3.3 sensitivity & specificity exercise (50 pts.)

Similar to converting Fahrenheit to Celsius (E.g., 98.6^o F - 32 x 5 / 9 = 37^o C) and back (E.g., 37^o C x 9 / 5 + 32 = 98.6^o F), these problems require you to work backwards and forward from the data given.Also, all the clues and formulas you need are in the recording and PPT, e.g. a + c = prevalence.Remember, be sensitive to the ill. May the Lord help you to enjoy the challenge!

Getting Started: Using the information in the Week 3 PPT, fill in the tables with the appropriate numbers in each cell of the table.Round to the nearest whole number, but only after you have calculated all the way down through question 14 (Scenario 1) and question 28 (Scenario 2).You may use the online calculator however you must read carefully to enter the data accurately. Condition absent or present is determined by symptoms.

(Hint: To get started, open the calculator in Microsoft Office, click on view, select Standard and Basic.)We know we have a population of 10,000. So that is the lower right hand corner (total). This does require some math agility so please bear with me.Now let's focus on a+c (aka, prevalence). We are told that prevalence is 1.5% so to determine how many that is of 10,000 people, it is easiest to simply subtract 1.5% from 10,000 which first converts the 1.5% to ___ for a+c and then hit = and it gives us ____ for b+d. Now to find a., put in the value you have for a+c, and subtract 22.9% which converts to ____ for a. and when you hit = it gives you ____ for c. Work it similarly for b+d and b by subtracting 99.8% from (b+d) to give d, then hit = to calculate b. Add c+d and enter that in the total column and a+b as well. Scenario 2 uses a different sensitivity and specificity but the same prevalence. Ask your prof if you get stuck! If you are using your phone calculator or any calculator other than Microsoft Office, when you subtract 1.5% prevalence from 10,000 population, you first end up with the answer to b+d, and the rest of the 10,000 population = a+c.

Scenario 1: The prevalence (a + c in the table below) of previously undetected diabetes in a population to be screened is approximately 1.5% and it is assumed that 10,000 persons will be screened.The screening test will measure blood serum sugar content.A value of 180 mg/dl or higher is considered positive.The sensitivity (a) and the specificity (d) associated with this screening are 22.9% and 99.8% respectively. (1 point per box)

+/ 8

Sensitivity (ill) =

a/(a+c) x 100 = 22.9%

Specificity (well) =

d/(d+b) x 100 = 99.8%

Total

people

Disease Present

Disease Absent

Positive tests

(A)True +

(B) False +

(A+B)

Negative tests

(C)False -

(D) True -

(C+D)

Total tests

(A+C) Prevalence of Ills = 1.5%

(B+D) Wells =

10,000

Population

For questions 9-13, use the above data to calculate: (10 points)

Points

9.The percentage of false positives among all those without the condition (the Type I Error Rate, or 1 - specificity), or b / (b + d)

1 - specificity =

or b / (b + d)

/2

10.The percentage of false negatives among all those with the condition (the Type II Error Rate, or 1 - sensitivity), or c / (a + c)

1 - sensitivity =

or c / (a + c)

/2

11.The predictive value of a positive (PPV) test,

or = a / (a + b)

PPV=

/2

12.The predictive value of a negative (NPV) test,

or = d /(d + c)

NPV=

/2

13.Based on the calculations above, how many false positives and negatives will occur if 100,000 people are screened? (100,000 / 10,000 = 10)

false positives=

false negatives=

/2

Scenario 2: To observe the effect of increasing sensitivity, assume a blood sugar screening level of 130 mg/dl, with (A) sensitivity of 44.3% and (D) specificity of 99.0%. Prevalence remains 1.5%.

Questions 14-21: Using the information in the Week 3 PPT, set up a two by two table with the appropriate numbers in each cell of the table.Round to the nearest whole number, but only after you have completed all the calculations down through.You may use the online calculator however you must read carefully to enter the data accurately. Condition absent or present is determined by symptoms. (1 point per box)

+/8 points

Sensitivity = 44.3%

Ills = a/(a+c) x 100

Specificity of 99% wells =

d/(d + b) x 100

Total people

Disease present

Disease absent

Positive tests

a. True +

b. False +, Type I

(A+B)

PPV

Negative tests

c. False -, Type II

d. True -

(C+D)

NPV

Total tests

(A+C) 150

Prevalence of Ill 1.5%

(B+D) Wells

10,000

Population

For questions 22-Use scenario 2 data to calculate:(10 points)

Points

22.The percentage of false positives among all those without the condition (the Type I Error Rate, or 1 - specificity), or b / (b + d)

1 - specificity of =

or b / (b + d)

/2

23.The percentage of false negatives among all those with the condition (the Type II Error Rate, or 1 - sensitivity), or c / (a + c)

1 - sensitivity =

or c / (a + c)

/2

24.The predictive value of a positive (PPV) test,

or = a / (a + b)

PPV =

/2

25.The predictive value of a negative (NPV) test, or d / (c + d)

NPV=

/2

26.Based on the calculations above, how many false positives (b x 10) and negatives (c x 10) will occur if 100,000 people are screened?

False Positives =

False Negatives=

/2

Do the numbers make sense based on the total population? If not, RECALCULATE!

27.Define sensitivity and its relationship to PPV:

/2

28.Define specificity and its relationship to NPV:

/2

Select a laboratory test and describe its:

Points

29.Sensitivity:

/1

30.Specificity:

/1

31.When we erroneously treat the well, (Type I error), or reject a true null, we wrongly act on a false:

/1

32.When we fail to believe the sick (Type II or error or fail to reject a false null, we wrongly act on a false:

/1

Fill in the information using the data from Scenarios 1 & 2 as indicated. Highlight the data which is most favorable for the criteria to help you formulate your answer to the last question, # 33 on page 3 below.

Comparative Data

Scenario 1 - 180mg/dl

Scenario 2 - 130mg/dl

Sensitivity of the test to accurately detect the abnormality.

Specificity of the test to accurately detect the normality.

The percentage of false positives among all those without the condition (the Type I Error, treating the well)

The percentage of false negatives among all those with the condition (the Type II Error, failing to treat the sick)

PPV or probability that the disease is present when the test is positive

NPV or probability that the disease is not present when the test is negative.

# of false positives

# of false negatives

33.Compare the findings of Scenario 1 and 2.If you were the director for the diabetes screening program would you prefer to screen at 130 mg or 180 mg percent? Explain why. (6 pts.)

/6