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:
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 20002004. (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 
0104 years  87  553,189  15.7 
0509 years  67  736,212  9.1 
1014 years  71  770,999  9.2 
1519 years  87  651,390  13.4 
2024 years  177  639,159  27.7 
2529 years  290  676,354  42.9 
3034 years  657  736,557  89.2 
3539 years  1,072  724,826  147.9 
4044 years  1,691  700,200  241.5 
4549 years  2,428  617,437  393.2 
5054 years  2,931  516,541  567.4 
5559 years  2,881  361,170  797.7 
6064 years  2,817  259,440  1,085.80 
6569 years  2,817  206,204  1,366.10 
7074 years  2,744  172,087  1,594.50 
7579 years  2,634  142,958  1,842.50 
8084 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:
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 
0104 years  87  553,189  15.7  15,191,619  0.055316  0.87 
0509 years  67  736,212  9.1  19,919,840  0.072532  0.66 
1014 years  71  770,999  9.2  20,056,779  0.073031  0.67 
1519 years  87  651,390  13.4  19,819,518  0.072167  0.96 
2024 years  177  639,159  27.7  18,257,225  0.066478  1.84 
2529 years  290  676,354  42.9  17,722,067  0.06453  2.77 
3034 years  657  736,557  89.2  19,511,370  0.071045  6.34 
3539 years  1,072  724,826  147.9  22,179,956  0.080762  11.94 
4044 years  1,691  700,200  241.5  22,479,229  0.081852  19.77 
4549 years  2,428  617,437  393.2  19,805,793  0.072117  28.36 
5054 years  2,931  516,541  567.4  17,224,359  0.062718  35.59 
5559 years  2,881  361,170  797.7  13,307,234  0.048454  38.65 
6064 years  2,817  259,440  1,085.80  10,654,272  0.038794  42.12 
6569 years  2,817  206,204  1,366.10  9,409,940  0.034264  46.81 
7074 years  2,744  172,087  1,594.50  8,725,574  0.031772  50.66 
7579 years  2,634  142,958  1,842.50  7,414,559  0.026998  49.74 
8084 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:
Where the variance for the age standardised rate is given by:
is the number of events in age group i in the study population
is the incidence rate in the study population for the persons in age group i
is the number of persons in age group i in the standard population
)
For this example is the ‘Count’, is the ‘Crude Rate’ and 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 
0104 years  87  553,189  15.7  15,191,619  0.055316  0.87  0.008669233 
0509 years  67  736,212  9.1  19,919,840  0.072532  0.66  0.006502378 
1014 years  71  770,999  9.2  20,056,779  0.073031  0.67  0.006358171 
1519 years  87  651,390  13.4  19,819,518  0.072167  0.96  0.010749024 
2024 years  177  639,159  27.7  18,257,225  0.066478  1.84  0.019157919 
2529 years  290  676,354  42.9  17,722,067  0.06453  2.77  0.026426391 
3034 years  657  736,557  89.2  19,511,370  0.071045  6.34  0.061126903 
3539 years  1,072  724,826  147.9  22,179,956  0.080762  11.94  0.133093072 
4044 years  1,691  700,200  241.5  22,479,229  0.081852  19.77  0.231071303 
4549 years  2,428  617,437  393.2  19,805,793  0.072117  28.36  0.331173315 
5054 years  2,931  516,541  567.4  17,224,359  0.062718  35.59  0.432057461 
5559 years  2,881  361,170  797.7  13,307,234  0.048454  38.65  0.518566003 
6064 years  2,817  259,440  1,085.80  10,654,272  0.038794  42.12  0.629872888 
6569 years  2,817  206,204  1,366.10  9,409,940  0.034264  46.81  0.777757794 
7074 years  2,744  172,087  1,594.50  8,725,574  0.031772  50.66  0.935288253 
7579 years  2,634  142,958  1,842.50  7,414,559  0.026998  49.74  0.939425621 
8084 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: