epiR (version 0.9-5)

epi.2by2: Summary measures for count data presented in a 2 by 2 table

Description

Computes summary measures of risk and a chi-squared test for difference in the observed proportions from count data presented in a 2 by 2 table. Multiple strata may be represented by additional rows of count data and in this case crude and Mantel-Haenszel adjusted measures of risk are calculated and chi-squared tests of homogeneity are performed.

Usage

epi.2by2(a, b, c, d, method = "cohort.count", conf.level = 0.95, 
   verbose = FALSE)

Arguments

a

number of observations where exposure present and outcome present.

b

number of observations where exposure present and outcome absent.

c

number of observations where exposure absent and outcome present.

d

number of observations where exposure absent and outcome absent.

method

a character string indicating the experimental design on which the tabular data has been based. Options are cohort.count, cohort.time, case.control, or cross.sectional.

conf.level

magnitude of the returned confidence interval. Must be a single number between 0 and 1.

verbose

logical indicating whether detailed or summary results are to be returned.

Value

• When method equals cohort.count the following measures of association are returned: incidence risk ratio, odds ratio, attributable risk, attributable fraction, population attributable risk, and population attributable fraction. When method equals cohort.time the following measures of association are returned: incidence rate ratio, attributable rate, attributable fraction, population attributable rate, and population attributable fraction. When method equals case.control the following measures of association are returned: odds ratio, attributable risk, and estimated attributable fraction, population attributable risk, estimated population attributable fraction. When method equals cross.sectional the following measures of association are returned: incidence risk ratio, odds ratio, attributable risk, attributable fraction, population attributable risk, and population attributable fraction.

Details

Where method is cohort.count, case.control, or cross.sectional the 2 by 2 table format required is: lll{ Disease + Disease - Expose + a b Expose - c d } Where method is cohort.time the 2 by 2 table format required is: lll{ Disease + Time at risk Expose + a b Expose - c d }

References

Elwoood JM (1992). Causal Relationships in Medicine - A Practical System for Critical Appraisal. Oxford Medical Publications, London, pp. 266 - 293. Feychting M, Osterlund B, Ahlbom A (1998). Reduced cancer incidence among the blind. Epidemiology 9: 490 - 494. Hanley JA (2001). A heuristic approach to the formulas for population attributable fraction. Journal of Epidemiology and Community Health 55: 508 - 514. Jewell NP (2004). Statistics for Epidemiology. Chapman & Hall/CRC, London, pp. 123 -146. Martin SW, Meek AH, Willeberg P (1987). Veterinary Epidemiology Principles and Methods. Iowa State University Press, Ames, Iowa, pp. 130. Robbins AS, Chao SY, Fonesca VP (2002). What's the relative risk? A method to directly estimate risk ratios in cohort studies of common outcomes. Annals of Epidemiology 12: 452 - 454. Rothman KJ (2002). Epidemiology An Introduction. Oxford University Press, London, pp. 130 - 143. Rothman KJ, Greenland S (1998). Modern Epidemiology. Lippincott Williams, & Wilkins, Philadelphia, pp. 271. Willeberg P (1977). Animal disease information processing: Epidemiologic analyses of the feline urologic syndrome. Acta Veterinaria Scandinavica. Suppl. 64: 1 - 48. Woodward MS (2005). Epidemiology Study Design and Data Analysis. Chapman & Hall/CRC, New York, pp. 163 - 214. Zhang J, Yu KF (1998). What's the relative risk? A method for correcting the odds ratio in cohort studies of common outcomes. Journal of the American Medical Association 280: 1690 - 1691.

Examples

## EXAMPLE 1
## A cross sectional study investigating the relationship between dry cat 
## food (DCF) and feline urologic syndrome (FUS) was conducted (Willeberg 
## 1977). Counts of individuals in each group were as follows:

## DCF-exposed cats (cases, non-cases) 13, 2163
## Non DCF-exposed cats (cases, non-cases) 5, 3349

epi.2by2(a = 13, b = 2163, c = 5, d = 3349, method = "cross.sectional", 
   conf.level = 0.95, verbose = FALSE)

## Risk ratio:
## The incidence risk of FUS in DCF exposed cats is 4.01 times (95\% CI 2.33 to 
## 6.89) greater than the incidence risk of FUS in non-DCF exposed cats.

## Attributable fraction:
## In DCF exposed cats, 75\% of FUS is attributable to DCF (95\% CI 30\% to 91\%).

## Population attributable fraction:
## Fifty-four percent of FUS cases in the cat population are attributable 
## to DCF (95\% CI 22\% to 66\%).

## EXAMPLE 2
## A study was conducted by Feychting et al (1998) comparing cancer occurrence
## among the blind with occurrence among those who were not blind but had 
## severe visual impairment. From these data we calculate a cancer rate of
## 136/22050 person-years among the blind compared with 1709/127650 person-
## years among those who were visually impaired but not blind.

rval <- epi.2by2(a = 136, b = 22050, c = 1709, d = 127650, method = 
   "cohort.time", conf.level = 0.90, verbose = TRUE)
round(rval$AR * 1000, digits = 3)

## The incidence rate of cancer was 7.22 cases per 1000 person-years less in the 
## blind, compared with those who were not blind but had severe visual impairment
## (90\% CI -8.2\% to -6.2\%).

round(rval$IRR, digits = 3)   

## The incidence rate of cancer in the blind group was less than half that of the 
## comparison group (risk ratio 0.46, 90\% CI 0.40 to 0.53).

## EXAMPLE 3
## The results of an unmatched case control study of the association between
## smoking and cervical cancer were stratified by age. Counts of individuals 
## in each group were as follows: 

## Age group 20 - 29 years (cases, controls)
## Smokers: 41, 6
## Non-smokers: 13, 53

## Age group 30 - 39 years (cases, controls)
## Smokers: 66, 25
## Non-smokers: 37, 83

## Age +40 years (cases, controls)
## Smokers: 23, 14
## Non-smokers: 37, 62

a <- c(41, 66, 23)
b <- c(6, 25, 14)
c <- c(13, 37, 37)
d <- c(53, 83, 62)
epi.2by2(a, b, c, d, method = "case.control", conf.level = 0.95, verbose = TRUE)

## Crude odds ratio:
## 6.57 (95\% CI 4.31 to 10.03)
  
## Mantel-Haenszel adjusted odds ratio:
## 6.27 (95\% CI 3.52 to 11.17)

## Summary chi-squared test for difference in proportions:
## Test statistic 83.31; df = 1; P < 0.01

## Test of homeogeneity of odds ratios:
## Test statistic 2.09; df = 2; P = 0.35

## We accept the null hypothesis that the strata level odds ratios 
## are homogenous. The crude odds ratio is 1.05 times the magnitude of the 
## Mantel-Haenszel adjusted odds ratio. We conclude that age does not 
## confound the association between smoking and risk of cervical
## cancer (using a ratio of greater than 1.10 or less than 0.90 as 
## indicative of the presence of confounding.)