Wald-type test for three-arm trials

Description

Wald-type test for superiority/non-inferiority of the experimental treatment versus reference treatment with respect to placebo.

Usage

1
test_RET(xExp, xRef, xPla, Delta, ...)

Arguments

xExp

A (non-empty) numeric vector of data values from the experimental treatment group.

xRef

A (non-empty) numeric vector of data values from the reference treatment group.

xPla

A (non-empty) numeric vector of data values from the placebo group.

Delta

A numeric value specifying the non-inferiority or superiority margin. Is between 0 and 1 in case of non-inferiority and larger than 1 in case of superiority.

...

Other named arguments such as distribution, var_estimation. See details for more information.

Details

Additional parameters include distribution and var_estimation.
The parameter distribution is a character string and indicates whether a parameteric model should be used. If not specified retention of effect hypothesis is tested using sample means and variances. The follwing options exist: "poisson" (Poisson distribution), "negbin" (negative binomial distribution), "normal" (normal distribution), "exponential" (censored exponential). "nonparametric" (non-parametric). If the parameter distribution is not specified the effect and the variance for the test statistic are estimated by the sample means and sample variances.
The parameter var_estimation defines how the variance is estimated in the parameteric models "poisson" and "negbin". The follwing options exist: RML for the restricted maximum-likelihood estimator and ML (default) for the unrestricted maximum-likelihood estimator.

Value

A list with class "htest" containing the following components:

statistic

The value of the Wald-type test statistic.

p.value

The p-value for the Wald-type test.

method

A character string indicating what type of Wald-type-test was performed.

estimate

The estimated rates for each of the group as well as the maximum-likelihood estimator for the shape parameter.

sample.size

The total number of data points used for the Wald-type test.

References

I. Pigeot, J. Schaefer, J. Roehmel, D. Hauschke. (2008). Assessing non-inferiority of a new treatment in a three-arm clinical trial including a placebo. Statistics in Medicine. 30(6):883-99.

M. Hasler, R. Vonk, and LA. Hothorn. (2008). Assessing non-inferiority of a new treatment in a three-arm trial in the presence of heteroscedasticity. Statistics in Medicine, 27(4):490-503.

M. Mielke and A. Munk. (2009). The assessment and planning of non-inferiority trials for retention of effect hypotheses-towards a general approach. arXiv preprint arXiv:0912.4169.

T. Muetze, A. Munk, and T. Friede. (2016). Design and analysis of three-arm trials with negative binomially distributed endpoints. Statistics in Medicine, 35(4):505-521.

See Also

power_RET

Examples

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# Negative binomially distributed endpoints
# Test for non-inferiority test. lambda_P=8, lambda_R = 4, lambda_E = 5, and phi = 1
# Delta = (lambda_P-lambda_E)/(lambda_P-lambda_R)
xExp <- rnbinom(60, mu = 5, size = 1)
xRef <- rnbinom(40, mu = 4, size = 1)
xPla <- rnbinom(40, mu = 8, size = 1)
Delta <- (8-5) / (8-4)
test_RET(xExp, xRef, xPla, Delta, var_estimation = 'RML', distribution = "negbin")
test_RET(xExp, xRef, xPla, Delta, var_estimation = 'ML', distribution = "negbin")

# Poisson distributed endpoints
# Test for non-inferiority test. lambda_P=8, lambda_R = 4, lambda_E = 5
# Delta = (lambda_P-lambda_E)/(lambda_P-lambda_R)
xExp <- rpois(60, lambda = 5)
xRef <- rpois(40, lambda = 4)
xPla <- rpois(40, lambda = 8)
Delta <- (8-5) / (8-4)
test_RET(xExp, xRef, xPla, Delta, var_estimation = 'RML', distribution = "poisson")
test_RET(xExp, xRef, xPla, Delta, var_estimation = 'ML', distribution = "poisson")

# Censored exponential distributed endpoints
# Test for non-inferiority test. lambda_P=3, lambda_R = 1, lambda_E = 2
# Probability for uncensored observation: 0.9
# Delta = (lambda_P-lambda_E)/(lambda_P-lambda_R)
x_exp <- matrix(c(rexp(40, rate = 1/2), rbinom(40, size = 1, prob = 0.9)),
                 ncol = 2, byrow = FALSE)
x_ref <- matrix(c(rexp(40, rate = 1/1), rbinom(40, size = 1, prob = 0.9)),
                 ncol = 2, byrow = FALSE)
x_pla <- matrix(c(rexp(40, rate = 1/3), rbinom(40, size = 1, prob = 0.9)),
                 ncol = 2, byrow = FALSE)
Delta <- log(2/3) / log(1/3)
test_RET(xExp = x_exp,
                 xRef = x_ref,
                 xPla = x_pla,
                 Delta = Delta,
                 distribution = "exponential")

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