Computation of adjusted p-values for commonly used multiple testing procedures based on univariate p-values (Bonferroni, Holm, Hommel, Hochberg, fixed-sequence and fallback procedures).
pvaladjp(rawp, weight, alpha, proc, printDecisionRules)
Vector of raw p-values.
Vector of hypothesis weights whose sum is equal to 1 (default is a vector of equal weights).
Familywise error rate (default is 0.05). Note that this argument
is not needed if the function is called to compute adjusted p-values, i.e.,
Vector of character strings containing the procedure name.
This vector should include any of the following:
Boolean indicator for printing the decision rules for
each of the procedures specified in
This function computes adjusted p-values and generates decision rules for the Bonferroni, Holm (Holm, 1979), Hommel (Hommel, 1988), Hochberg (Hochberg, 1988), fixed-sequence (Westfall and Krishen, 2001) and fallback (Wiens, 2003; Wiens and Dmitrienko, 2005) procedures.
The adjusted p-values are computed using the closure principle (Marcus, Peritz and Gabriel, 1976) in general hypothesis testing problems (equally or unequally weighted null hypotheses). The decision rules are generated only in hypothesis testing problems with equally weighted null hypotheses. For more information on the algorithms used in the function, see Dmitrienko et al. (2009, Section 2.6).
A data frame
result with columns for the raw p-values, weights, and adjusted
p-values for each of the procedures.
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.
Hochberg, Y. (1988). A sharper Bonferroni procedure for multiple significance testing.
Biometrika. 75, 800–802.
Holm, S. (1979). A simple sequentially rejective multiple test procedure.
Scandinavian Journal of Statistics. 6, 65–70.
Hommel, G. (1988). A stagewise rejective multiple test procedure based on a
modified Bonferroni test. Biometrika. 75, 383–386.
Marcus, R. Peritz, E., Gabriel, K.R. (1976). On closed testing
procedures with special reference to ordered analysis of variance.
Biometrika. 63, 655–660.
Westfall, P. H., Krishen, A. (2001). Optimally weighted, fixed
sequence, and gatekeeping multiple testing procedures. Journal of
Statistical Planning and Inference. 99, 25–40.
Wiens, B. (2003). A fixed-sequence Bonferroni procedure for
testing multiple endpoints. Pharmaceutical Statistics. 2, 211–215.
Wiens, B., Dmitrienko, A. (2005). The fallback procedure for evaluating a single family of hypotheses. Journal of Biopharmaceutical Statistics. 15, 929–942.
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# 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 # Null hypotheses of no treatment effect are equally weighted weight<-c(1/3,1/3,1/3) # 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 degrees of freedom nu<-2*(n-1) # Compute raw one-sided p-values rawp<-1-pt(stat,nu) # Compute adjusted p-values for the Bonferroni procedure pvaladjp(rawp, weight, proc="Bonferroni") # Compute adjusted p-values for the Hommel and Fallback procedures pvaladjp(rawp, weight, proc=c("Hommel", "Fallback")) # Generate decision rules for the Holm procedure # using a one-sided alpha=0.025 pvaladjp(rawp, weight, alpha=0.025, proc="Holm", printDecisionRules=TRUE)
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