Calculating Age Standardised Incidence Rates

October 29, 2014 | Alan

Why Do We Need to Calculate Age Standardised Incidence Rates?

When comparing incidence rates between different countries the distribution of the population needs to be taken into account to compare these accurately. This is why we calculate age standardised incidence rates. There are two methods of standardisation, the direct and indirect methods. We will work through an example using the direct method here.

Calculating Crude Incidence Rates

As a starting point, we need to calculate the crude incidence rate per 100,000 people. This is calculated using the following formula:
rate=count/population×100,000

where count is the number of people of interest in the population. We’ll use an example from SEER (Surveillance, Epidemiology and End Results program) to work through the methodology: To calculate the rates, we begin with counts: the number of tumors for each of the 19 age groups for the same geographic, race, sex, cancer site combination ie. the number of malignant incident cases for black females in the SEER 9 registries from 2000-2004. (Note: these values were calculated using the SEER 9 registry database from the Nov 2006 submission.) (http://seer.cancer.gov/seerstat/tutorials/aarates/step1.html)

Age Count Population Crude Rate
00 years 29 139,879 20.7
01-04 years 87 553,189 15.7
05-09 years 67 736,212 9.1
10-14 years 71 770,999 9.2
15-19 years 87 651,390 13.4
20-24 years 177 639,159 27.7
25-29 years 290 676,354 42.9
30-34 years 657 736,557 89.2
35-39 years 1,072 724,826 147.9
40-44 years 1,691 700,200 241.5
45-49 years 2,428 617,437 393.2
50-54 years 2,931 516,541 567.4
55-59 years 2,881 361,170 797.7
60-64 years 2,817 259,440 1,085.80
65-69 years 2,817 206,204 1,366.10
70-74 years 2,744 172,087 1,594.50
75-79 years 2,634 142,958 1,842.50
80-84 years 1,884 99,654 1,890.50
85+ years 1,705 92,692 1,839.40

Calculating Age Standardised Incidence Rates

To calculate the age standardised rates you need to use a standard population. For this example the 2000 Standard US population is used. There are various standard populations that can be used. More information can be found at http://seer.cancer.gov/stdpopulations/. Proportions based on the standard population are calculated and shown in the column ‘Age Distribution of Std Population’. For example the first row is calculated by:
3,794,901/274,633,642=0.013818

These proportions are used as weights. The final column is calculated by multiplying the ‘Age Distribution of Std Population’ column by the ‘Crude Rate’. Finally, the age standardised incidence rate is the sum of these products, which is calculated as 400.3 per 100,000 in this example.

Age Count Population Crude Rate US 2000 Standard Population Age Distribution of Std Population

 

00 years 29 139,879 20.7 3,794,901 0.013818 0.29
01-04 years 87 553,189 15.7 15,191,619 0.055316 0.87
05-09 years 67 736,212 9.1 19,919,840 0.072532 0.66
10-14 years 71 770,999 9.2 20,056,779 0.073031 0.67
15-19 years 87 651,390 13.4 19,819,518 0.072167 0.96
20-24 years 177 639,159 27.7 18,257,225 0.066478 1.84
25-29 years 290 676,354 42.9 17,722,067 0.06453 2.77
30-34 years 657 736,557 89.2 19,511,370 0.071045 6.34
35-39 years 1,072 724,826 147.9 22,179,956 0.080762 11.94
40-44 years 1,691 700,200 241.5 22,479,229 0.081852 19.77
45-49 years 2,428 617,437 393.2 19,805,793 0.072117 28.36
50-54 years 2,931 516,541 567.4 17,224,359 0.062718 35.59
55-59 years 2,881 361,170 797.7 13,307,234 0.048454 38.65
60-64 years 2,817 259,440 1,085.80 10,654,272 0.038794 42.12
65-69 years 2,817 206,204 1,366.10 9,409,940 0.034264 46.81
70-74 years 2,744 172,087 1,594.50 8,725,574 0.031772 50.66
75-79 years 2,634 142,958 1,842.50 7,414,559 0.026998 49.74
80-84 years 1,884 99,654 1,890.50 4,900,234 0.017843 33.73
85+ years 1,705 92,692 1,839.40 4,259,173 0.015509 28.53
All Ages 274,633,642 1 400.3

Calculating 95% Confidence Intervals based on a Poisson Approximation

The 95% confidence interval for the age standardised rate is given by:
RATE±1.96*√var

Where the variance for the age standardised rate is given by:

d_i is the number of events in age group i in the study population

r_i is the incidence rate in the study population for the persons in age group i

p_i is the number of persons in age group i in the standard population

(http://www.apheo.ca/resources/indicators/Standardization%20report_NamBains_FINALMarch16.pdf)

For this example d_i is the ‘Count’, r_i is the ‘Crude Rate’ and p_i is the ‘US 2000 Standard Population’. By substituting these values into the formula  above for each row, we can calculate the variance for the age standardised rate.

Age Count Population Crude Rate US 2000 Standard Population Age Distribution of Std Population

 

Variance
00 years 29 139,879 20.7 3,794,901 0.013818 0.29 0.002821215
01-04 years 87 553,189 15.7 15,191,619 0.055316 0.87 0.008669233
05-09 years 67 736,212 9.1 19,919,840 0.072532 0.66 0.006502378
10-14 years 71 770,999 9.2 20,056,779 0.073031 0.67 0.006358171
15-19 years 87 651,390 13.4 19,819,518 0.072167 0.96 0.010749024
20-24 years 177 639,159 27.7 18,257,225 0.066478 1.84 0.019157919
25-29 years 290 676,354 42.9 17,722,067 0.06453 2.77 0.026426391
30-34 years 657 736,557 89.2 19,511,370 0.071045 6.34 0.061126903
35-39 years 1,072 724,826 147.9 22,179,956 0.080762 11.94 0.133093072
40-44 years 1,691 700,200 241.5 22,479,229 0.081852 19.77 0.231071303
45-49 years 2,428 617,437 393.2 19,805,793 0.072117 28.36 0.331173315
50-54 years 2,931 516,541 567.4 17,224,359 0.062718 35.59 0.432057461
55-59 years 2,881 361,170 797.7 13,307,234 0.048454 38.65 0.518566003
60-64 years 2,817 259,440 1,085.80 10,654,272 0.038794 42.12 0.629872888
65-69 years 2,817 206,204 1,366.10 9,409,940 0.034264 46.81 0.777757794
70-74 years 2,744 172,087 1,594.50 8,725,574 0.031772 50.66 0.935288253
75-79 years 2,634 142,958 1,842.50 7,414,559 0.026998 49.74 0.939425621
80-84 years 1,884 99,654 1,890.50 4,900,234 0.017843 33.73 0.603946726
85+ years 1,705 92,692 1,839.40 4,259,173 0.015509 28.53 0.477277619
All Ages 274,633,642 1 400.3 6.15134129

Therefore the 95% confidence interval for the age standardised rate in this population is:
400.3±1.96*√6.15134129<br /> =400.3 (395.4-405.2)
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