Question

Consider a 68 years old woman who complains of dyspnea on exertion. You estimate the P(D) of left ventricular failure ( LVF) as 0.20. But other conditions exist. These conditions may change the probability of diagnosis. There are multiple symptoms to make the diagnosis.

These symptoms are:
LVF Other
Initial Likelihood: 0.20 0.80
Chronic Hypertension0.6 0.4
Chronic Cough 0.4 0.6
Orthopnea 0.5 0.5
Basel Rales 0.6 0.4
S3 at the Apex 0.8 0.2
Large Heart 0.95 0.05
Calculate the min/max probabilities of the disease, and ratio of LVF : Other, given that all the symptoms are existing.
Calculate the ratios for the cases below:
a. all the clues are maximally independent
b. all the clues are maximally dependent.

Answer 1

a. Minimum P(D): 0.20, Maximum P(D): 0.95; Ratio LVF:Other = 0.20:0.80

b. Minimum P(D): 0.20, Maximum P(D): 0.95; Ratio LVF:Other = 0.20:0.80

In the given diagnostic scenario for a 68-year-old woman with dyspnea on exertion, the probability of left ventricular failure (LVF) is initially estimated at 0.20. However, this probability is subject to change based on the presence of specific symptoms or clinical clues. The probabilities of having LVF or another condition (Other) are influenced by the existence of symptoms such as chronic hypertension, chronic cough, orthopnea, basal rales, S3 at the apex, and a large heart.

a. When all the clues are maximally independent, the minimum probability of having LVF is 0.20, and the maximum probability is 0.95. The ratio of LVF to Other in this scenario is 0.20:0.80.

b. In the case where all the clues are maximally dependent, the probabilities of LVF and Other can still range from 0.20 to 0.95. The ratio of LVF to Other remains 0.20:0.80. Even when the clues are dependent, the overall likelihood of LVF and Other may vary within the specified bounds, but the ratio between them remains constant.