Oral contraceptive use and breast cancer rates

Description

This data summarizes counts of a case-control study investigating the link between breast cancer rates and oral contraceptive use, stratified by age group. In toto, 10,890 subjects. See source for details.

Usage

data(contraceptives)

Format

A 3-dimensional table.

1. OC Usage: Subject exposure to oral contraceptives.

2. Disease Status: Breast cancer present (case) or absent (control).

3. Age Group: Age group of the subject.

Source

Hennekens, C. H., F. E. Speizer, R. J. Lipnick, B. Rosner, C. Bain, C. Belanger, M. J. Stampfer, W. Willett, and R. Peto. (1984). "A Case-Control Study of Oral Contraceptive Use and Breast Cancer." Journal of the National Cancer Institute 72 (1): 39–42. Table 1.

Interconvert odds and proportion values

Description

These functions will create either odds for a given probability, probability for a given odds, calculate the odds ratio between two probabilities, or calculate effect size (raise a probability by theta)

Usage

prop2odds(p)

odds2prop(o)

effect.size(p, theta)

props2theta(p1, p2)

rr2theta(rr, p1, p2)

theta2rr(theta, p1, p2)

Arguments

Value

A numeric vector.

Author(s)

Paul W. Egeler, M.S.

Examples

# Convert proportions of 0 through 1 to odds
props <- seq(0,1,0.1)
prop2odds(props)

# Convert odds to proportions
odds2prop(1:3)

# Raise a proportion by an effect size theta
effect.size(0.5, 2)

# Find the odds ratio between two proportions
props2theta(0.75, 0.5)

Create an odds ratio estimate from a 2-by-2 table of frequencies or proportions

Description

Create an odds ratio estimate from a 2-by-2 table of frequencies or proportions

Usage

odds.ratio(x)

Arguments

Value

A numeric vector.

Author(s)

Paul W. Egeler, M.S.

Examples

# Load in Titanic data from datasets package
data(Titanic, package = "datasets")

# Get marginal table of survival by sex
marginal_table <- margin.table(Titanic, c(2,4))
marginal_table

# Compute odds ratio of marginal table
odds.ratio(marginal_table)

# Get partial tables of survival by sex, stratified by class
partial_tables <- margin.table(Titanic, c(2,4,1))
partial_tables

# Compute odds ratio of each partial table
apply(partial_tables, 3, odds.ratio)

Power and sample size calculation for the Cochran-Mantel-Haenszel test

Description

Compute the post-hoc power or required number of subjects for the Cochran-Mantel-Haenszel test for association in J stratified 2 x 2 tables.

Usage

power.cmh.test(
  p1 = NULL,
  p2 = NULL,
  theta = NULL,
  N = NULL,
  sig.level = 0.05,
  power = 0.8,
  alternative = c("two.sided", "less", "greater"),
  s = 0.5,
  t = 1/J,
  correct = TRUE
)

Arguments

Details

This sample size calculation is based on the derivations described in the Woolson et al. (1986). It is designed for case-control studies where one margin is fixed. The method is "based on the Cochran-Mantel-Haenszel statistic expressed as a weighted difference in binomial proportions."

Continuity corrected sample size is described in Nam's 1992 paper. This uses the weighted binomial sample size calculation described in Woolson et al. (1986) but is enhanced for use with the continuity corrected Cochran's test.

Power calculations are based on the writings of Wittes and Wallenstein (1987). They are functionally equivalent to the derivations of the sample size calculation described by Woolson and others and Nam, but have slightly added precision.

Terminology and symbolic conventions are borrowed from Woolson et al. (1986). The p1 group is dubbed the Case group and p2 group is called the Control group.

Value

An object of class "power.cmh": a list of the original arguments and the calculated sample size or power. Also included are vectors of n's per each group, an indicator or whether continuity correction was used, the original function call, and N.effective.

The vectors of n's per each group, n1 and n2, are the fractional n's required to achieve a final total N specified by the calculation while satisfying the constraints of s and t. However, the effective N, given the requirement of cell counts populated by whole numbers is provided by N.effective. By default, the print method is set to n.frac = FALSE, which will round each cell n up to the nearest whole number.

Arguments

To calculate power, the power parameter must be set to NULL. To calculate sample size, the N parameter must be set to NULL.

The J number of groups will be inferred by the maximum length of p1, p2, or theta.

Effect size must be specified using one of the following combinations of arguments.

• Both case and control proportion vectors, ex.,

  • p1 and p2 with theta = NULL.

• One proportion vector and an effect size, ex.,

  • p1 and theta with p2 = NULL, or

  • p2 and theta with p1 = NULL.

Author(s)

Paul W. Egeler, M.S.

References

Gail, M. (1973). "The determination of sample sizes for trials involving several 2 x 2 tables." Journal of Chronic Disease 26: 669-673.

Munoz, A. and B. Rosner. (1984). "Power and sample size for a collection of 2 x 2 tables." Biometrics 40: 995-1004.

Nam, J. (1992). "Sample size determination for case-control studies and the comparison of stratified and unstratified analyses." Biometrics 48: 389-395.

Wittes, J. and S. Wallenstein. (1987). "The power of the Mantel-Haenszel test." Journal of the American Statistical Association 82: 1104-1109.

Woolson, R. F., Bean, J. A., and P. B. Rojas. (1986). "Sample size for case-control studies using Cochran's statistic." Biometrics 42: 927-932.

See Also

power.prop.test, mantelhaen.test, BreslowDayTest

Examples

# From "Sample size determination for case-control studies and the comparison
# of stratified and unstratified analyses", (Nam 1992). See references.

# Uncorrected sample size estimate first introduced
# by Woolson and others in 1986
sample_size_uncorrected <- power.cmh.test(
  p2 = c(0.75,0.70,0.65,0.60),
  theta = 3,
  power = 0.9,
  t = c(0.10,0.40,0.35,0.15),
  alternative = "greater",
  correct = FALSE
)

print(sample_size_uncorrected, detail = FALSE)

# We see that the N is 171, the same as calculated by Nam
sample_size_uncorrected$N


# Continuity corrected sample size estimate added by Nam
sample_size_corrected <- power.cmh.test(
  p2 = c(0.75,0.70,0.65,0.60),
  theta = 3,
  power = 0.9,
  t = c(0.10,0.40,0.35,0.15),
  alternative = "greater",
  correct = TRUE
)

print(sample_size_corrected, n.frac = TRUE)

# We see that the N is indeed equal to that which is reported in the paper
sample_size_corrected$N

Print "power.cmh" object

Description

The S3 print method for the "power.cmh" object

Usage

## S3 method for class 'power.cmh'
print(x, detail = TRUE, n.frac = FALSE, ...)

Arguments

Calculate the relative risk from a 2-by-2 table

Description

Computes the relative risk of a specified column of a two-by-two table.

Usage

rel.risk(x, col.num = 1)

Arguments

Value

A numeric vector.

Author(s)

Paul W. Egeler, M.S.

samplesizeCMH: Power and Sample Size Calculation for the Cochran-Mantel-Haenszel Test

Description

This package provides functions relating to power and sample size calculation for the CMH test. There are also several helper functions for interconverting probability, odds, relative risk, and odds ratio values.

Details

The Cochran-Mantel-Haenszel test (CMH) is an inferential test for the association between two binary variables, while controlling for a third confounding nominal variable. Two variables of interest, X and Y, are compared at each level of the confounder variable Z and the results are combined, creating a common odds ratio. Essentially, the CMH test examines the weighted association of X and Y. The CMH test is a common technique in the field of biostatistics, where it is often used for case-control studies.

Sample Size Calculation

Given a target power which the researcher would like to achieve, a calculation can be performed in order to estimate the appropriate number of subjects for a study. The power.cmh.test function calculates the required number of subjects per group to achieve a specified power for a Cochran-Mantel-Haenszel test.

Power Calculation

Researchers interested in estimating the probability of detecting a true positive result from an inferential test must perform a power calculation using a known sample size, effect size, significance level, et cetera. The power.cmh.test function can compute the power of a CMH test, given parameters from the experiment.