In the 1960's a group medical practice (Health Insurance Plan or HIP) undertook a

large scale randomized trial to evaluate the eectiveness of mammography. There were

62000 subjects in the experiment (women members of HIP aged 40-64) of whom 31000

were randomly selected to be the control group and the other half were randomized

into treatment (i.e. chosen for treatment). These individuals were sent an invitation

to four rounds of annual screening (a clinical exam and mammography) and we will

call them the treatment group. The control group received no such invitation and was

provided with the usual level of health care.

(a) The researchers followed the subjects for ve years and recorded the number of

deaths due to breast cancer that occurred in each group. They found that in

the treatment group there were 39 such deaths or 1.3 deaths per 1000 women.

while the corresponding gure for the control group was 63 (2.0 deaths per 1000

women). Compute the OLS estimate of the eect of the treatment on death rates

given this information.

(b) The researchers found, however, that not everyone in the treatment group ac-

cepted the invitation for screening (we ignore compliance problems in the control

group). In fact, of the 31000 individuals who received the invitation, about 10800

(1/3 roughly) refused the screening. The number of deaths from breast cancer

in this group was 16 (death rate per 1000 women 1.5) the corresponding gure

among the 20200 who actually accepted the treatment was 23 (death rate per

1000 women 1.1). Compute the IV estimate of the eect of the treatment on

death rates using treatment assignment as an instrument and compare it to the

eect you estimated in part (a) above.

(c) The researchers also recorded all other deaths (excluding breast cancer) in the

treatment and control groups and obtained the following. In the control group,

there were 879 deaths from other causes (death rate per 1000 women: 28) while the

corresponding gure for those in the treatment group who refused the invitation

was 409 (death rate per 1000 women: 38) and for those in the treatment group

who accepted the invitation was 428 (death rate per 1000 women 21). Does

this information cause you to doubt the OLS estimates of the treatment eect

computed in (a) above and if so why (be as precise as possible)?