In: Statistics and Probability
Scenario 1: A team of Epidemic Intelligence Service officers from the CDC arrives in Rhode Island to assist the state health department with investigation and control of an outbreak of measles. The team is asked to include the entire state in the investigation; thus, a confirmed case of measles in this outbreak is any resident of Rhode Island with an illness clinically compatible with measles who either has a positive laboratory test for measles or is a contact of someone with a positive test. Individuals with clinically compatible illnesses who did not have laboratory confirmation and were not contacts were classified as “possible cases”. (No recovery date would mean that the individual is still sick, or did not recover during the time frame of interest. No lab or contact is a non-confirmed case and these are considered the "possible cases". These cases are not included depending on the question being asked, specifically prevalence & incidence, because they are not confirmed with the illness.) The team members arrive in Rhode Island on March 1st and spent a month investigating. They found case information as detailed in the chart below.
Case # |
RI resident |
Onset date |
Recovery date |
Lab confirmed |
Contact |
1 |
yes |
2/4/2015 |
2/19/2015 |
X |
|
2 |
no |
2/18/2015 |
2/22/2015 |
X |
|
3 |
Yes |
2/18/2015 |
3/2/2015 |
X |
|
4 |
No |
2/18/2015 |
3/2/2015 |
X |
|
5 |
Yes |
2/19/2015 |
3/6/2015 |
X |
|
6 |
No |
2/20/2015 |
2/27/2015 |
X |
|
7 |
Yes |
2/20/2015 |
3/6/2015 |
X |
|
8 |
Yes |
2/20/2015 |
3/9/2015 |
X |
|
9 |
Yes |
2/23/2015 |
3/9/2015 |
X |
|
10 |
Yes |
2/23/2015 |
3/10/2015 |
X |
|
11 |
Yes |
2/23/2015 |
3/15/2015 |
X |
|
12 |
Yes |
2/23/2015 |
3/29/2015 |
X |
|
13 |
Yes |
2/24/2015 |
3/29/2015 |
X |
|
14 |
yes |
3/7/2015 |
3/18/2015 |
X |
|
15 |
yes |
3/7/2015 |
3/19/2015 |
X |
|
16 |
yes |
3/7/2015 |
3/19/2015 |
X |
|
17 |
yes |
3/7/2015 |
3/20/2015 |
X |
|
18 |
yes |
3/7/2015 |
3/29/2015 |
X |
|
19 |
yes |
3/7/2015 |
4/1/2015 |
X |
|
20 |
yes |
3/8/2015 |
3/17/2015 |
X |
|
21 |
yes |
3/8/2015 |
3/22/2015 |
X |
|
22 |
yes |
3/9/2015 |
3/22/2015 |
X |
|
23 |
yes |
3/11/2015 |
3/29/2015 |
X |
|
24 |
yes |
3/11/2015 |
3/29/2015 |
X |
|
25 |
yes |
3/16/2015 |
3/29/2015 |
X |
|
26 |
yes |
3/17/2015 |
3/29/2015 |
X |
|
27 |
yes |
3/18/2015 |
3/29/2015 |
X |
|
28 |
yes |
3/21/2015 |
3/29/2015 |
X |
|
29 |
yes |
3/21/2015 |
3/29/2015 |
X |
|
30 |
yes |
3/21/2015 |
3/29/2015 |
X |
|
31 |
yes |
3/21/2015 |
3/29/2015 |
X |
|
32 |
yes |
3/21/2015 |
4/1/2015 |
X |
|
33 |
yes |
3/21/2015 |
4/2/2015 |
X |
|
34 |
yes |
3/21/2015 |
4/2/2015 |
X |
|
35 |
yes |
3/21/2015 |
4/2/2015 |
X |
|
36 |
yes |
3/21/2015 |
4/2/2015 |
||
37 |
yes |
3/21/2015 |
X |
||
38 |
yes |
3/21/2015 |
X |
||
39 |
yes |
3/22/2015 |
4/3/2015 |
X |
|
40 |
yes |
3/23/2015 |
X |
||
41 |
yes |
3/23/2015 |
X |
||
42 |
yes |
3/29/2015 |
X |
||
43 |
yes |
3/29/2015 |
|||
44 |
yes |
3/29/2015 |
X |
For the purposes of this exercise, use one million for the Rhode Island state resident population, and answer the questions using confirmed cases only unless otherwise specified. Note: remember to express all rates (incidence is a rate) per unit of population and per unit of time. Prevalence (a ratio) needs only to be expressed per unit of population. (2 points each; 8 points total) |
|
What was the prevalence of measles in Rhode Island as of March 1st? |
|
What was the prevalence of measles in Rhode Island as of March 24th? |
|
What was the incidence of measles in Rhode Island for March? |
|
What would the incidence be for March if possible cases were also included? |
a) What was the prevalence of measles in Rhode Island as of March 1st?
Prevalence is a measure of disease that allows us to determine a person's likelihood of having a disease. Therefore, the number of prevalent cases is the total number of cases of the disease existing in a population. A prevalence rate is the total number of cases of a disease existing in a population divided by the total population.
For the purposes of this exercise, use one million for the Rhode Island state resident population.
A confirmed case of measles in this outbreak is any resident of Rhode Island with an illness clinically compatible with measles who either has a positive laboratory test for measles or is a contact of someone with a positive test.
Individuals with clinically compatible illnesses who did not have laboratory confirmation and were not contacts were classified as “possible cases”.
The number of confirmed as of 1st March from the table above is equal to 10 counting the cases from 2/4/15 to 2/24/15 out of which two are non-residents and one recovered before 1st march thus are excluded. The cases are as follows:
Case # | RI resident | Onset date | Recovery date | Lab confirmed | Contact |
3 | Yes | 2/18/2015 | 03/02/15 | X | |
4 | No | 2/18/2015 | 03/02/15 | X | |
5 | Yes | 2/19/2015 | 03/06/15 | X | |
7 | Yes | 2/20/2015 | 03/06/15 | X | |
8 | Yes | 2/20/2015 | 03/09/15 | X | |
9 | Yes | 2/23/2015 | 03/09/15 | X | |
10 | Yes | 2/23/2015 | 03/10/15 | X | |
11 | Yes | 2/23/2015 | 3/15/2015 | X | |
12 | Yes | 2/23/2015 | 3/29/2015 | X | |
13 | Yes | 2/24/2015 | 3/29/2015 | X |
Prevalence rate = the total number of cases of a disease existing/total population = 10/1 million = 0.000010
b) What was the prevalence of measles in Rhode Island as of March 24th?
There are 22 confirmed cases as of March 24th. The cases which have recovered before the 24th march are excluded.
The cases are as follows:
Case # | RI resident | Onset date | Recovery date | Lab confirmed | Contact |
12 | Yes | 2/23/2015 | 3/29/2015 | X | |
13 | Yes | 2/24/2015 | 3/29/2015 | X | |
18 | yes | 03/07/15 | 3/29/2015 | X | |
19 | yes | 03/07/15 | 04/01/15 | X | |
23 | yes | 03/11/15 | 3/29/2015 | X | |
24 | yes | 03/11/15 | 3/29/2015 | X | |
25 | yes | 3/16/2015 | 3/29/2015 | X | |
26 | yes | 3/17/2015 | 3/29/2015 | X | |
27 | yes | 3/18/2015 | 3/29/2015 | X | |
28 | yes | 3/21/2015 | 3/29/2015 | X | |
29 | yes | 3/21/2015 | 3/29/2015 | X | |
30 | yes | 3/21/2015 | 3/29/2015 | X | |
31 | yes | 3/21/2015 | 3/29/2015 | X | |
32 | yes | 3/21/2015 | 04/01/15 | X | |
33 | yes | 3/21/2015 | 04/02/15 | X | |
34 | yes | 3/21/2015 | 04/02/15 | X | |
35 | yes | 3/21/2015 | 04/02/15 | X | |
37 | yes | 3/21/2015 | X | ||
38 | yes | 3/21/2015 | X | ||
39 | yes | 3/22/2015 | 04/03/15 | X | |
40 | yes | 3/23/2015 | X | ||
41 | yes | 3/23/2015 | X |
The prevalence rate = 22/1 million = 0.000022
c) What was the incidence of measles in Rhode Island for March?
Incidence - the number of new occurrences of a condition (or disease) in a population over a period of time. The incidence rate uses new cases in the numerator; individuals with a history of a condition are not included. The denominator for incidence rates is the population at risk.
There are 29 cases with a new occurrence of measles in March. the cases are as follows:
Case # | RI resident | Onset date | Recovery date | Lab confirmed | Contact |
14 | yes | 03/07/15 | 3/18/2015 | X | |
15 | yes | 03/07/15 | 3/19/2015 | X | |
16 | yes | 03/07/15 | 3/19/2015 | X | |
17 | yes | 03/07/15 | 3/20/2015 | X | |
18 | yes | 03/07/15 | 3/29/2015 | X | |
19 | yes | 03/07/15 | 04/01/15 | X | |
20 | yes | 03/08/15 | 3/17/2015 | X | |
21 | yes | 03/08/15 | 3/22/2015 | X | |
22 | yes | 03/09/15 | 3/22/2015 | X | |
23 | yes | 03/11/15 | 3/29/2015 | X | |
24 | yes | 03/11/15 | 3/29/2015 | X | |
25 | yes | 3/16/2015 | 3/29/2015 | X | |
26 | yes | 3/17/2015 | 3/29/2015 | X | |
27 | yes | 3/18/2015 | 3/29/2015 | X | |
28 | yes | 3/21/2015 | 3/29/2015 | X | |
29 | yes | 3/21/2015 | 3/29/2015 | X | |
30 | yes | 3/21/2015 | 3/29/2015 | X | |
31 | yes | 3/21/2015 | 3/29/2015 | X | |
32 | yes | 3/21/2015 | 04/01/15 | X | |
33 | yes | 3/21/2015 | 04/02/15 | X | |
34 | yes | 3/21/2015 | 04/02/15 | X | |
35 | yes | 3/21/2015 | 04/02/15 | X | |
37 | yes | 3/21/2015 | X | ||
38 | yes | 3/21/2015 | X | ||
39 | yes | 3/22/2015 | 04/03/15 | X | |
40 | yes | 3/23/2015 | X | ||
41 | yes | 3/23/2015 | X | ||
42 | yes | 3/29/2015 | X | ||
44 | yes | 3/29/2015 | X |
Incidence rate = 29/1 million = 0.000029
d) What would the incidence be for March if possible cases were also included?
The number of cases will be 31 and as follows:
Case # | RI resident | Onset date | Recovery date | Lab confirmed | Contact |
14 | yes | 03/07/15 | 3/18/2015 | X | |
15 | yes | 03/07/15 | 3/19/2015 | X | |
16 | yes | 03/07/15 | 3/19/2015 | X | |
17 | yes | 03/07/15 | 3/20/2015 | X | |
18 | yes | 03/07/15 | 3/29/2015 | X | |
19 | yes | 03/07/15 | 04/01/15 | X | |
20 | yes | 03/08/15 | 3/17/2015 | X | |
21 | yes | 03/08/15 | 3/22/2015 | X | |
22 | yes | 03/09/15 | 3/22/2015 | X | |
23 | yes | 03/11/15 | 3/29/2015 | X | |
24 | yes | 03/11/15 | 3/29/2015 | X | |
25 | yes | 3/16/2015 | 3/29/2015 | X | |
26 | yes | 3/17/2015 | 3/29/2015 | X | |
27 | yes | 3/18/2015 | 3/29/2015 | X | |
28 | yes | 3/21/2015 | 3/29/2015 | X | |
29 | yes | 3/21/2015 | 3/29/2015 | X | |
30 | yes | 3/21/2015 | 3/29/2015 | X | |
31 | yes | 3/21/2015 | 3/29/2015 | X | |
32 | yes | 3/21/2015 | 04/01/15 | X | |
33 | yes | 3/21/2015 | 04/02/15 | X | |
34 | yes | 3/21/2015 | 04/02/15 | X | |
35 | yes | 3/21/2015 | 04/02/15 | X | |
36 | yes | 3/21/2015 | 04/02/15 | ||
37 | yes | 3/21/2015 | X | ||
38 | yes | 3/21/2015 | X | ||
39 | yes | 3/22/2015 | 04/03/15 | X | |
40 | yes | 3/23/2015 | X | ||
41 | yes | 3/23/2015 | X | ||
42 | yes | 3/29/2015 | X | ||
43 | yes | 3/29/2015 | |||
44 | yes | 3/29/2015 | X |
The incidence rate = 31/1million = 0.000031