crsize {designsize} R Documentation

## Sample size determination for crossover study design

### Description

Determination of sample sizes for two factors of each group using one of the tests for equality, non-inferiority/superiority or equivalence

### Usage

crsize(type, delta, m, k, mur, mut, sigbr, sigbt, rho, sigwr, sigwt,
alpha, beta, r1, r2)

### Arguments

 type The three different types of tests are (1) test for equality, (2) test for non-inferiority/ superiority, (3) test for equivalence i.e. type = c("equal", "noninf.sup", "equiv") delta Non-inferiority/Superiority margin m Number of responses observed from each subject in each sequence under a fixed treatment k Ratio of the sample sizes of the two sequences mur Mean value of reference therapy mut Mean value of test therapy sigbr Between standard deviation due to the effect of reference therapy sigbt Between standard deviation due to the effect of test therapy rho Correlation between reference and test therapy sigwr Within standard deviation due to the effect of reference therapy sigwt Within standard deviation due to the effect of test therapy alpha Level of significance beta The probability of type-II error r1 Proportion of factor-1 r2 Proportion of factor-2

### Details

Consider a 2x2m replicated crossover design for comparing mean responses of a test drug and a reference drug. Under both treatments the design consists of two sequences with m subjects each.

### Value

crsize returns the required sample sizes for each sequence and their factors in a 2x2 contingency table.

### Author(s)

Atanu Bhattacharjee, Rajashree Dey ,Soutik Halder and Akash Pawar

ABdesign crt.match crt.unmatch phsize precsize

### Examples

# (a) Test for equality:

# This is a crossover design. The type = "equal" tests the equality of mean responses of
# a test drug (mut = 9) and a reference drug (mur = 8.5) and the number of responses are
# m = 4 observed from  each subject in each  sequence. k = 1 indicates the  ratio of the
# sample sizes of the two sequences are equal. The between standard deviation due to the
# effect of reference therapy is sigbr = 1.5 and that of test therapy is 1.5. The corre-
# lation between reference and test  therapy is rho = 0.7. The within standard deviation
# due to the effect of reference therapy is sigwr = 1 as well as test therapy is sigwt =
# 1. The alpha = 0.05 is level of significance and the probability of type - II error is
# beta = 0.10. The proportion  of factor - 1 and factor - 2 are taken to be r1 = 0.5 and
# r2 = 0.5 respectively.

crsize(type= "equal", delta = 0.4, m = 4, k = 1, mur = 8.5, mut = 9, sigbr = 1.5,
sigbt = 1.5, rho = 0.7, sigwr = 1, sigwt = 1, alpha = 0.05, beta = 0.10,
r1 = 0.5, r2 = 0.5)

# (b) Test for non-inferiority/superiority:

# This is a crossover design. The type = "noninf.sup", tests  whether the  difference of
# mean responses of a test drug (mut = 9) and a reference drug (mur = 8.5) being greater
# than or equal to  the marginal value delta = 0.4. The  number of  responses are m = 4,
# observed from each subject in each sequence. The value of k = 1 indicates the ratio of
# the sample sizes of the two sequences are equal. The between standard deviation due to
# the effect of  reference  therapy is sigbr = 1.5 and that of  test therapy is 1.5. The
# correlation between reference and test therapy is rho = 0.7. The within standard devi-
# ation due to  the effect of reference therapy is sigwr = 1, as well as test therapy is
# sigwt = 1. A alpha = 0.05 is the level of significance and  the probability of type-II
# error is beta = 0.10. The proportion of factor-1 (r1) and factor-2 (r2) both are taken
# to be 0.5.

crsize(type = "noninf.sup", delta = 0.4, m = 4, k = 1, mur = 8.5, mut = 9, sigbr = 1.5,
sigbt = 1.5, rho = 0.7, sigwr = 1, sigwt = 1, alpha = 0.05, beta = 0.10,
r1 = 0.5, r2 = 0.5)

#(c) Test for equivalence:

# This is a crossover design. The type = "equiv" tests whether the absolute value of the
# difference of mean responses of a test drug (mut = 9) and a reference drug (mur = 8.5)
# being  less than or equal to  the marginal value delta = 0.6. The number  of responses
# are m = 4 observed from each subject in each sequence. k = 1, indicates that the ratio
# of the sample sizes of the two sequences are equal. The between standard deviation due
# to the effect of reference therapy is sigbr = 1.5 and that of test therapy is 1.5. The
# correlation between reference and test therapy is rho = 0.7. The within standard devi-
# ation due to  the effect of reference therapy is sigwr = 1 as well as  test therapy is
# sigwt = 1. alpha = 0.05 is  the level of significance and the probability of type - II
# error is beta = 0.10. The proportion of factor-1 (r1) and factor-2 (r2) both are taken
# to be 0.5.

crsize(type = "equiv", delta = 0.6, m = 4, k = 1, mur = 8.5, mut = 9, sigbr = 1.5,
sigbt = 1.5,rho = 0.7, sigwr = 1, sigwt = 1, alpha = 0.05, beta = 0.10,
r1 = 0.5, r2 = 0.5)

[Package designsize version 0.1.0 Index]