## Newborn Testing and Conditional Probability

How is the knowledge about the frequency of different genes and genotypes in the population useful? As mentioned already, all fifty states test for PKU among their newborns. The accuracy of most of the newborn testing is better than 99.9 percent. Thus, these tests are very accurate but not perfect. Because the tests are accurate, we expect that any baby born with the disease will be detected. However, there is a 0.1 percent chance that even if a baby does not have the disease it will test positive. That is, there is a 0.1 percent chance of false positive. So, let's see the consequences of this false positive result.

Figure 10.6 shows how many babies will test truly positive compared to the false positives. First, we begin by choosing the total number of individuals tested. In Figure 10.6.A we chose 10,000, since the frequency of PKU among U.S. Caucasians is 1 in 10,000. Then we make a row for those that test positive and a row for those that test negative. After that, we make a column for the number of individuals we expect to be affected and for those that are not affected. Only one affected baby is expected, and that baby will test positive. Under the designation "normal," we use the information we have regarding false

 1 T 0.00171 IT 1 IT 0.0017 Tt 0.00171 0.0017 Tt 3x10 6 tt B IT 0.0141 1 T 1 TT 0.014 Tt 0.014 t 0.014 Tt 2x10 4 tt

Figure 10.5 Using the Punnett Square to Calculate the Proportion of Tay-Sachs Carriers. A. Among the general population. B. Among Ashkenazi Jews of Eastern European origin.

Figure 10.5 Using the Punnett Square to Calculate the Proportion of Tay-Sachs Carriers. A. Among the general population. B. Among Ashkenazi Jews of Eastern European origin.

positives to fill in the "test positive" category. The false positive rate is 0.1 percent; 0.1 percent of 10,000 is 10. Thus ten normal babies will test positive! The remainder of the babies will test negative. Now we can calculate the total for those that test positive. Of the 11 that test positive, only 1 is expected to actually have PKU. Any baby that tests positive for any disease is automatically tested again because of these unavoidable false positives. It is highly unlikely that testing the same baby will yield a false positive twice in a row. It is only after a baby tests positive twice that doctors are contacted to check the diagnosis and begin treatment.

Now, let's do the same analysis, using this time the PKU rate among ethnic Japanese. In this population, PKU is found at the much lower rate of 1 in 110,000. We fill in the same table as before in figure 10.6.B, but we choose 110,000 as the total population, since now there is only 1 case of PKU in 110,000 births. The number of affected babies

 affectcd normal total lest positive 1 10 11 test negative (1 9,989 9,989 total 1 9,999 10,000
 affected normal total test positive 1 no 111 test negative 0 109,889 109889 total 1 109,999 110,000

Figure 10.6 Calculating the Number of False Positives for PKU. A. In the case of the U.S. Caucasian population. B. In the case of the Japanese population.

Figure 10.6 Calculating the Number of False Positives for PKU. A. In the case of the U.S. Caucasian population. B. In the case of the Japanese population.

is just one, and that one will be detected as positive. However, although the accuracy of the test does not change, the false positive rate of 0.1 percent now applies to a much larger population, so the actual number of false positives is 110. So now out of a 111 that test positive, only 1 baby actually has PKU! This conclusion strongly reinforces the necessity of conducting more than a single test to determine which babies are truly PKU positive.

The actual number of disease cases relative to the number of false positives is an important consideration when deciding whether to screen the general population. Another example of this is maple syrup (or fenugreek) urine disease. This is a metabolic genetic disease that can be easily treated with vitamins and dietary control. This disease is quite rare in the general population, and the estimated frequency is about 1 in 300,000. In several years of testing newborns in Iowa, all babies that tested positive turned out to be false positives. Therefore, testing for this disease was discontinued in Iowa in 1995. There are populations that have unusually high rates of this disease, for whom testing is advised. For example, a Mennonite community in eastern Pennsylvania has a rate of 1 in less than 200! We discuss possible reasons for such differences in disease frequency in the next chapter.

 xH xh y xH xHxH xV xhy xh xhxH xV 10'4 xhy 1xh ioV y 1xh ixV io'4xHxh ixhy 10-V 10-4xhxh io-s x"xh 10'4 xhy 1 in 100,000,000 girls are hemophiliac 2 in 10,000 girls arc carriers 1 in 10,000 boys arc hemophiliac

Figure 10.7 Punnett Squares Used to Calculate the Frequency of a Sex-Linked Trait in a Population. A. Punnett square representing the males at the top and the females on the side. The males are represented by two X chromosomes for the frequency of the normal and disease gene on the X chromosome and by their Y chromosome. The 1 in 10,000 frequency for hemophilia A among males of is shown for XhY. B. Completed Punnett square with the hemophilia gene frequencies.

Figure 10.7 Punnett Squares Used to Calculate the Frequency of a Sex-Linked Trait in a Population. A. Punnett square representing the males at the top and the females on the side. The males are represented by two X chromosomes for the frequency of the normal and disease gene on the X chromosome and by their Y chromosome. The 1 in 10,000 frequency for hemophilia A among males of is shown for XhY. B. Completed Punnett square with the hemophilia gene frequencies.