Suppose we consider the serum vitamin E assay as a screening test for compliance with vitamin E supplementation. Participants whose change in serum vitamin E is ‰¥ Δ mg/dL will be considered vitamin E takers, and participants whose change is < Δ mg/dL will be considered placebo takers. Choose several possible values for Δ, and construct the receiver operating characteristic (ROC) curve for this test. What is the area under the ROC curve? 

Cancer

A treatment trial is proposed to test the efficacy of vitamin E as a preventive agent for cancer. One problem with such a study is how to assess compliance among participants. A small pilot study is undertaken to establish criteria for compliance with the proposed study agents. In this study, 10 patients are given 400 IU/day of vitamin E and 10 patients are given similar-sized placebo capsules over a 3-month period. Their serum vitamin E levels are measured before and after the 3-month period, and the change (3-month €“ baseline) is shown in Table 5.2.

Table 5.2: Change in serum vitamin E (mg/dL) in pilot study

 

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Group Mean sd Vitamin E 0.48 0.80 10 Placebo 0.05 0.16 10