multxpert (version 0.1.1)

parci: Common parametric procedures: Simultaneous confidence intervals

Description

Computation of simultaneous confidence intervals for commonly used parametric multiple testing procedures (single-step and step-down Dunnett procedures).

Usage

parci(stat, n, est, stderror, covprob, proc)

Arguments

stat

Vector of test statistics.

n

Common sample size in each treatment group.

est

Vector of point estimates.

stderror

Vector of standard errors associated with the point estimates.

covprob

Simultaneous coverage probability (default is 0.975).

proc

Vector of character strings containing the procedure name. This vector should include any of the following: "Single-step Dunnett", "Step-down Dunnett".

Value

A data frame result with columns for the test statistics, point estimates, standard errors, adjusted \(p\)-values, and lower simultaneous confidence limits for the specified procedure.

Details

This function computes lower one-sided simultaneous confidence limits for the single-step Dunnett procedure (Dunnett, 1955) and step-down Dunnett procedure (Naik, 1975; Marcus, Peritz and Gabriel, 1976) in one-sided hypothesis testing problems with a balanced one-way layout and equally weighted null hypotheses.

The simultaneous confidence intervals are computed using the methods developed in Bofinger (1987) and Stefansson, Kim and Hsu (1988). For more information on the algorithms used in the function, see Dmitrienko et al. (2009, Section 2.7).

References

Bofinger, E. (1987). Step-down procedures for comparison with a control. Australian Journal of Statistics. 29, 348--364.

Dmitrienko, A., Bretz, F., Westfall, P.H., Troendle, J., Wiens, B.L., Tamhane, A.C., Hsu, J.C. (2009). Multiple testing methodology. Multiple Testing Problems in Pharmaceutical Statistics. Dmitrienko, A., Tamhane, A.C., Bretz, F. (editors). Chapman and Hall/CRC Press, New York.

Dunnett, C.W. (1955). A multiple comparison procedure for comparing several treatments with a control. Journal of the American Statistical Association. 50, 1096--1121.

Marcus, R. Peritz, E., Gabriel, K.R. (1976). On closed testing procedures with special reference to ordered analysis of variance. Biometrika. 63, 655--660.

Naik, U.D. (1975). Some selection rules for comparing \(p\) processes with a standard. Communications in Statistics. Series A. 4, 519--535.

Stefansson, G., Kim, W.-C., Hsu, J.C. (1988). On confidence sets in multiple comparisons. Statistical Decision Theory and Related Topics IV. Gupta, S.S., Berger, J.O. (editors). Academic Press, New York, 89--104.

See Also

parci

Examples

# NOT RUN {
# Consider a clinical trial conducted to evaluate the effect of three
# doses of a treatment compared to a placebo with respect to a normally
# distributed endpoint

# Three null hypotheses of no effect are tested in the trial:
# Null hypothesis H1: No difference between Dose 1 and Placebo
# Null hypothesis H2: No difference between Dose 2 and Placebo
# Null hypothesis H3: No difference between Dose 3 and Placebo

# Treatment effect estimates (mean  dose-placebo differences)
est<-c(2.3,2.5,1.9)

# Pooled standard deviation
sd<-9.5

# Study design is balanced with 180 patients per treatment arm
n<-180

# Standard errors
stderror<-rep(sd*sqrt(2/n),3)

# T-statistics associated with the three dose-placebo tests
stat<-est/stderror

# Compute lower one-sided simultaneous confidence limits
# for the single-step Dunnett procedure
parci(stat,n,est,stderror,covprob=0.975,proc="Single-step Dunnett")

# Compute lower one-sided simultaneous confidence limits
# for the single-step and step-down Dunnett procedures
parci(stat,n,est,stderror,covprob=0.975,proc=c("Single-step Dunnett", "Step-down Dunnett"))

# }