DescTools (version 0.99.15)

BreslowDayTest: Breslow-Day Test for Homogeneity of the Odds Ratios

Description

Calculates a Breslow-Day test of homogeneity for a $2 \times 2 \times k$ tables, to see if all strata have the same OR. If OR is not given, the Mantel-Haenszel estimate is used.

Usage

BreslowDayTest(x, OR = NA, correct = FALSE)

Arguments

x

a $2 \times 2 \times k$ table.

OR

the odds ratio to be tested against. If left undefined (default) the Mantel-Haenszel estimate will be used.

correct

If TRUE, the Breslow-Day test with Tarone's adjustment is computed, which subtracts an adjustment factor to make the resulting statistic asymptotically chi-square.

Details

For the Breslow-Day test to be valid, the sample size should be relatively large in each stratum, and at least 80% of the expected cell counts should be greater than 5. Note that this is a stricter sample size requirement than the requirement for the Cochran-Mantel-Haenszel test for tables, in that each stratum sample size (not just the overall sample size) must be relatively large. Even when the Breslow-Day test is valid, it might not be very powerful against certain alternatives, as discussed in Breslow and Day (1980).

References

source: https://onlinecourses.science.psu.edu/stat504/sites/onlinecourses.science.psu.edu.stat504/files/lesson04/breslowday.test_.R Breslow, N. E., N. E. Day (1980) The Analysis of Case-Control Studies Statistical Methods in Cancer Research: Vol. 1. Lyon, France, IARC Scientific Publications. Tarone, R.E. (1985) On heterogeneity tests based on efficient scores, Biometrika, 72, pp. 91-95. Jones, M. P., O'Gorman, T. W., Lemka, J. H., and Woolson, R. F. (1989) A Monte Carlo Investigation of Homogeneity Tests of the Odds Ratio Under Various Sample Size Configurations Biometrics, 45, 171-181 Breslow, N. E. (1996) Statistics in Epidemiology: The Case-Control Study Journal of the American Statistical Association, 91, 14-26.

See Also

WoolfTest

Examples

migraine <- xtabs(freq ~ ., 
            cbind(expand.grid(treatment=c("active", "placebo"), 
                              response =c("better", "same"), 
                              gender   =c("female", "male")),
                  freq=c(16, 5, 11, 20, 12, 7, 16, 19))
            )

# get rid of gender
tab <- xtabs(Freq ~ treatment + response, migraine)
Desc(tab)

# only the women
female <- migraine[,, 1]
Desc(female)

# .. and the men
male <- migraine[,, 2]
Desc(male)

BreslowDayTest(migraine)
BreslowDayTest(migraine, correct = TRUE)


salary <- array(
      c(38, 12, 102, 141, 12, 9, 136, 383),
      dim=c(2, 2, 2),
      dimnames=list(exposure=c("exposed", "not"), 
                    disease =c("case", "control"),
                    salary  =c("<1000", ">=1000"))
                    )

# common odds ratio = 4.028269
BreslowDayTest(salary, OR = 4.02)