Investigators develop a study to determine if the yearly influenza vaccine is effective in preventing influenza in those persons 65 years of age and older. A local survey identified 117 persons who...

PUBH 395 Epidemiology
1) Following is the analysis.
a) It is case-control type of epidemiological study.
b) Following is the required 2x2 table
Table no-1.1
    Persons who in last year
    Had influenza
    Not had influenza
    Total
    Received vaccine
    47
    287
    334
    Did not received vaccine
    70
    96
    166
    Total
    117
    383
    500
Above table 1.1 tells the observed frequencies.
Table no- 1.2 below shows expected frequencies.
Table no-1.2
    Persons who in last year
    Had influenza
    Not had influenza
    Total
    Received vaccine
    334*117/500=78.16
    334*383/500=255.84
    334
    Did not received vaccine
    166*117/500=38.84
    166*383/500=127.16
    166
    Total
    117
    383
    500
c) Chi square is the appropriate measure of association in this case. Our hypothesis is:
H0: annual influenza vaccination is not effective in preventing influenza infections in those over 65 years of age.
H1: annual influenza vaccination is effective in preventing influenza infections in those over 65 years of age.
Formula of test statistics is
(
)
2
22
;1
i
n
i
OiE
E
a
cc
-
-
=
:
Where O and E are observed and expected frequencies. n=(r-1)(c-1)= is degree of freedom where r is number of rows and c is number of column.
So we have
(
)
(
)
(
)
222
2
2
2
287255.847038.8496127.16
(4778.16)
78.16255.8438.84127.16
12.423.8024.107.6447.96
c
c
---
-
=+++
=+++=
And tabulated value of chi-square at 1 degree of freedom is 3.84 which is less than calculated value so we reject null hypothesis at 5% level of significance and conclude that annual influenza vaccination is effective in preventing influenza infections in those over 65 years of age.
2) Following is the analysis
a) It is Cohart...