Suppose that an investigator considers conducting a case-control study to evaluate the relationship between invasive epithelial ovarian cancer and the history of infertility (yes/no). It is estimated that the proportion of controls with a history of infertility is about 10% and the investigator wishes to detect a relative risk of 2.0 with a power of 80% using a two- sided level of significance of 0.05.

(a) Find the total sample size needed if the two groups, cases and controls, are designed to have the same size.

(b) Find the total sample size needed if the investigator likes to have the number of controls four times the number of cases.

(c) Find the number of cases needed if the design is 1:1 matched; matching criteria are various menstrual characteristics, exogenous estrogen use, and prior pelvic surgeries.