Blood plasma proteins of patients with malignant breast tumors differ from proteins of healthy people in their solubility in the presence of various polymers. When the polymers dextran and poly(ethylene glycol) are mixed with water, a two-phase mixture is formed. When plasma proteins of tumor patients are added, the distribution of proteins between the two phases is different from that of plasma proteins of a healthy person. The distribution coefficient (K) for any substance is defined as K = [concentration of the substance in phase A]/[concentration of the substance in phase B]. Proteins of healthy people have a mean distribution coefficient of 0.75 with a standard deviation of 0.07. For the proteins of people with cancer, the mean is 0.92 with a standard deviation of 0.11.
(a) Suppose that K were used as a diagnostic tool and that a positive indication of cancer is taken as K 0.92. What fraction of people with tumors would have a false negative indication of cancer because K (b) What fraction of healthy people would have a false positive indication of cancer? This number is the fraction of healthy people with K ‰¥ 0.92, shown by the shaded area in the adjoining graph.
Estimate an answer with Table 4-1 and obtain a more exact result with the NORMDIST function in Excel.
(c) Vary the first argument of the NORMDIST function to select a distribution coefficient that would identify 75% of people with tumors. That is, 75% of patients with tumors would have K above the selected distribution coefficient. With this value of K, what fraction of healthy people would have a false positive result indicating they have a tumor?
Question continue over next page

Distribution coefficients of plasma proteins from healthy people and from people with malignant breast tumors

Transcribed Image Text:

6 Healthy people K 0.92 4. People with malignant breast tumors 0 0.5 0.6 0.7 0.8 0.91.0 1.1 1.2 1.3 Partition coefficient (K)