epiR (version 0.9-46)

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 association are calculated and chi-squared tests of homogeneity are performed.

Usage

epi.2by2(dat, method = "cohort.count", conf.level = 0.95, 
   units = 100, homogeneity = "breslow.day", verbose = FALSE)

Arguments

dat

an object of class table containing the individual cell frequencies.

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.

units

multiplier for prevalence and incidence estimates.

homogeneity

a character string indicating the type of homogeneity test to perform. Options are breslow.day or woolf.

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: the incidence risk ratio (RR), the odds ratio (OR), the attributable risk (AR), the attributable risk in the population (ARp), the attributable fraction in the exposed (AFe), and the attributable fraction in the population (AFp). When method equals cohort.time the following measures of association are returned: the incidence rate ratio (IRR), the attributable rate (AR), the attributable rate in the population (ARp), the attributable fraction in the exposed (AFe), and the attributable fraction in the population (AFp). When method equals case.control the following measures of association are returned: the odds ratio (OR), the attributable prevalence (AR), the attributable prevalence in population (ARp), the estimated attributable fraction in the exposed (AFest), and the estimated attributable fraction in the population (AFp). When method equals cross.sectional the following measures of association are returned: the prevalence ratio (PR), the odds ratio (OR), the attributable prevalence (AR), the attributable prevalence in the population (ARp), the attributable fraction in the exposed (AFe), and the attributable fraction in the population (AFp). When there are multiple strata, the function returns the appropriate measure of association for each strata (e.g. OR.strata), the crude measure of association across all strata (e.g. OR.crude) and the Mantel-Haenszel adjusted measure of association (e.g. OR.mh). Strata-level weights (i.e. inverse variance of the strata-level measures of assocation) are provided --- these are useful to understand the relationship between the crude strata-level measures of association and the Mantel-Haenszel adjusted measure of association. chisq.strata returns the results of a chi-squared test for difference in exposed and non-exposed proportions for each strata. chisq.crude returns the results of a chi-squared test for difference in exposed and non-exposed proportions across all strata. chisq.mh returns the results of the Mantel-Haenszel chi-squared test. The tests of homogeneity (e.g. OR.homogeneity) assess the similarity of the strata-level measures of association.

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

Altman D, Machin D, Bryant T, Gardner M (2000). Statistics with Confidence. British Medical Journal, London, pp. 69. Elwood JM (2007). Critical Appraisal of Epidemiological Studies and Clinical Trials. Oxford University Press, London. 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. 84 - 85. Martin SW, Meek AH, Willeberg P (1987). Veterinary Epidemiology Principles and Methods. Iowa State University Press, Ames, Iowa, pp. 130. McNutt L, Wu C, Xue X, Hafner JP (2003). Estimating the relative risk in cohort studies and clinical trials of common outcomes. American Journal of Epidemiology 157: 940 - 943. 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

dat <- as.table(matrix(c(13,2163,5,3349), nrow = 2, byrow = TRUE))
epi.2by2(dat = dat, method = "cross.sectional", 
   conf.level = 0.95, units = 100,  homogeneity = "breslow.day", 
   verbose = FALSE)

## Prevalence ratio:
## The prevalence of FUS in DCF exposed cats is 4.01 times (95\% CI 1.43 to 
## 11.23) greater than the prevalence 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 4\% to 78\%).


## EXAMPLE 2
## This example shows how the table function can be used to pass data to
## epi.2by2. Generate a case-control data set comprise of 1000 subjects. 
## The probability of exposure is 0.50. The probability of disease in the 
## exposed is 0.75, the probability of disease in the unexposed is 0.45.

n <- 1000; p.exp <- 0.50; pd.exp <- 0.75; pd.exn <- 0.45 
dat <- data.frame(exp = rep(0, times = n), stat = rep(0, times = n))
dat$exp <- rbinom(n = n, size = 1, prob = p.exp)
dat$stat[dat$exp == 1] <- rbinom(n = length(dat$stat[dat$exp == 1]), 
   size = 1, prob = pd.exp)
dat$stat[dat$exp == 0] <- rbinom(n = length(dat$stat[dat$exp == 0]), 
   size = 1, prob = pd.exn)
dat$exp <- factor(dat$exp, levels = c("1", "0"))
dat$stat <- factor(dat$stat, levels = c("1", "0"))
head(dat)

## Create a 2 by 2 table from this simulated data set:
dat <- table(dat$exp, dat$stat, dnn = c("Exposure", "Disease"))
dat

## 2 by 2 table analysis:
epi.2by2(dat = dat, method = "case.control", 
   conf.level = 0.95, units = 100, homogeneity = "breslow.day",
   verbose = FALSE)
   

## EXAMPLE 3
## 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.

dat <- as.table(matrix(c(136,22050,1709,127650), nrow = 2, byrow = TRUE))
rval <- epi.2by2(dat = dat, method = "cohort.time", conf.level = 0.90, 
   units = 1000,  homogeneity = "breslow.day", verbose = TRUE)
round(rval$AR, 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 6.20 to 8.24 cases per 1000 person-years).

round(rval$IRR, digits = 3)   

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


## EXAMPLE 4
## Adapted from Elwood (2007, pages 194 -- 295):
## 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

## Coerce the count data that has been provided into tabular format (take
## care when setting strata labels to make sure they match up with appropriate
## contingency table data):
slabel <- c("20-29 yrs", "30-39 yrs", "40+ yrs")
dat <- data.frame(strata = rep(slabel, each = 2), 
   exp = rep(c("+","-"), times = length(slabel)), dis = rep(c("+","-"), 
   times = length(slabel)))
dat$exp <- factor(dat$exp, levels = c("+", "-"))
dat$dis <- factor(dat$dis, levels = c("+", "-"))
dat <- table(dat$exp, dat$dis, dat$strata, 
   dnn = c("Exposure", "Disease", "Strata"))

dat[1,1,] <- c(41,66,23)
dat[1,2,] <- c(6,25,14)
dat[2,1,] <- c(13,37,37)
dat[2,2,] <- c(53,83,62)

rval <- epi.2by2(dat = dat, method = "case.control", conf.level = 0.95,
   units = 100, homogeneity = "breslow.day", verbose = TRUE)
rval

## Crude odds ratio:
## 6.57 (95\% CI 4.22 to 10.28)
  
## Mantel-Haenszel adjusted odds ratio:
## 6.27 (95\% CI 3.52 to 11.17)

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

## Breslow Day test of homeogeneity of odds ratios:
## Test statistic 12.66; df = 2; P < 0.01

## We reject the null hypothesis and conclude that the strata level odds ratios 
## are inhomogenous. The crude odds ratio is 6.57 (95\% CI 4.31 -- 10.03). 
## The Mantel-Haenszel adjusted odds ratio is 6.27 (95\% CI 3.52 to 11.17). 
## The crude odds ratio is 1.05 times the magnitude of the Mantel-Haenszel 
## adjusted odds ratio so 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).

## Now plot the individual strata-level odds ratio and compare them with the 
## Mantel-Haenszel adjusted odds ratio.

## Not run: 
library(latticeExtra)
nstrata <- 1:dim(dat)[3]
strata.lab <- paste("Strata ", nstrata, sep = "")
y.at <- c(nstrata, max(nstrata) + 1)
y.labels <- c("Mantel-Haenszel", strata.lab)
x.labels <- c(0.5, 1, 2, 4, 8, 16, 32, 64, 128)

or.l <- c(rval$OR.mh$lower, rval$OR.strata$lower)
or.u <- c(rval$OR.mh$upper, rval$OR.strata$upper)
or.p <- c(rval$OR.mh$est, rval$OR.strata$est)
vert <- 1:length(or.p)
 
segplot(vert ~ or.l + or.u, centers = or.p, horizontal = TRUE, 
   aspect = 1/2, col = "grey", 
   ylim = c(0,vert + 1), 
   xlab = "Odds ratio", ylab = "", 
   scales = list(y = list(at = y.at, labels = y.labels)), 
   main = "Strata level and summary measures of association")
## End(Not run)

## In this example the precision of the odds ratio estimate for both strata 
## 2 and 3 is high (i.e. the confidence intervals are narrow) so strata 2 
## and 3 carry most of the weight in determining the value of the 
## Mantel-Haenszel adjusted odds ratio.