indiv.rm.ssc: 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.

integer, r = 1, ..., m. Desired number of endpoints to be declared significant.

integer. Number of endpoints.

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.

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.

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.

logical. Should we use a load balancing parallel computation.

orig.Hochberg

logical. To use the standard Hochberg's procedure.

Value

The required sample size.

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

Run this code

# 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)

# }