Often there is more than one test result, or more than one set of pedigree information, or both, that can be incorporated as conditional probabilities in a single Bayesian analysis. For example, consider the pedigree in Figure 5-4a, in which the two maternal great uncles of the consultand were affected with Duchenne muscular dystrophy (DMD; OMIM #310200),a severe X-linked recessive disease caused by mutations in the DMD gene (OMIM #300377). The con-sultand's maternal grandmother's carrier risk was 1/2, her mother's carrier risk was 1/4, and therefore the consul-tand's prior carrier risk is 1/8. Suppose that her carrier testing is negative using a highly specific test (an analysis for heterozygous deletions in the DMD gene) that detects 2/3 of carriers. Suppose also that her serum creatine phos-phokinase (CPK), which is elevated in two-thirds of carriers, is within normal limits. Taking into account her prior probability of 1/8, her normal molecular and CPK test results, and, in addition, her three normal sons, what is the probability that she is a carrier?

The Bayesian analysis for this scenario is shown in Figure 5-4b. Each conditional probability is given its own line. Because the genetic test detects 2/3 of carriers and is highly specific, the conditional probabilities of a negative genetic test result under the hypotheses that she is a carrier and noncarrier are 1/3 and 1, respectively. Because serum CPK is elevated in 2/3 of carriers, the conditional

-H | ||

1/ |

1 |
a | |

Hypothesis | ||

Carrier |
Non-carrier | |

Prior Probability |
1/8 |
7/8 |

Conditional probability (of negative genetic test result) |
1/3 |
1 |

Conditional Probability (of normal CPK result) |
1/3 |
19/20 |

Conditional Probability (of three normal sons) |
1/8 |
1 |

Joint Probability |
1/576 |
133/160 |

Posterior Probability |
0.002 |
0.998 |

Figure 5-4. (a) Pedigree of a family with individuals affected with DMD (see text). Consultand is indicated by an arrow. (b) Bayesian analysis for the consultand in Figure 5-4a, taking into account her normal carrier test result, her normal CPK test result, and her three normal sons.

Figure 5-4. (a) Pedigree of a family with individuals affected with DMD (see text). Consultand is indicated by an arrow. (b) Bayesian analysis for the consultand in Figure 5-4a, taking into account her normal carrier test result, her normal CPK test result, and her three normal sons.

probability of a normal serum CPK for the hypothesis that she is a carrier is 1/3. Because 5% of noncarrier women have an abnormal serum CPK (i.e., the normal range is defined as comprising 95% of normal individuals),the conditional probability of a normal serum CPK under the hypothesis that she is a noncarrier is 95% or 19/20. Finally, as in Figure 5-1b, the conditional probabilities of three normal sons under the hypotheses that she is a carrier and noncarrier are 1/8 and 1, respectively. The joint probabilities for each hypothesis are the products of the prior probability, and all conditional probabilities, for each hypothesis (Figure 5-4b). Calculation of posterior probabilities then proceeds exactly as in Table 5-1. In this scenario, taking into account her normal test results and her three normal sons, the consultand's carrier risk is lowered from 1/8 to 0.002, or approximately 1/500.

Was this article helpful?

## Post a comment