test_RET | R Documentation |
Wald-type test for superiority/non-inferiority of the experimental treatment versus reference treatment with respect to placebo.
test_RET(xExp, xRef, xPla, Delta, ...)
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 |
Additional parameters include distribution
and var_estimation
.
The parameter distribution
is a character string and indicates
whether a parametric model should be used. If not specified retention of
effect hypothesis is tested using sample means and variances.
The following 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 parametric models "poisson"
and "negbin"
.
The following options exist:
RML
for the restricted maximum-likelihood estimator
and ML
(default) for the unrestricted maximum-likelihood estimator.
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. |
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.
power_RET
# 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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