Age Adjusted Rates

R.M. PandeyAdditional Professor

Department of BiostatisticsAll India Institute of Medical Sciences

New Delhi

Crude Rates:

• a single number computed as a summary measure for an entire group

• disregards differences caused by age, sex and other characteristics

Adjusted Rates:

• a single number obtained by adjusting for imbalance in age, sex and other characteristics while comparing a rate for two or more groups

Employment status Population Impairment Rate per 1,000

Currently employed 98,917 552 5.58

Currently unemployed 7,462 27 3.62

Not in the labor force 56,778 368 6.48

Total 163,157 947 5.80

Example: Hearing Impairment Due to Injury in 17+ persons

Conclusion: compare the crude rates between the groups ?Is the conclusion valid ?

The groups may differ substantially with respect to age, sex and other important characteristics

e.g.: two populations from different geographical areas:

– (A) composed of entirely males; (B) entirely females

- Can never be sure whether the difference in mortality is due to location or due to gender.

Such a situation, gender is referred as a confounder, because it associated with with both location and death rate.

It obscures the relationship between location and death rate.

Age

Currently Employed Not in labor Force

Population % Population %

17-44 67,987 68.7 20,760 36.6

45-64 27,592 27.9 15,108 26.6

65+ 3,338 3.4 20,910 36.8

Total 98,917 100.0 56,778 100.0

Compare age structure of the two populations:

Age Population Impairments Rate per 1,000

17-44 94,930 441 4.65

45-64 43,857 308 7.02

65+ 24,370 198 8.12

Total 163,157 947 5.80

Age-specific impairment rates:

5.80 is the weighted average of the age specific rates

Age is a confounder in the relationship between hearing impairment and employment status

AgeCurrently Employed Not in Labor Force

Popn. Impaire-ments

Rate/1000

Popn. Impaire-ments

17-44 67,987 346 5.09 20,760 80

45-64 27,592 179 6.49 15,108 117

65+ 3,338 27 8.09 20,910 171

Total 98,917 552 5.58 56,778 368

Rate/1000

3.85

7.74

8.18

6.48

More accurate comparison: age-specific comparisons

AgeCurrently Employed Not in Labor Force

Popn. Impaire-ments

Rate/1000

Popn. Impair-Ements

17-44 67,987 346 5.09 20,760 80

45-64 27,592 179 6.49 15,108 117

65+ 3,338 27 8.09 20,910 171

Total 98,917 552 5.58 56,778 368

Rate/1000

3.85

7.74

8.18

6.48

More accurate comparison: age-specific comparisons

Crude rate provided an incomplete picture of the true situation

Subgroup specific rates:

• More accurate comparison than crude rates

• We would end up with overwhelming number of rates to compare

More Convenient:

Summarize an entire situation with a single number calculated for each subpopulation, a number that adjusts for difference in composition

Two Ways:

1. Direct method of standardization

2. Indirect method of standardization

Direct Method of Standardization:

Step 1: Select the standard population.

Step 2: compute the expected events that would result if , instead of having different age distributions, all

populations were to have same standard age structure

Step 3:Compute the adjusted rate as total expected events in the group divided by the total standard

population

Total Currently Employed Not in Labor Force

Age (1) (2) (3) (4) (5)StandardPopn.

Rate/1000 Expected Impairm.

Rate/1000 ExpectedImpairm.

17-44 94,930 5.09 483.2 3.85 365.5

45-64 43,857 6.49 284.6 7.74 339.5

65+ 24,370 8.09 197.2 8.18 199.3

Total 163,157 965.0 904.3

Age adjusted impairment rate for:

Currently employed = 965.0/163,157 = 5.91 per 1,000

Not in the labor force = 904.3/163,157 = 5.54 per 1,000

Indirect Method of Standardization:

Step 1: use a set of standard age-specific rates along with the actual age composition of each population

Step 2: compute the number of events that would have occurred in the two groups if each took on the age specific rates of the standard population while retaining

its own age distribution

Step 3: compute standardized event ratio as observed/expected events for each group

The indirect method often concludes with this ratio.

Step 4: actual age adjusted rates for each group

= event rate in the standard population x standardized event ratio of the group

Total Currently Employed Not in Labor Force

Age (1)

(2) (3) (4) (5)

Rate/1,000

Population Expected Impairm.

Population ExpectedImpairm.

17-44 4.65 67,987 316.1 20,760 96.545-64 7.02 27,592 193.7 15,108 106.165+ 8.12 3,338 27.1 20,910 169.8

Total 5.80 98,917 536.9 56,778 372.4

Standardized event rate

Currently employed = 552/536.9 = 1.03 = 103%

Not in the labor force = 368/372.4 = 0.99 = 99%

Age adjusted rates

5.08 x 1.03 = 5.97

5.08 x 0.99 = 5.74

Uses of Standardised Rates

Smoking Group

Death rate per 1,000 person years

A B C

Non smokers 20.2 11.3 13.5

Cigarettes 20.5 14.1 13.5

Cigar/pipes 35.5 20.7 17.4

Smoking Group

Mean age(years)

A B C

Non smokers 54.9 49.1 57.0

Cigarettes 50.5 49.8 53.2

Cigar/pipes 65.9 55.7 59.7

Smoking Group

Death rate per 1,000 person years

A B C

Non smokers 20.2 11.3 13.5

Cigarettes 28.3 12.8 17.7

Cigar/pipes 21.2 12.0 14.2

Taking age group of non-smokers as standard

• Must know when to use an adjusted rate rather than crude rate

• If no confounders: the crude rate is adequate

• If confounders present: subgroup specific rates are sufficient

• Adjusted rates should be considered if they are meaningful

• If distribution of standard population is radically different than the populations being compared, standardization is inappropriate

• Also, when direct standardization is applied, subgroup specific rates should have same general trends in all the groups being compared as well as in the standard population

•Direct method of standardization is used more frequently than indirect method

• Direct method requires subgroup specific rates for all popns.

• Application of either method should lead to same conclusion