Question

Age adjustment worksheet

Population and Number of Deaths, by Age, Communities A and B

Community A				Community B
Age (Years)	Population	Deaths	Death Rate	Population	Deaths	Death Rate
Under 1	1,000	15	.015	5,000	100	.02
1-4	3,000	3	.001	20,000	10	.0005
15-34	6,000	6	.001	35,000	35	.001
5-54	13,000	52	.004	17,000	85	.005
55-64	7,000	105	.015	8,000	160	.020
Over 64	20,000	1,600	.080	15,000	1,350	.090
Total	50,000	1,781		100,000	1,740

1.    Compute and compare the crude mortality rates x 1000 for communities A and B.

To do this simply divide the total deaths by the total population. Then multiply that number by 1000. The result is your crude mortality rate.

A-Total death:1781/ total population:50000 =0.03562 *1000=35.62

B-Total death:1740/ total population:100000= 0.0174*1000=17.4

Crude death rate for community A: 35.62

Crude death rate for community B: 17.4

2.    Look at the population distribution for communities A and B. Based on the population distribution, why do you think there is such a large difference between the crude mortality rates for the two communities?

Age (Years)	Standard Population(A and B)	Death Rate A	Expected deaths at A's rates	Death Rate B	Expected deaths at B's rates
Under 1	6,000
1-4	23,000
15-34	41,000
35-54	30,000
55-64	15,000
Over 64	35,000
Total	150,000

3.    Calculate the age-adjusted mortality rate for communities A & B.

To do this, first bring the death rates for the two communities down from the previous table. Then, multiply the standard population for each age group by the death rate for that age group for each community to fill in the “expected deaths” columns. Finally, add up the expected deaths and divide by the total number for the standard population to get the age-adjusted rate for each community.

Age-adjusted death rate for community A:

Age-adjusted death rate for community B:

4.    Did age adjustment reduce the difference between the mortality rates between the two communities?

Age (Years)	Population in A	Standard death rate = Population B	Expected deaths in A at Standard Rate
Under 1	1,000	.020
1-4	3,000	0.0005
15-34	6,000	.001
35-54	13,000	.005
55-64	7,000	.020
Over 64	20,000	.090
Total	50,000

5.    This table presents data for two communities that you will use the indirect method of age adjustment to compare mortality rates in. The mortality rates from population B will be used as the standard rates. First, compute the expected deaths in A by multiplying the population in A by the mortality rate in B. Fill these in in the table above.

6.    Now, calculate the standardized mortality ratio (SMR). The observed deaths in community A were 1781.

To calculate the SMR, divide the observed deaths in community A by the total expected deaths in community A.

SMR =

7.    What does the SMR tell you about the differences in mortality between community A and community B?

Answer 1

1)

For community A,

Total population=50,000

Total deaths=1781

For community B,

Total population=1,00,000

Total deaths=1740

Hence crude mortality rate is given by,

For A,

For B,

Crude death rate for A= 35.62

Crude death rate for B= 17.4

Crude death rate for community A is higher than the community B. There is large difference in crude death rate in both the community.

2)

As total deaths in bth the community is almost equal. But the population size is not equal. There is large difference in populatio size.Population size of community B is twice the community A and crude death rate involves the population size. Hence there is large difference in the crude death rates of both the community.

3)

R-code with output for calculating the age adjucted rate for both the community is give bellow:

> D_rate_A=c(0.015,0.001,0.001,0.004,0.015,0.08) ## Death rate of A
> D_rate_B=c(0.02,0.0005,0.001,0.005,0.02,0.09) ## Death rate of B
> Std_pop=c(6000,23000,41000,30000,15000,35000) #Standard population
> Exp_D_A=D_rate_A*Std_pop
> Exp_D_B=D_rate_B*Std_pop
> Exp_D_A
[1] 90 23 41 120 225 2800
> Exp_D_B
[1] 120.0 11.5 41.0 150.0 300.0 3150.0
> age_adj_rate_A=sum(Exp_D_A)/sum(Std_pop)
> age_adj_rate_B=sum(Exp_D_B)/sum(Std_pop)
> age_adj_rate_A ##Age adjusted rate for community A
[1] 0.02199333
> age_adj_rate_B ##Age adjusted rate for community B
[1] 0.02515  

Age-adjusted death rate for community A: 0.02199

Age-adjusted death rate for community B: 0.025

Age adjusted death rate for both the community is almost same.

4)

Age adjusted death rate for both the community is almost same. Age adjustment reduce the difference between the mortality rate between the both the community.