Approach: In the 1960s a group medical practice (Health Insurance Plan or HIP) undertook a large scale randomized trial to evaluate the effectiveness 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 five 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 figure for the control group was 63 (2.0 deaths per 1000 women). Compute the OLS estimate of the effect of the treatment on death rates given this information. (b) The researchers found however that not everyone in the treatment group accepted 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 figure among the 20200 who actually accepted the treatment was 23 (death rate per 1000 women 1.1). Compute the IV estimate of the effect of the treatment on death rates using treatment assignment as an instrument and compare it to the effect 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 figure 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 effect computed in (a) above and if so why (be as precise as possible)?