Multinomial Cochran-Armitage Trend Test

Description

Implements a generalization of the Cochran-Armitage trend test to multinomial data. In addition to an overall test, multiple testing adjusted p-values for trend in individual outcomes and power calculation is available.

Details

The DESCRIPTION file:

Index of help topics:

cnonct                  Non-centrality parameter for chi-square
                        distribution
multiCA-package         Multinomial Cochran-Armitage Trend Test
multiCA.test            Multinomial Cochran-Armitage trend test
power.CA.test           Power calculations for the Cochran-Armitage
                        trend test
power.multiCA.test      Power calculations for the multinomial
                        Cochran-Armitage trend test
stroke                  Stroke types over time

The main functionality is implemented in the multiCA.test function. The power.multiCA.test function can be used for power and sample size calculation.

Author(s)

NA

Maintainer: NA

References

Szabo, A. (2018). Test for Trend With a Multinomial Outcome. The American Statistician, 73(4), 313–320.

Non-centrality parameter for chi-square distribution

Description

Calculates the non-centrality parameter for a chi-square distribution for a given quantile. This is often needed for sample size calculation for chi-square based tests.

Usage

cnonct(x, p, df)

Arguments

Details

The function is modeled after the SAS function CNONCT. If p is larger than the cumulative probability of the central chi-square distribution at x, then there is no solution and NA is returned.

Examples

(ncp <- cnonct(qchisq(0.95, df=10), 0.8, df=10))
## check
pchisq(qchisq(0.95, df=10), df=10, ncp=ncp)  ## 0.8

Internal functions

Description

These internal functions perform the closed set p-value adjustment calculation for the multivariate Cochran-Armitage trend test. The logical constraint on the possible number of true null hypotheses is incorporated.

Usage

.bit2boolean(x, N)

.p.adjust.closed(test, hypotheses, remove = FALSE, ...)

Arguments

Value

numeric vector of adjusted p-values for each hypothesis

Multinomial Cochran-Armitage trend test

Description

The multiCA.test function performs a multinomial generalization of the Cochran-Armitage trend test.

Usage

multiCA.test(x, ...)

## Default S3 method:
multiCA.test(
  x,
  scores = 1:ncol(x),
  outcomes = 1:nrow(x),
  p.adjust.method = c("none", "closed.set", "Holm-Shaffer", "single-step", "Westfall"),
  ...
)

## S3 method for class 'formula'
multiCA.test(formula, data, subset, na.action, weights, ...)

Arguments

Value

a list with two components

Author(s)

Aniko Szabo

References

Szabo, A. (2018). Test for Trend With a Multinomial Outcome. The American Statistician, 73(4), 313–320.

Examples

data(stroke)
## using formula interface
multiCA.test(Type ~ Year, weights=Freq, data=stroke)

##using Westfall's multiple testing adjustment
multiCA.test(Type ~ Year, weights=Freq, data=stroke, p.adjust.method="Westfall")

## using matrix interface and testing only the first 3 outcomes
strk.mat <- xtabs(Freq ~ Type + Year, data=stroke)
multiCA.test(strk.mat, outcomes=1:3)

Power calculations for the Cochran-Armitage trend test

Description

Power calculations for the Cochran-Armitage trend test

Usage

power.CA.test(
  N = NULL,
  power = NULL,
  pvec = NULL,
  scores = seq_along(pvec),
  n.prop = rep(1, length(pvec)),
  sig.level = 0.05,
  alternative = c("two.sided", "less", "greater")
)

Arguments

Value

object of class "power.htest"

References

Nam, J. (1987). A Simple Approximation for Calculating Sample Sizes for Detecting Linear Trend in Proportions. Biometrics, 43(3), 701-705.

Examples

# sample size required to detect with 80% power a decreasing trend over 4 groups 
# with 3:2:1:2 sample-size distribution at a 2.5% significance level
power.CA.test(power=0.8, pvec=c(0.4, 0.3, 0.2, 0.1), n.prop=c(3,2,1,2),
              alternative = "less", sig.level=0.025)

# power of a 2-sided test to detect a logistic increase with slope 0.2 over 5 groups
# with groups of size 10 with unequal dose spacing
doses <- c(0,1,2,4,8)
p0 <- 0.05 # event probability at lowest dose
logit.props <- log(p0/(1-p0)) + doses * 0.2
p <- 1 / (1 + exp(-logit.props)) # hypothesized probabilities at each dose
power.CA.test(N = 10 * 5, pvec=p, scores = doses)

Power calculations for the multinomial Cochran-Armitage trend test

Description

Given the probabilities of outcomes, compute the power of the overall multinomial Cochran-Armitage trend test or determine the sample size to obtain a target power.

Usage

power.multiCA.test(
  N = NULL,
  power = NULL,
  pmatrix = NULL,
  p.ave = NULL,
  p.start = NULL,
  p.end = NULL,
  slopes = NULL,
  scores = 1:G,
  n.prop = rep(1, G),
  G = length(p.ave),
  sig.level = 0.05
)

Arguments

Details

The sample size calculation depends only on p.ave - the weighted average probability of each outcome, and slopes - the weighted regression slope of each outcome.

The values of these two key inputs can be specified in three ways:

1. directly passing p.ave and slopes, or

2. specifying exactly two of the parameters p.ave, slopes, p.start, and p.end. In this case the full matrix of outcome probabilities will be inferred assuming linearity within each outcome.

3. specifying the full matrix of outcome probabilities pmatrix.

The calculation is based on approximating the distribution of the test statistic under the alternative with a non-central chi-squared distribution instead of the correct weighted mixture of multiple non-central chi-squares. This results in bias in the power away from 50 underestimated.

Value

object of class "power.htest"

References

Szabo, A. (2018). Test for Trend With a Multinomial Outcome. The American Statistician, 73(4), 313–320.

See Also

power.CA.test for simpler (and more precise) power calculation with a binomial outcome

Examples

power.multiCA.test(power=0.8, p.start=c(0.1,0.2,0.3,0.4), p.end=c(0.4, 0.3, 0.2, 0.1), 
                     G=5, n.prop=c(3,2,1,2,3))

## Power of stroke study with 100 subjects per year and observed trends
data(stroke)
strk.mat <- xtabs(Freq ~ Type + Year, data=stroke)
power.multiCA.test(N=900, pmatrix=prop.table(strk.mat, margin=2))

Stroke types over time

Description

Nakajima et al. (2014) collected information on stroke patients over a 9-year period. For each patient, the type of stroke was classified into one of 5 categories by etiology.

Usage

data("stroke")

Format

A data frame with 45 observations on the following 3 variables.

Type

a factor with levels Small vessel occlusion, Large artery atherosclerosis, Cardioembolism, Other determined aetiology, and Undetermined aetiology giving the etiology of the stroke

Year

a numeric vector with the year of the observation

Freq

a numeric vector with the number of patients with a stroke of the given etiology that year

Source

Nakajima, M., Y. Inatomi, T. Yonehara, Y. Hashimoto, T. Hirano, and Y. Ando (2014). Temporal trends in oral intake ability 3 months after acute ischaemic stroke: analysis of a single-centre database from 2003 to 2011. J Rehabil Med 46 (3), 200–205.

Examples

data(stroke)
xtabs(Freq ~ Type + Year, data=stroke)

strk.props <- prop.table(xtabs(Freq ~ Year+Type, data=stroke), margin=1)
matplot(strk.props, type="l")