|P(Tran=good|Car=lemon)= .4 P(Tran=good|Car=peach) = .9|
Example 5.16 This example is taken from [Nease and Owens, 1997]. Suppose a patient has a non-small-cell carcinoma of the lung. The primary tumor is 1 cm. in diameter, a chest X-ray indicates the tumor does not abut the chest wall or mediastinum, and additional workup shows no evidence of distant metas-tases. The preferred treatment in this situation is thoracotomy. The alternative treatment is radiation. Of fundamental importance in the decision to perform thoracotomy is the likelihood of mediastinal metastases. If mediastinal metas-tases are present, thoracotomy would be contraindicated because it subjects the patient to a risk of death with no health benefit. If mediastinal metastases are ab-sent, thoracotomy offers a substantial survival advantage as long as the primary tumor has not metastasized to distant organs.
We have two tests available for assessing the involvement of the mediastinum. They are computed tomography (CT scan) and mediastinoscopy. This problem instance involves three decisions. First, should the patient undergo a CT scan? Second, given this decision and any CT results, should the patient undergo medi-astinoscopy? Third, given these decisions and any test results, should the patient undergo thoracotomy.
P(CTest = cpos|MedMet = absent) = .19.
The mediastinoscopy is an invasive test of mediastinal lymph nodes for deter-mining whether the tumor has spread to those nodes. If we let Mtest be a variable whose values are mpos and mneg depending on whether or not the mediastinoscopy is positive, we have
P(MedDeath = mdie|M = m2) = 0.
The thoracotomy has a greater chance of causing death than the alternative treat-ment radiation. If we let T be the decision concerning which treatment to have, t1 be the choice to undergo thoracotomy, and t2 be the choice to undergo radi-ation, and Thordeath be a variables whose values are tdie and tlive depending on whether the patient dies from the treatment, we have
P(MedMet = present) = .46.
Figure 5.22 shows an influence diagram representing this problem instance. Note that we considered quality adjustments to life expectancy (QALE) and fi-nancial costs to be insignificant in this example. The value node is only in terms of life expectancy.