catt_exact {CATTexact}

Conditional exact Cochran-Armitage trend test

Description

catt_exact calculates the Cochran-Armitage trend test statistic (Cochran (1954), Armitage (1955)) and the one-sided p-value for the corresponding conditional exact test. The conditional exact test has been established by Williams (1988). The computation of its p-value is performed using an algorithm following an idea by Mehta, et al. (1992).

Usage

catt_exact(dose.ratings, totals, cases)

Arguments

dose.ratings

A vector of dose ratings, the i-th entry corresponds to the dose-rating of the i-th group. This vector must be strictly monotonically increasing

totals

The vector of total individuals per group, the i-th entry corresponds to the total number of individuals in the i-th group.

cases

The vector of incidences per groups, the i-th entry corresponds to the number of incidences in the i-th group.

Value

A list containing the value of the Cochran-Armitage Trend Test Statistic, its exact and asymptotic p-value.

References

Armitage, P. Tests for linear trends in proportions and frequencies. Biometrics, 11 (1955): 375-386.

Cochran, W. G. Some methods for strengthening the common \chi^2 tests, Biometrics. 10 (1954): 417-451.

Mehta, C. R., Nitin P., and Pralay S. Exact stratified linear rank tests for ordered categorical and binary data. Journal of Computational and Graphical Statistics, 1 (1992): 21-40.

Portier, C., and Hoel D. Type 1 error of trend tests in proportions and the design of cancer screens. Communications in Statistics-Theory and Methods, 13 (1984): 1-14.

Williams, D. A. Tests for differences between several small proportions. Applied Statistics, 37 (1988): 421-434.

Examples

d <- c(1,2,3,4)
n <- rep(20,4)
r <- c(1,4,3,8)

catt_exact(d, n, r)