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Last data update: 2014.03.03

R: Sample size determination in the context of multiple...

indiv.rm.ssc

R Documentation

Sample size determination in the context of multiple continuous endpoints with a control of the q-gFWER, for a given value of r-power (generalized disjunctive power).

Description

This function computes the sample size for an analysis of m multiple tests with a control of the q-gFWER.

Usage

indiv.rm.ssc(method, asympt = FALSE, r, m, p = m, nCovernE = 1,
muC = NULL, muE = NULL, d = NULL, delta = NULL, SigmaC = NULL,
SigmaE = NULL, power = 0.8, alpha = 0.05, interval = c(2, 2000), q = 1,
maxpts = 25000, abseps = 0.001, releps = 0, nbcores = 1, LB = FALSE,
orig.Hochberg = FALSE)

Arguments

`method`	"Bonferroni", "Hochberg" or "Holm". When `method = "Hochberg"`, we use critical values involving the D1 term in formula (11) of Romano et al. in order to control strongly the q-FWER. If you want to use the original Hochberg's procedure, set `orig.Hochberg` to `TRUE`. Even for q=1, this is a bad idea except when the p-values can be assumed independent.
`asympt`	logical. `TRUE` for the use of the asymptotic approximation by a multivariate normal distribution or `FALSE` for the multivariate Student distribution.
`r`	integer, r = 1, ..., m. Desired number of endpoints to be declared significant.
`m`	integer. Number of endpoints.
`p`	integer, p = 1, ..., m. Indicates the number of false null hypotheses.
`nCovernE`	ratio of `nC` over `nE`.
`muC`	`NULL` or a vector of length `m` of the true means of the control group for all endpoints under the alternative hypothesis. If `muC`, `muE` and `d` are `NULL`, then `delta` should be provided instead.
`muE`	`NULL` or a vector of length `m` of the true means of the experimental (test) group for all endpoints under the alternative hypothesis.
`d`	`NULL` or a a vector of length `m` indicating the true value of the differences in means under the null hypothesis.
`delta`	should be `NULL` if `muC`, `muE` and `d` are provided. If not, it is equal to `muE - muC - d` and these parameters should be set to `NULL`.
`SigmaC`	matrix giving the covariances between the `m` primary endpoints in the control group.
`SigmaE`	matrix giving the covariances between the `m` primary endpoints in the experimental (test) group.
`power`	a value which correponds to the chosen r-power.
`alpha`	a value which corresponds to the chosen q-gFWER type-I control bound.
`interval`	an interval of values in which to search for the sample size. Left endpoint should be greater than or equal to 2.
`q`	integer. Value of 'q' (q=1,...,m) in the q-gFWER of Romano et al., which is the probability to make at least `q` false rejections. The default value `q=1` corresponds to the classical FWER control.
`maxpts`	convergence parameter used in the `GenzBretz` function. A good choice is `min(25000 * 10 ^ true.complexity, .Machine$integer.max)` where `true.complexity` is computed with the `complexity` function. But note that this might considerably increase the computation time!
`abseps`	convergence parameter used in the `GenzBretz` function. A good choice is `max(0.001 / true.complexity, 1e-08)` where `true.complexity` is computed with the `complexity` function. But note that this might considerably increase the computation time!
`releps`	relative error tolerance as double used in the `GenzBretz` function.
`nbcores`	integer. Number of cores to use for parallel computations.
`LB`	logical. Should we use a load balancing parallel computation.
`orig.Hochberg`	logical. To use the standard Hochberg's procedure.

Value

The required sample size.

Note

Results can differ from one time to another because the results of the function pmvt are random. If this is the case, you should consider increasing maxpts and decreasing abseps. In any case, you should always double check using one of the functions Psirms, Psirmu or Psirmd if the sample size you obtained gives you the intended power, with an acceptable error (or at least compute the power a few times with various seeds to see if results are stable).

Author(s)

P. Lafaye de Micheaux, B. Liquet and J. Riou

References

Delorme P., Lafaye de Micheaux P., Liquet B., Riou, J. (2015). Type-II Generalized Family-Wise Error Rate Formulas with Application to Sample Size Determination. Submitted to Statistics in Medicine.

Romano J. and Shaikh A. (2006) Stepup Procedures For Control of Generalizations of the Familywise Error Rate. The Annals of Statistics, 34(4), 1850–1873.

Examples

## Not run: 
# Pneumovacs example (takes 37 mn to compute on 1 core)

# Treatment effect
delta <- c(0.55, 0.34, 0.38, 0.20, 0.70, 0.38, 0.86)

# Variances of the m endpoints
var <- c(0.3520, 0.6219, 0.5427, 0.6075, 0.6277,
0.5527, 0.8066) ^ 2

# Covariance matrix
cov <- matrix(1, ncol = 7, nrow = 7)
cov[1, 2:7] <- cov[2:7, 1] <- c(0.1341692, 0.1373891, 0.07480123,
0.1401267, 0.1280336, 0.1614103)
cov[2, 3:7] <- cov[3:7, 2] <- c(0.2874531, 0.18451960, 0.3156895,
0.2954996, 0.3963837)
cov[3, 4:7] <- cov[4:7, 3] <- c(0.19903400, 0.2736123, 0.2369907, 0.3423579)
cov[4, 5:7] <- cov[5:7, 4] <- c(0.1915028, 0.1558958, 0.2376056)
cov[5, 6:7] <- cov[6:7, 5] <- c(0.2642217, 0.3969920)
cov[6, 7] <- cov[7, 6] <- 0.3352029
diag(cov) <- var

indiv.rm.ssc(method = "Hochberg", asympt = FALSE, r = 3, m = 7, p = 7, nCovernE = 1,
muC = NULL, muE = NULL, d = NULL, delta = delta, SigmaC = cov,
SigmaE = cov, power = 0.8, alpha = 0.05, interval = c(10, 2000), q = 1)

# Pre-RELAX-AHF example from the paper by Teerlink et al. (2009),
# Relaxin for the treatment of patients with acute heart failure
# (Pre-RELAX-AHF): a multicentre, randomised,
# placebo-controlled, parallel-group, dose-finding phase IIb
# study, Lancet, 373: 1429--39

# Table 2 page 1432:
# ------------------
# Proportion with moderately or markedly better dyspnoea at 6 h, 12 h, and 24 h (Likert): 23% 40%
# Dyspnoea AUC change from baseline to day 5 (VAS [mmxh]): 1679 (2556) 2567 (2898) 
# Worsening heart failure through day 5: 21% 12%
# Length of stay (days): 12.0 (7.3) 10.2 (6.1) 
# Days alive out of hospital: 44.2 (14.2) 47.9 (10.1) 
# KM cardiovascular death or readmission (HR, 95% CI): 17.2% 2.6% (0.13, 0.02--1.03); p=0.053 
# KM cardiovascular death (HR, 95% CI):  14.3% 0.0% (0.00, 0.00--0.98); p=0.046 

# Table 4 page 1436:
# ------------------
# >=25% increase at day 5: 8 (13%) 9 (21%) 
# >=26 micro-mol/L increase at days 5 and 14: 4 (7%)  3 (7%) 
muC <- c(23 / 100, 1679, 1 - 21 / 100, -12.0, 44.2, 1 - 17.2 / 100, 1 -
          14.3 / 100, 13 / 100, 7 / 100)
muE <- c(40 / 100, 2567, 1 - 12 / 100, -10.2, 47.9, 1 - 2.60 / 100, 1,
         21 / 100, 7 / 100)

sdC <- c(sqrt(0.23 * (1 - 0.23)), 2556, sqrt(0.79 * (1 - 0.79)), 7.3,
 14.2, sqrt(0.828 * (1 - 0.828)), sqrt(0.857 * (1 - 0.857)), sqrt(0.13 *
 (1 - 0.13)), sqrt(0.07 * (1 - 0.07)))
sdE <- c(sqrt(0.4 * (1 - 0.4))  , 2898, sqrt(0.88 * (1 - 0.88)), 6.1,
 10.1, sqrt(0.974 * (1 - 0.974)), 1e-12                    , sqrt(0.21 * (1 - 0.21)), 
 sqrt(0.07 * (1 - 0.07)))

m <- 9
rho <- 0.1
cor <- matrix(rho, nrow = m, ncol = m)
diag(cor) <- 1
sd.pooled <- sqrt(0.5 * sdE + 0.5 * sdC)
SigmaE <- diag(sdE) %*% cor %*% diag(sdE)
SigmaC <-diag(sdC) %*% cor %*% diag(sdC)
indiv.rm.ssc(method = "Bonferroni", asympt = FALSE, r = 6, m = 9, p = 9, nCovernE = 1,
  muC = NULL, muE = NULL, d = rep(0.0, m), delta = (muE - muC) / sd.pooled,
  SigmaC = cor, SigmaE = cor, power = 0.8, alpha = 0.1, interval = c(2, 500),
  q = 1, maxpts = 25000, abseps = 0.01, nbcores = 1, LB = TRUE)


## End(Not run)