prsize {designsize}

Sample size determination for parallel study design.

Description

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

Usage

prsize(type, mu1, mu2, s, alpha, beta, k, r1, r2, del)

Arguments

type

There are three types of test, (1) test of equality, (2) test for non-inferiority/superiority,

mu1

The mean value of 1st group

mu2

The mean value of 2nd group

s

The common standard deviation

alpha

The level of significance

beta

The probability of the type II error i.e. 1 - power

k

The ratio of 1st sample size(n1) and 2nd sample size(n2) i.e k=n1/n2

r1

The ratio of n1fac1 (sample size of the 1st factor for 1st group) and n1 i.e r1=n1fac1/n1

r2

The ratio of n2fac2 (sample size of the 1st factor for 2nd group) and n2 i.e r2=n2fac1/n2

del

The superiority or non-inferiority margin

Details

Parallel arm design is the most commonly used study design where subjects are randomized to one or more study arms. Each study arm will be allocated a different intervention. After randomization each subject will stay in their assigned arm during the whole study. The randomized subjects should not inadvertently contaminate with the other group. A major characteristic of a parallel study is randomization, which ensures accuracy of the results and lower risk of being biased.

Value

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

Author(s)

Atanu Bhattacharjee, Rajashree Dey ,Soutik Halder and Akash Pawar

See Also

ABdesign crt.match crt.unmatch phsize precsize crsize

Examples

# (a) Test for equality:

# This is a parallel study design. The type = "equal" tests the equality of mean respon-
# ses of a test drug (mu1 = 12) and a reference drug (mur = 8). The common standard dev-
# iation of the drugs is s = 5. k = 2 indicates the ratio of the sample sizes of the two
# groups. alpha = 0.05 is the 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 = 0.6 and
# r2 = 0.6 respectively.


 prsize(type="equal", mu1=12, mu2=8, s=5, alpha=0.05, beta=0.10, k=2, r1=0.6, r2=0.6)


 # (b) Test for superiority/noninferiority:

# This is a Parallel design. The type = "noninf.sup" test whether the difference of mean
# responses  of a test drug (mu1 = 12) and a reference drug (mu2 = 8) being greater than
# or equal to the marginal value delta = 0.8. s = 5 is the  common standard deviation of
# the drugs. The value k = 2 indicates the ratio of the  sample sizes of the two groups.
# alpha = 0.05 is the 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 = 0.6 and r2 = 0.6
# respectively.


 prsize(type="noninf.sup", mu1=12, mu2=8, s=5, alpha=0.05, beta=0.10, k=2, r1=0.6,
        r2=0.6, del=0.8)


# (c) Test for equivalence:

# This is a Parallel design. The type = "equiv" tests  whether the absolute value of the
#  difference of mean responses of a test drug (mu1 = 12) and a reference drug (mu2 = 8)
# being less  than or equal to the  marginal value delta = 0.8. The  number of responses
# are m = 4 observed from each subject in each sequence.The s = 5 is the common standard
# deviation of the drugs. The value k = 2 indicates the ratio of the sample sizes of the
# two groups. The 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 equal to 0.6.


 prsize(type="equiv", mu1=12, mu2=8, s=5, alpha=0.05, beta=0.10, k=2, r1=0.6,
        r2=0.6, del=0.8)