Cochran-Armitage Trend Test for Binomial Data

Performs a Cochran-Armitage test for trend in binomial proportions across ordered groups, with an optional Rao-Scott correction for overdispersion.

Usage

cochranArmitageTrendTest(
  successes,
  totals,
  doses,
  scoring = c("doses", "ranks", "log_doses", "equal_spaced"),
  alternative = c("two.sided", "greater", "less"),
  rao_scott = FALSE,
  phi = NULL,
  phi_method = c("simple", "trend_adjusted")
)

Arguments

successes

Numeric vector of successes (e.g., number of survivors).

totals

Numeric vector of total observations (e.g., total organisms).

doses

Numeric vector of dose levels or scores corresponding to each observation.

scoring

Method for defining trend

alternative

Character string specifying the alternative hypothesis. Must be one of "two.sided" (default), "greater", or "less".

rao_scott

Logical indicating whether to apply Rao-Scott correction for overdispersion (default: FALSE).

phi

Overdispersion parameter for Rao-Scott correction. If NULL (default), it will be estimated from the data.

phi_method

simple without trend adjustment or trend_adjusted.

Value

A list containing:

statistic

Test statistic (Z score)

p.value

P-value for the test

method

Description of the test performed

alternative

The alternative hypothesis

data.name

Description of the data

phi

Overdispersion parameter (only if rao_scott = TRUE)

Details

The Cochran-Armitage test is used to detect trends in binomial proportions across ordered groups. The test statistic follows a standard normal distribution under the null hypothesis of no trend.

When rao_scott = TRUE, the function applies a correction for overdispersion, which is often present in clustered binomial data. The correction divides the test statistic by the square root of the estimated dispersion parameter.

Examples

# Example with simulated data
successes <- c(20, 18, 15, 10, 5)
totals <- rep(20, 5)
doses <- c(0, 1, 2, 5, 10)

# Standard Cochran-Armitage test
result <- cochranArmitageTrendTest(successes, totals, doses)
print(result)
#> 
#> 	Cochran-Armitage test for trend (doses scoring)
#> 
#> data:  proportions 1, 0.9, 0.75, 0.5, 0.25 at doses 0, 1, 2, 5, 10
#> = -5.7465, p-value = 9.108e-09
#> alternative hypothesis: two.sided
#> 

# With Rao-Scott correction
result_rs <- cochranArmitageTrendTest(successes, totals, doses, rao_scott = TRUE)
#> Estimated phi = 8.571 using simple method with doses scoring
print(result_rs)
#> 
#> 	Rao-Scott corrected Cochran-Armitage test for trend (doses scoring)
#> 
#> data:  proportions 1, 0.9, 0.75, 0.5, 0.25 at doses 0, 1, 2, 5, 10
#> = -1.9629, p-value = 0.04966
#> alternative hypothesis: two.sided
#>