## Age standardization by direct method, with exact confidence intervals

### Description

Calculates age standardized (adjusted) rates and "exact" confidence intervals using the direct method

### Usage

ageadjust.direct(count, pop, rate = NULL, stdpop, conf.level = 0.95)


### Arguments

 count vector of age-specific count of events pop vector of age-specific person-years or population estimates rate vector of age-specific rates stdpop vector of age-specific standarad population conf.level confidence level (default = 0.95)

### Details

To make valid comparisons between rates from different groups (e.g., geographic area, ethnicity), one must often adjust for differences in age distribution to remove the confounding affect of age. When the number of events or rates are very small (as is often the case for local area studies), the normal approximation method of calculating confidence intervals may give a negative number for the lower confidence limit. To avoid this common pitfall, one can approximate exact confidence intervals. This function implements this method (Fay 1997).

Original function written by TJ Aragon, based on Anderson, 1998. Function re-written and improved by MP Fay, based on Fay 1998.

### Value

 crude.rate crude (unadjusted) rate adj.rate age-adjusted rate lci lower confidence interval limit uci upper confidence interval limit

### Author(s)

Michael P. Fay, mfay@niaid.nih.gov; Tomas Aragon, aragon@berkeley.edu, http://www.phdata.science

### References

Fay MP, Feuer EJ. Confidence intervals for directly standardized rates: a method based on the gamma distribution. Stat Med. 1997 Apr 15;16(7):791-801. PMID: 9131766

Steve Selvin. Statistical Analysis of Epidemiologic Data (Monographs in Epidemiology and Biostatistics, V. 35), Oxford University Press; 3rd edition (May 1, 2004)

Anderson RN, Rosenberg HM. Age Standardization of Death Rates: Implementation of the Year 200 Standard. National Vital Statistics Reports; Vol 47 No. 3. Hyattsville, Maryland: National Center for Health Statistics. 1998, pp. 13-19. Available at http://www.cdc.gov/nchs/data/nvsr/nvsr47/nvs47_03.pdf.

See also ageadjust.indirect

### Examples

## Data from Fleiss, 1981, p. 249
population <- c(230061, 329449, 114920, 39487, 14208, 3052,
72202, 326701, 208667, 83228, 28466, 5375, 15050, 175702,
207081, 117300, 45026, 8660, 2293, 68800, 132424, 98301,
46075, 9834, 327, 30666, 123419, 149919, 104088, 34392,
319933, 931318, 786511, 488235, 237863, 61313)
population <- matrix(population, 6, 6,
dimnames = list(c("Under 20", "20-24", "25-29", "30-34", "35-39",
"40 and over"), c("1", "2", "3", "4", "5+", "Total")))
population
count <- c(107, 141, 60, 40, 39, 25, 25, 150, 110, 84, 82, 39,
3, 71, 114, 103, 108, 75, 1, 26, 64, 89, 137, 96, 0, 8, 63, 112,
262, 295, 136, 396, 411, 428, 628, 530)
count <- matrix(count, 6, 6,
dimnames = list(c("Under 20", "20-24", "25-29", "30-34", "35-39",
"40 and over"), c("1", "2", "3", "4", "5+", "Total")))
count

### Use average population as standard
standard<-apply(population[,-6], 1, mean)
standard

### This recreates Table 1 of Fay and Feuer, 1997
round(10^5*birth.order1,1)

round(10^5*birth.order2,1)