	385

Point Estimate of RR = (A(A+B)) / (C / (C+D))

= (10/50) / (15/335)

=  4.47

95% confidence interval of RR is,

RR 1.96 *

4.47 1.96 *

(4.47 - 1.96 * 0.4413521 ,  4.47 + 1.96 * 0.4413521)

( 3.60 ,  5.34)

Since the 95% confidence interval of RR of miscarriages does not contain the value 1, RR was statistically significant at 95% confidence level.

Interpretation: We are 95% confident that the relative risk of miscarriages among smoking cigarettes during pregnancy compared to non-smoking subgroups is between 3.60 and 5.34.