Description Usage Arguments Details Value References See Also Examples

View source: R/waldtype_test.R

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

1 |

`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 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.

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 | ```
# 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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