## Bayesian Analysis Used in Risk Modification

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When collected pedigrees are used to provide risk assessment, a variety of data may be relevant to the overall assessment. Numerous factors, some listed above, influence the likelihood that a given individual in the family may be affected by the condition in question or may be a carrier of the gene in question. When it is not possible to do direct diagnostic testing for the condition (for example, if the causative gene is unknown), when the affected relative is not available for testing, or for complex traits, it is possible to combine incremental contributors to risk by utilizing Bayesian analysis. Bayesian analysis is a statistical construct that uses information about the likelihood of occurrence of past events or conditions, and the current status of those events or conditions for the individual, to predict the likelihood of a future event or condition, in this case, the presence or absence of a particular gene or genetic condition.18 Some factors that may be considered in genetic risk assessment using Bayesian analysis include number and pattern of affected and unaffected family members, laboratory data, and natural history of the condition. The probability assigned based on past events is called the prior probability; that based on current information or observations is called the conditional probability. The calculated probability for each possible outcome of an event or condition is the joint probability, and the final probability of one outcome as a percentage of all possible outcomes is the posterior probability. Calculations often utilize data from multiple generations and are usually done in tabular form. In the example pedigree in Figure 4-7 for an autosomal dominant cancer predisposition syndrome affecting males and females equally, based on Mendelian inheritance alone, the risk that individual III.5 is a gene carrier is 25%. However, knowing that 75% of gene carriers have been diagnosed with cancer by age 50, risk can be recalculated as demonstrated. (See chapter 5 for a complete discussion of Bayesian analysis.)

 For ll.3 Gene present Gene not present Prior probability 1/2 1/2 Conditional probability 1/4 1 Joint probability 1/8 1/2 1/8+1/2 1/8 +1/2 Posterior probability 1/5 =20% 4/5 =20% For lll.5 /5x1/2=1/10=10%

Figure 4-7. Bayesian analysis for risk assessment in an autosomal dominant, adult-onset hereditary cancer disorder. Ages of selected individuals in generation II are shown below the pedigree symbols.

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