Question

large outbreak of measles in Licking County, Ohio population of just over 100,000 persons. 2. 10 marks] In October 1976 there was a A total of 411 cases were observed in a O Age at Vaccination (months) Unvac- cinated 11 11 12 13 14 Cases 34 16 4 4 1 12 Person-Weeks 219 404 266 567 191 2558 Table 1: Measles cases by age of vaccination, Licking County, Ohio, 1976 Marks, J. S., Halpin, T. J., & Orenstein, W. A. (1978). Measles vaccine efficacy in children previously vaccinated at 12 months of age. Pediatrics, 62(6), 955-960. 1 In 1965 the American Academy of Pediatrics changed the recommendation for measles vac- cination to occur at 9 months of age to 12 months of age. This is because even at up to 11 months of age some maternal antibodies persist and may interfere with vaccine seroconver- sion. Then later the recommendation was changed to 15 months. Because of these changes researchers sought to measure measles vaccine efficacy by age at time of vaccination. (a) The data in Table 1 elementary schools in Licking County. For each group calculate: come from a special investigation into the measles outbreak in three i. The incidence (density) of measles (per 1,000 person-weeks) ii. The Relative Risk versus the oldest vaccination age group V iii The vaccine efficacy (b) Give a 2-4 sentence written summary of any trends you observed in the the effectiveness of the measles vaccine (c) Why did researchers have to wait for an outbreak to occur in order to analyze vaccine efficacy in this way?

Answer 1

This is a simple problem related to analysis of a measeles case in ohio .

We shall try to solve each question one by one

1. Density - It is given by the ratio of total number of cases to the person weeks per thousand)

Mathematically, Density (per thousand person -weeks) =cases /person weeks *1000

This is calculated in the table as follows.

	Unvaccinated	Age at vaccination
		<11	11	12	13	14
Cases	34	16	4	4	1	12
Person-weeks	219	404	266	567	191	2558
Density (Cases/Person Weeks *1000)	155.25	39.60	15.04	7.05	5.24	4.69

b). Relative risk of each group with respect to the oldest group (age 14)

This is simple .it is calculated by dividing the density of each group to the density of age 14 (vaccinated)

This is shown in table below

	Unvaccinated	Age at vaccination
		<11	11	12	13	14
Cases	34	16	4	4	1	12
Person-weeks	219	404	266	567	191	2558
Density (Cases/Person Weeks *1000)	155.25	39.60	15.04	7.05	5.24	4.69
Relative Risk (Group density/ Density of vaccinated group 14))	33.09	8.44	3.21	1.50	1.12	1.00

c). Vaccine Efficacy :-

It is the defined as the ratio of the difference between unvacinated density and vaccinated group density to the unvaccinated group density

Mathematcially ,

Vaccine efficacy = (Unvaccinated density -Vacciniated density )/Unvaccinated density *100%

	Unvaccinated	Age at vaccination
		<11	11	12	13	14
Cases	34	16	4	4	1	12
Person-weeks	219	404	266	567	191	2558
Density (Cases/Person Weeks *1000)	155.25	39.60	15.04	7.05	5.24	4.69
Relative Risk (Group density/ Density of vaccinated group 14))	33.09	8.44	3.21	1.50	1.12	1.00
Vaccine efficacy (Unvaccinated density-Vacicnated density)/Unvaccinated dnesity *100%	0.00	74.49	90.31	95.46	96.63	96.98
Relative Risk(relative to Unvaccinated) (Group density/ Density of vaccinated group 14)) %	100.00	25.51	9.69	4.54	3.37	3.02

b). We observe the following

1. there is 100 % risk for unvacicnated group

2. as the age group increases from below 11 to 14, the relative risk of the disease decreases consitantly

3. The vaccine is most effective on age group of 14 years .

4. The vaccination is least effective for less than 11 year old kids.

d). The reseracher had to wait for hte outbreak because

1. It gave them hance to do the study under the effect of the disease (control and open groups)

2. It gave them a better sample space to measure their observation accurately.

3. It reduced the effect of infereces due to other facotrs.