Medical Test Blood Assignment Help: How to Answer This Question

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What This Question Is About

This question relates to medical test blood and requires a structured academic response.

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Key Explanation

This topic involves medical test blood. A strong answer should include explanation, application, and examples.

Original Question

10) In a medical test, blood analysis is performed to measure the level of a certain protein. The process is modeled as Y=A+Z, where A is the protein level, and Z is the measurement noise, which is known to be zero-mean, Gaussian, with variance \(σ_Z^2\). The level A is either \(A_0\)(normal) or \(A_1\)> \(A_0\)(elevated). The following procedure is applied: If y < γ-Δ/2, the level is declared to be normal. If y > γ+ Δ/2, the level is declared to be elevated. If y∈[γ-Δ/2, γ+ Δ/2], a second test is requested. In the second test, a new sample is taken from the same patient, and a simple binary decision is made based on whether y < γ(normal) or y > γ(elevated). The threshold γ is set in accordance with the maximum likelihood decision principle (mid-way between two expected values \(A_0\) and \(A_1\). Determine the probability of correctly detecting an elevated level, \(P_{cd}\), as a function of D=\(A_1\)-\(A_0\) and Δ =αD. What specific value do you get for and? How does it compare with performing a single ML test? (a) \(P_{cd}\)= 90.15\%, which is better than 84.13\% obtained with a single ML test. (b) \(P_{cd}\)= 95.5\%, which is better than 80.1\%obtained with a single ML test. (c) \(P_{cd}\)= 92.6\%, which is worse than 94.3\%obtained with a single ML test. (d) None of the offered answers are correct.

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