** Key** Chapter 7
Even
7.4 Direct
age-adjustment, fictitious State
All rates are “per
100,000”
(A) ...crude mortality rate in fictitious State. 15,984 / 2,450,000 � 100,000 =
652
(B) age-specific
rates in fictitious State:
|
Age
|
Rate
(per 100,000)
|
|
0 - 4
|
238
|
|
5 -24
|
64
|
|
25 - 44
|
208
|
|
45 - 64
|
809
|
|
65 - 74
|
2221
|
|
75+
|
6887
|
Compare these to Florida's….The age-specific rates are identical.
(C)
Explain... Florida's population is much older. For
example, 8% of Florida's
residents are over 75, compared to 4% of this State's.
(D)� adjust the fictitious state's death rate
using the direct method
Method A formula aRdirect
= ∑(Ni � ri)
/ ∑Ni
|
Age
|
Fictitious
state
|
Standard
Million (Ni)
|
Product
(Niri)
|
|
0 - 4
|
238
|
76158
|
18125604
|
|
5 -24
|
64
|
286501
|
18336064
|
|
25 - 44
|
208
|
325971
|
67801968
|
|
45 - 64
|
809
|
185402
|
149990218
|
|
65 - 74
|
2221
|
72494
|
161009174
|
|
75+
|
6887
|
53474
|
368275438
|
|
SUMS
|
|
1,000,000
|
783,538,466
|
aRdirect = Sum(Niri) / Sum(Ni) = 783538466
/ 1000000 = 784
Method
B formula aRdirect = ∑ wi�ri where wi = Ni / N
|
Age
|
Fictitious
state
|
Standard
Million (wi)
|
Product
(wiri)
|
|
0 - 4
|
238
|
0.076158
|
18.125604
|
|
5 -24
|
64
|
0.286501
|
18.336064
|
|
25 - 44
|
208
|
0.325971
|
67.801968
|
|
45 - 64
|
809
|
0.185402
|
149.990218
|
|
65 - 74
|
2221
|
0.072494
|
161.009174
|
|
75+
|
6887
|
0.053474
|
368.275438
|
|
|
|
1.0000000
|
784
|
aRdirect = Sum(wiri)
= sum or last column = 784
How do the adjusted rates compare? The adjusted rate in the
fictitious state and Florida
are the same.
7.6 Ahlbom & Norell, 1990, p.
44, #10
�
Use
the formula �i = ni � Ri to
calculate the expected number of cases within stratum i.
�1 = (8000 � 0.5/1000) = 4
�2 = (2000 � 4/1000) = 8
�3 = (2000 � 9/1000) = 18
�
Expected
frequency (�) = �1 + �2 + �3 = 4 + 8 + 18 = 30
�
The
observed number of cases was 40. Thus, SMR = observed / expected = 40 / 30 =
1.33
�
Interpretation:
the incidence was 33% higher than expected.
7.8 Ahlbom & Norell,
1990, p. 45, #12
|
|
Age-specific rates
|
|
Age
|
Group A
|
|
Group B
|
|
Younger
|
4 / 2000 = 0.002
|
|
20 / 4000 = 0.005
|
|
Older
|
32 / 4000 = 0.008
|
|
15 / 1000 = 0.015
|
aRGroup A = (0.5)(0.002) + (0.5)(0.008) =
0.005
aRGroup B = (0.5)(0.005) + (0.5)(0.015) =
0.010
The adjusted rate in Group B
is half that of Group A.