The following table shows the number of patients classified

The following table shows the number of patients classified as underweight, normal weight, overweight, and obese according to level of protein in diet. You may need to use the Addition/Multiplication Law for one or more of the probabilities.

Underweight

Normal

Overweight

Obese

TOTAL

Low Protein Diet

5

120

100

50

275

High Protein Diet

45

130

50

25

250

TOTAL

50

250

150

75

525

If a patient is selected at random, what is the probability that this individual does have a low protein diet? (2)

Assuming that BMI and amount of protein in diet are dependent on one another, what is the probability that an individual is of normal weight and does consumes a high protein diet? (4)

What proportion of patients is underweight OR obese? (4)

The Lateral Flow Test has been used in developing countries as a low cost way to diagnose patients with human immunodeficiency virus (HIV). The Lateral Flow Test is more cost effective and portable than the gold standard assessment. The validity of this test was assessed in 1176 patients by comparing the screening result with a gold standard procedure, the enzyme-linked immunosorbent assays (ELISAs). The results are displayed in the table below.

Table. Comparison of Test Results: Lateral Flow Test vs. Gold Standard ELISA

Gold Standard Assessment of HIV Status with Enzyme-Linked Immunosorbent Assays (ELISAs)

Lateral Flow Test

HIV Diagnosis

No HIV Diagnosis

Total

HIV Positive Screening Result

323

17

340

HIV Negative Screening Result

178

658

836

Total

518

675

1176

                      

Calculate the sensitivity & specificity of the Lateral Flow screening test. (3)

Calculate the false positive and false negative rates. Which one would worry you the most in practice and why? (4)

What is the probability of having the disease (as evidenced by the gold standard test) if a patient screens positive for HIV with the Lateral Flow screening test? What is this type of probability called? (3)

	Underweight	Normal	Overweight	Obese	TOTAL
Low Protein Diet	5	120	100	50	275
High Protein Diet	45	130	50	25	250
TOTAL	50	250	150	75	525

Solution

If a patient is selected at random, what is the probability that this individual does have a low protein diet? (2)

Low Protein Diet 275

TOTAL 525

275/525 = 0.5238

what is the probability that an individual is of normal weight and does consumes a high protein diet?

NORMAL AND CONSUMES HIGH PROTEIN = 130

TOTAL = 525

PROBABILITY = 130/525 = 0.2476

What proportion of patients is underweight OR obese? (4)

underweight   50/525= 0.0952

obese = 75/525 =0.1428

0.1428+0.0952 = 0.2380

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