# Age-adjusted Rates

An

Crude rates provide a useful summary measure to compare similar populations of different sizes. But crude rates are sensitive to differences in age compositions.

For example, a county with an older population will have higher crude death rates for cancer, even though its risk exposure levels and age-specific cancer rates may the same as those in other counties. One might incorrectly attribute the high cancer rates to some characteristic of the county other than age. Age-adjustment may also be used to control for age effects when comparing across several years of data, as the age distribution of the population changes over time. Calculating age-adjusted rates may be accomplished using direct or indirect age standardization.

# Direct Age Adjustment

Direct age-adjustment (or age standardization) is the same as calculating a weighted average. It weights the age-specific rates observed in a population of interest by the proportion of each age group in a standard population (Lilienfeld & Stolley, 1994).In 1998, the Centers for Disease Control and Prevention revised the standard population weights for direct age-adjustment (Klein & Schoenborn), replacing the 1940 U.S. standard population weights that had been used for the previous several decades. Table 1., below, contains the standard population weights published by the CDC. They represent the proportion of the U.S. 2000 population in each age group, and sum to 1.0.

Age-adjusted rates should be viewed as

## Weights for Direct Age Adjustment

The following table includes the weights that are currently recommended by the CDC, Klein & Schoenborn, for calculation of the Directly Age-adjusted Rate.

### Table 1. U.S. 2000 Standard Population Weights for Age Standardization

Age Group | U.S. 2000 Population Projection (in thousands) |
Weight | |
---|---|---|---|

1 |
Under 1 Year | 3,795 |
0.013818 |

2 |
1 - 4 Years | 15,192 |
0.055317 |

3 |
5 - 14 Years | 39,977 |
0.145565 |

4 |
15 - 24 Years | 38,077 |
0.138646 |

5 |
25 - 34 Years | 37,233 |
0.135573 |

6 |
35 - 44 Years | 44,659 |
0.162613 |

7 |
45 - 54 Years | 37,030 |
0.134834 |

8 |
55 - 64 Years | 23,961 |
0.087247 |

9 |
65 - 74 Years | 18,136 |
0.066037 |

10 |
75 - 84 Years | 12,315 |
0.044842 |

11 |
85 Years and Over | 4,259 |
0.015508 |

## Calculating Age-Adjusted Rates Using the Direct Method

To apply direct age-adjustment to a set of rates, the age-specific rate for each age group in the study population is multiplied by the appropriate weight in the standard population. The sum of these products is the directly age-adjusted, or age-standardized rate. The age-adjusted rate can be considered an average of each of the individual age-specific rates, but rather than being a simple average, it is a weighted average with each age-specific rate weighted by the proportion of people in the same age group in the standard population.

Tables 2a. and 2b. demonstrate the method used by IBIS-Q in calculating age-adjusted rates. Notice that using crude death rates in Tables 2a. and 2b., one might conclude that persons in Sierra County have a higher underlying risk for Diabetes death compared with the state of Hawaii. How should the age-adjusted death rates be interpreted? You could use confidence intervals to assist in interpreting these data (IBIS automatically provides 95% confidence intervals for all rates).

### Table 2a. Age-adjusted Death Rate for Diabetes Mellitus, State of Hawaii, 2003-2005

Age Group | Number of Deaths (3-Year Sum) | Population Counts (3-Year Sum)(1) | Age- Specific Rate (2) | US2000 Std Pop Weight | Cross Products (3) |
---|---|---|---|---|---|

Under 1 Year | 0 |
84,952 |
0 |
0.013818 |
0 |

1 - 4 years | 0 |
325,508 |
0 |
0.055317 |
0 |

5 - 14 years | 2 |
828,663 |
0.24 |
0.145565 |
0.30502 |

15 - 24 years | 2 |
893,809 |
0.22 |
0.138646 |
0.030502 |

25 - 34 years | 19 |
718,484 |
2.64 |
0.135573 |
0.357918 |

35 - 44 years | 61 |
810,632 |
7.52 |
0.162613 |
1.222855 |

45 - 54 years | 160 |
833,948 |
19.19 |
0.134834 |
2.587478 |

55 - 64 years | 297 |
602,768 |
49.27 |
0.087247 |
4.298757 |

65 - 74 years | 443 |
381,451 |
116.14 |
0.066037 |
7.669339 |

75 - 84 years | 546 |
235,030 |
232.31 |
0.044842 |
10.41697 |

85 years and over | 369 |
82,660 |
446.41 |
0.015508 |
6.923177 |

All Ages | 1,899 |
5,797,906 |
32.754 (4) |
1 |

### Table 2b. Age-adjusted Rate for Diabetes Mellitus, Sierra County, Hawaii, 2003-2005

Age Group | Number of Deaths (3-Year Sum) | Population Counts (3-Year Sum)(1) | Age- Specific Rate (2) | US2000 Std Pop Weight | Cross Products (3) |
---|---|---|---|---|---|

Under 1 Year | 0 |
350 |
0 |
0.013818 |
0 |

1 - 4 years | 0 |
1,266 |
0 |
0.055317 |
0 |

5 - 14 years | 0 |
4,384 |
0 |
0.145565 |
0 |

15 - 24 years | 0 |
4,526 |
0 |
0.138646 |
0 |

25 - 34 years | 0 |
2,977 |
0 |
0.135573 |
0 |

35 - 44 years | 1 |
4,269 |
23.43 |
0.162613 |
3.81038 |

45 - 54 years | 0 |
5,581 |
0 |
0.134834 |
0 |

55 - 64 years | 1 |
5,985 |
16.71 |
0.087247 |
1.457931 |

65 - 74 years | 11 |
5,946 |
185.01 |
0.066037 |
12.21719 |

75 - 84 years | 6 |
4,086 |
146.85 |
0.044842 |
6.584872 |

85 years and over | 3 |
1,584 |
189.45 |
0.015508 |
2.938097 |

All Ages | 22 |
40,952 |
53.72 (4) |
1 |

(1) Bureau of Business and Economic Research (BBER), UNM. |

(2) Rate per 100,000 = (Age-specific death count * 100,000) / Age-specific population count |

(3) Age-specific death rate * US2000 Std Pop Weight |

(4) Crude death rate |

(5) |

Age adjustment is not appropriate if the age-specific death rates in the population of interest do not have a consistent relationship. For example, if death rates among younger persons is increasing over time, but death rates among older persons is decreasing over time, you would not want to age-adjust rates across years. One's conclusion of the trend in this death rate would be different, depending on which standard population is used. A younger standard population (such as the US 1940) would show an increase, whereas an older standard population (such as the US 2000) would show a decrease, or no change at all. Care should be taken so that the selection of the standard population does not affect the comparisons. For more information, see Curtin & Klein.

When reporting age-adjusted rates, always report the standard population used, and when comparing results to other data, be sure to document that those data were also age-adjusted and report the standard population. The age-adjusted rate is hypothetical, and is useful only for

## FAQs for Age-adjustment:

### Event Rates for a Subpopulation

### When NOT to Age-Adjust

- You are comparing populations with similar age distributions, and age-adjustment does not produce a rate that is substantively different from the crude rate.
- You are comparing groups with the same, narrow, age range.
- Do not use Direct Age-adjustment if you have too few cases (you should have a least 25 events across all age groups). Instead, use Indirect Age-Adjustment.

### Age Subpopulations

### Age/Sex Adjusted Rates

### Confidence Intervals for Age-adjusted Rates

# Indirect Age-adjustment

In some cases, such as when there are too few cases to stratify by age, indirect age adjustment, or indirect age standardization may be used. Indirect standardization is based on standardized mortality and morbidity ratio (SMR), and adjusts the age-specific rates found in the standard population to the age distribution of the smaller area or sub-population. According to Curtin & Klein, "One of the problems with [direct age adjustment] is that rates based on small numbers of deaths will exhibit a large amount of random variation. A very rough guideline is that there should be at least 25 total deaths over all age groups." When fewer than 25 health events occurred over a time period, you may consider combining years, or using indirect age-adjustment.

The direct method can present problems when population sizes are particularly small. Calculating directly standardized rates requires calculating age-group-specific rates, and for small areas these age-specific rates may be based on one or two events. In such cases, indirect standardization of rates may be used.

Indirectly standardized rates are based on the standard mortality or morbidity ratio (SMR) and the crude rate for a standard population. Indirect standardization adjusts the overall standard population death rate to the age distribution of the small area (Lilienfeld & Stolley, 1994). It is technically appropriate to compare indirectly standardized rates only with the rate in the standard population, not with each other.

# Deciding Which Measure to Use

If your question is: | Then use: |
---|---|

MAGNITUDE: How big is the problem? | Number of events (count) |

PROBABILITY: What is the underlying risk in my population? | Crude rate and confidence interval |

DISPARITY: Does the risk level differ across population groups after controlling for age? | Age-adjusted rate and confidence interval |

## References

1. Anderson RN, Rosenberg HM. Age Standardization of Death Rates: Implementation of the Year 2000 Standard. National vital statistics reports; vol 47 no.3. Hyattsville, Maryland: National Center for Health Statistics. 1998.

2. Klein RJ, Schoenborn CA. Age-Adjustment Using the 2000 Projected U.S. Population. Statistical notes; no.20. Hyattsville, Maryland: National Center for Health Statistics. January 2001.

3. Curtin, LR, Klein, RJ. Direct Standardization (Age-Adjusted Death Rates). Statistical notes; no.6. Hyattsville, Maryland: National Center for Health Statistics. March 1995.

4. Fleis, JL. Statistical methods for rates and proportions. John Wiley and Sons, New York, 1973.

5. Klein RJ, Schoenborn CA., 2001.

6. Lilienfeld, DE and Stolley, PD. Foundations of Epidemiology, 3rd Ed. Oxford University Press, 1994.