Sample Size calculation in Clinical Research

Description

More than 80 functions in this package are widely used to calculate sample size in clinical trial research studies.

This package covers the functions in Chapter 3,4,6,7,9,10,11,12,14,15 of the reference book.

Details

Author(s)

author: Ed Zhang <ed.zhang.jr@gmail.com>

Vicky Qian Wu <wuqian7@gmail.com>

Harry G. Zhang (Quality check)

Shein-Chung Chow

maintainer: Vicky Qian Wu <wuqian7@gmail.com>

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2008

A + B Escalation Design with Dose De-escalation

Description

The general A+B designs with dose de-escalation. There are A patients at dose level i.

(1) If less than C/A patients have dose limiting toxicity (DLTs), then the dose is escalated to the next dose level i+1.

(2)If more than D/A (D \ge C) patients have DLTs, then it will come back to dose i-1.If more than A patients have already been treated at dose level i-1, it will stop here and dose i-1 is the MTD. If there are only A patients treated at dose i-1, then Bmore patients are treated at this dose level i-1. This is dose de-escalation. The de-escalation may continue to the next dose level i-2 and so on if necessary.

(3)If no less than C/A but no more than D/A patients have DLTs, B more patients are treated at this dose level i.

(4)If no more than E (where E \ge D) of the total A+B patients have DLT, then the dose is escalated.

(5)If more than E of the total of A+B patients have DLT, and the similar procedure in (2) will be applied.

Usage

AB.withDescalation(A, B, C, D, E, DLT)

Arguments

Note

For this design, the MTD is the dose level at which no more than E/(A+B) patients experience DLTs, and more than D/A or (no less than C/A and no more than D/A) if more than E/(A+B) patients treated with the next higher dose have DLTs.

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

DLT=c(0.01,0.014,0.025,0.056,0.177,0.594,0.963)
Example.11.6.2<-AB.withDescalation(A=3,B=3,C=1,D=1,E=1,DLT=DLT)
Example.11.6.2
# Example.11.6.2[7]=0.2 

A + B Escalation Design without Dose De-escalation

Description

The general A+B designs without dose de-escalation. There are A patients at dose level i.

(1) If less than C/A patients have dose limiting toxicity (DLTs), then the dose is escalated to the next dose level i+1.

(2)If more than D/A (D \ge C) patients have DLTs, then the previous dose i-1 will be considered the maximum tolerable dose (MTD).

(3)If no less than C/A but no more than D/A patients have DLTs, B more patients are treated at this dose level i.

(4)If no more than E (where E \ge D) of the total A+B patients have DLT, then the dose is escalated.

(5)If more than E of the total of A+B patients have DLT, then the previous dose i-1 will be considered the MTD.

Usage

AB.withoutDescalation(A, B, C, D, E, DLT)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

DLT=c(0.01,0.014,0.025,0.056,0.177,0.594,0.963)
Example.11.6.1<-AB.withoutDescalation(A=3,B=3,C=1,D=1,E=1,DLT=DLT)
Example.11.6.1
# Example.11.6.1[1]=3.1

Average Bioequivalence

Description

The most commonly used design for ABE is a standard two-sequence and two-period crossover design. Ft is the fixed effect of the test formulation and Fr is the fixed effect of the reference formulation.

Ho: Ft-Fr \le \delta_{L} or Ft-Fr \le \delta_{U}

Ha: \delta_{L} < Ft-Fr < \delta_{U}

Usage

ABE(alpha, beta, sigma1.1, delta, epsilon)

Arguments

Value

\sigma_{a.b}^{2}=\sigma_{D}^{2}+a*\sigma_{WT}^{2}+b*\sigma_{WR}^{2}

.

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.10.2<-ABE(0.05,0.2,0.4,0.223,0.05)
Example.10.2
# 21

ANOVA with Repeat Measures

Description

The study has multiple assessments in a parallel-group clinical trial. \alpha_i is the fixed effect for the ith treatment \sum \alpha_i =0.

Ho: \alpha_{i} = \alpha_{i'}

Ha: not equal

Usage

ANOVA.Repeat.Measure(alpha, beta, sigma, delta, m)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.15.3.4<-ANOVA.Repeat.Measure(0.05,0.2,1.25,1.5,3)
Example.15.3.4
# 15

Test the Carry-over effect

Description

2 by 2 crossover design. Test the treatment-by-period interaction (carry-over effect)

H0: the difference of the two sequence carry-over effects is equal to 0

Ha: not equal to 0

The test is finding whether there is a difference between the carry-over effect for sequence AB and BA.

Usage

Carry.Over(alpha, beta, sigma1, sigma2, gamma)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.6.5.2<-Carry.Over(0.025,0.2,2.3,2.4,0.89)
Example.6.5.2 # 110

Cochran-Armitage's Test for Trend

Description

H0: p0=p1=p2=...=pK

Ha: p0 <= p1 <= p2 <=...<= pK with p0 < pK

Usage

Cochran.Armitage.Trend(alpha, beta, pi, di, ni, delta)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

pi=c(0.1,0.3,0.5,0.7);
di=c(1,2,3,4);
ni=c(10,10,10,10);

Example.11.5<-Cochran.Armitage.Trend(alpha=0.05,beta=0.2,pi=pi,di=di,ni=ni,delta=1)
Example.11.5
# 7.5 for one group. Total 28-32. 

Test for equality in Cox PH model.

Description

b is the log hazard ratio for treatment, b0 is the log hazard ratio for the controls

H0: b=b0

Ha: not equal to b0

The test is finding whether there is a difference between the hazard rates of the treatment and control.

Usage

Cox.Equality(alpha, beta, loghr, p1,d)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.7.3.4<-Cox.Equality(0.05,0.2,log(2),0.5,0.8)
Example.7.3.4

Test for Equivalence in Cox PH model.

Description

b is the log hazard ratio for treatment, delta is the margin

Ho: |b| \ge \delta

Ha: |b| < \delta

Usage

Cox.Equivalence(alpha, beta, loghr, p1, d, delta)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.7.3.4<-Cox.Equivalence(0.05,0.2,log(2),0.5,0.8,0.5)
Example.7.3.4

Test for non-inferiority/superiority in Cox PH model.

Description

b is the log hazard ratio for treatment, \delta is the margin

H0: b \le \delta

Ha: b > \delta

Usage

Cox.NIS(alpha, beta, loghr, p1, d, delta)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.7.3.4<-Cox.NIS(0.05,0.2,log(2),0.5,0.8,0.5)
Example.7.3.4

Test for Equality of Intra-Subject Variabilities in Crossover Design

Description

H0: within-subject variance of treatment T is equal to within-subject variance of treatment R

Ha: not equal

The test is finding whether two drug products have the same intra-subject variability in crossover design

Usage

CrossOver.ISV.Equality(alpha, beta, sigma1, sigma2, m)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Test for Similarity of Intra-Subject Variabilities in Crossover Design

Description

the ratio = within-subject variance of treatment T / within-subject variance of treatment R

H0: the ratio \ge \delta or the ratio \le \frac{1}{\delta}

Ha: \frac{1}{\delta} < the ratio < \delta

Usage

CrossOver.ISV.Equivalence(alpha, beta, sigma1, sigma2, m, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Test for Non-Inferiority/Superiority of Intra-Subject Variabilitie in Crossover Design

Description

H0: the ratio that within-subject variance of treatment T / within-subject variance of treatment R \ge \delta

Ha: the ratio < \delta

if \delta < 1, the rejection of Null Hypothesis indicates the superiority of the test drug over the reference for the intra-subject variability;

if \delta > 1, the rejection of the null hypothesis implies the non-inferiority of the test drug against the reference for the intra-subject variability; .

Usage

CrossOver.ISV.NIS(alpha, beta, sigma1, sigma2, m, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.9.1.1<-CrossOver.ISV.NIS(0.05,0.2,0.3^2,0.45^2,2,1.1)
Example.9.1.1

Williams' Test for Minimum effective dose (MED)

Description

Ho: \mu_1=\mu_2=...=\mu_K Ha: \mu_1=\mu_2=...=\mu_{i-1} < \mu_{i} < \mu_{i+1} < \mu_{K}

Usage

Dose.Min.Effect(alpha, beta, qt, sigma, delta)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.11.4.1<-Dose.Min.Effect(0.05,0.2,1.75,0.22,0.11)
Example.11.4.1
#54

Linear Contrast Test for Dose Response Study

Description

For a multi-arm dose response design, we use a linear contrast coefficients ci with \sum ci = 0.

H0: L(mu)=\sum ci \times \mu_i = 0

Ha: L(mu)=\sum ci \times \mu_i = \epsilon, not equal to 0

Usage

Dose.Response.Linear(alpha, beta, sigma, mui, ci, fi)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

mui=c(0.05,0.12,0.14,0.16);
ci=c(-6,1,2,3);

Example.11.1<-Dose.Response.Linear(alpha=0.05,beta=0.2,sigma=0.22,mui=mui,ci=ci,fi=1/4)
Example.11.1
#178

Linear Contrast Test for Binary Dose Response Study

Description

pi is the proportion of response in the ith group.

Ho: p1=p2=...=pk

Ha: L(p)= \sum ci \times pi = \epsilon, not equal to 0

Usage

Dose.Response.binary(alpha, beta, pi, ci, fi)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

pi=c(0.05,0.12,0.14,0.16);
ci=c(-6,1,2,3);

Example.11.2<-Dose.Response.binary(alpha=0.05,beta=0.2,pi=pi,ci=ci,fi=1/4)
Example.11.2
#382

Linear Contrast Test for Time-to-Event Endpoint in dose response study

Description

Under the exponential survival model, let lambdai be the proportion hazard rate for group i.

\sum ci = 0.

Ho: L(\mu) = \sum ci \times \lambda_i =0

Ha: L(p) = \sum ci \times \lambda_i = \epsilon > 0

Usage

Dose.Response.time.to.event(alpha, beta, T0, T, Ti, ci, fi)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Ti=c(14,20,22,24);
ci=c(-6,1,2,3);

Example.11.3.1<-Dose.Response.time.to.event(alpha=0.05,beta=0.2,T0=9,T=16,Ti=Ti,ci=ci,fi=1/4)
Example.11.3.1
#412

fi1=c(1/9,2/9,2/9,2/9);
Example.11.3.2<-Dose.Response.time.to.event(alpha=0.05,beta=0.2,T0=9,T=16,Ti=Ti,ci=ci,fi=fi1)
Example.11.3.2
#814

fi2=c(1/2.919,0.711/2.919,0.634/2.919,0.574/2.919);
Example.11.3.3<-Dose.Response.time.to.event(alpha=0.05,beta=0.2,T0=9,T=16,Ti=Ti,ci=ci,fi=fi2)
Example.11.3.3
#349

Individual Bioequivalence

Description

Consider 2 by 2 crossover design. \gamma=\delta^2+\sigma_D^2+\sigma_{WT}^2-\sigma_{WR}^2-\theta_{IBE}*max(\sigma_{0}^2,\sigma_{WR}^2)

Ho: \gamma \ge 0

Ha: \gamma < 0

Usage

IBE(alpha, beta, delta, sigmaD, sigmaWT, sigmaWR, a, b, thetaIBE)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.10.4<-IBE(0.05, 0.2, 0, 0.2,0.3,0.3,0.5,0.5,2.5)
Example.10.4

# n=22 IBE reach 0 

Test for Equality of Intra-Subject CVs

Description

H0: CVr = CVt

Ha: not equal

The test is finding whether two drug products have the same intra-subject CVs

Usage

ISCV.Equality(alpha, beta, CVt, CVr, m)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Test for Equivalence of Intra-Subject CVs

Description

H0: |CVr - CVt| \ge \delta

Ha: |CVr - CVt| < \delta

Usage

ISCV.Equivalence(alpha, beta, CVt, CVr, m, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Test for Non-Inferiority/Superiority of Intra-Subject CVs

Description

H0: CVr - CVt < \delta

Ha: CVr - CVt \ge \delta

if \delta > 0, the rejection of Null Hypothesis indicates the superiority of the test drug over the reference;

if \delta < 0, the rejection of the null hypothesis implies the non-inferiority of the test drug against the reference.

Usage

ISCV.NIS(alpha, beta, CVt, CVr, m, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.9.2.1<-ISCV.NIS(0.05,0.2,0.7,0.5,2,0.1)
Example.9.2.1

Test for Equality of Intra-Subject Variabilities

Description

H0: within-subject variance of treatment T is equal to within-subject variance of treatment R

Ha: not equal

The test is finding whether two drug products have the same intra-subject variability.

Usage

ISV.Equality(alpha, beta, sigma1, sigma2, m)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Test for Similarity of Intra-Subject Variabilities

Description

the ratio = within-subject variance of treatment T / within-subject variance of treatment R

Ho: the ratio \ge \delta or the ratio \le \frac{1}{\delta}

Ha: \le \frac{1}{\delta} < the ratio < \delta

Usage

ISV.Equivalence(alpha, beta, sigma1, sigma2, m, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Test for Non-Inferiority/Superiority of Intra-Subject Variabilities

Description

the ratio = within-subject variance of treatment T / within-subject variance of treatment R

H0: the ratio \ge \delta

Ha: the ratio < \delta

if \delta < 1, the rejection of Null Hypothesis indicates the superiority of the test drug over the reference for the intra-subject variability;

if \delta > 1, the rejection of the null hypothesis implies the non-inferiority of the test drug against the reference for the intra-subject variability; .

Usage

ISV.NIS(alpha, beta, sigma1, sigma2, m, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.9.1.1<-ISV.NIS(0.05,0.2,0.3^2,0.45^2,3,1.1)
Example.9.1.1

Test for Equality of Inter-Subject Variabilities

Description

H0: between-subject variance of treatment T is equal to between-subject variance of treatment R

Ha: not equal

The test is finding whether two drug products have the same inter-subject variability.

Usage

InterSV.Equality(alpha, beta, vbt, vwt, vbr, vwr, m)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Test for Equality of Inter-Subject Variabilities

Description

H0: between-subject variance of treatment T is equal to between-subject variance of treatment R

Ha: not equal

The test is finding whether two drug products have the same inter-subject variability.

Usage

InterSV.NIS(alpha, beta, vbt, vwt, vbr, vwr, m,margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

McNemar Test in 2 by 2 table

Description

2 by 2 table. Test either a shift from 0 to 1 or a shift from 1 to 0 before treatment and after treatment.

p_{1+}=P_{10}+P_{11}, p_{+1}=P_{01}+P_{11}

Ho: p_{1+} = p_{+1}

Ha: not equal

The test is finding whether there is a categorical shift after treatment.

Usage

McNemar.Test(alpha, beta, psai, paid)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.6.4.3<-McNemar.Test(0.05,0.2,0.2/0.5,.7)
Example.6.4.3
# 59

Test for Equality in Multiple-Sample William Design

Description

Compare more than two treatment under a crossover design.

H0: margin is equal to 0 Ha: margin is not equal to 0

The test is finding whether there is a difference between treatment i and treatment j

Usage

MeanWilliamsDesign.Equality(alpha, beta, sigma, k, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.3.5.4<-MeanWilliamsDesign.Equality(0.025,0.2,0.1,6,0.05)
Example.3.5.4 # 6
Example.3.5.4<-MeanWilliamsDesign.Equality(0.025,0.2,0.1,6,-0.05)
Example.3.5.4 # 6
Example.3.5.4<-MeanWilliamsDesign.Equality(0.025,0.2,0.1,6,-0.1)
Example.3.5.4 # 2

Test for Equivalence in Multiple-Sample William Design

Description

Compare more than two treatment under a crossover design.

H0: |margin| \ge \delta Ha: |margin| < \delta

This test is whether the test drug is equivalent to the control in average if the null hypothesis is rejected at significant level alpha

Usage

MeanWilliamsDesign.Equivalence(alpha, beta, sigma, k, delta, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Test for Non-Inferiority/Superiority in Multiple-Sample William Design

Description

Compare more than two treatment under a crossover design.

H0: margin \le \delta Ha: margin > \delta

if \delta >0, the rejection of Null Hypothesis indicates the superiority of the test over the control;

if \delta <0, the rejection of the null hypothesis implies the non-inferiority of the test against the control.

Usage

MeanWilliamsDesign.NIS(alpha, beta, sigma, k, delta, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Multiple Testing procedures

Description

Ho: \mu_{1j}-\mu_{2j} = 0

Ha: \mu_{1j}-\mu_{2j} > 0

Usage

Multiple.Testing(s1, s2, m, p, D, delta, BCS, pho, K, alpha, beta)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Test for independence for nonparametric study

Description

Ho: P(x \le a ~and~ y \le b) = P( x \le a ) P(y \le b) for all a and b. Ha: not equal

Usage

Nonpara.Independ(alpha, beta, p1, p2)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.14.4<-Nonpara.Independ(0.05,0.2,0.6,0.7)
Example.14.4
# 135

One Sample Location problem in Nonparametric

Description

Ho: theta=0

Ha: theta is not equal to 0.

Usage

Nonpara.One.Sample(alpha, beta, p2, p3, p4)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.14.2<-Nonpara.One.Sample(0.05,0.2,0.3,0.4,0.05)
Example.14.2
# 383

Two sample location problem for Nonparametric

Description

Ho: theta=0;

Ha: theta is not equal to 0.

Usage

Nonpara.Two.Sample(alpha, beta, k, p1, p2, p3)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.14.3<-Nonpara.Two.Sample(0.05,0.2,1,0.7,0.8,0.8)
Example.14.3
#54

One Sample Mean Test for Equality

Description

H0: margin is equal to 0 Ha: margin is not equal to 0

The test is finding whether there is a difference between the mean response of the test \bar{x} and the reference value \mu_0

Usage

OneSampleMean.Equality(alpha, beta, sigma, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

OneSampleMean.Equality(0.05,0.2,1,0.5)
# 32

One Sample Mean Test for Equivalence

Description

Ho: |margin| \ge delta Ha: |margin| < delta

The test is concluded to be equivalent to a gold standard on average if the null hypothesis is rejected at significance level alpha

Usage

OneSampleMean.Equivalence(alpha, beta, sigma,margin, delta)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

OneSampleMean.Equivalence(0.05,0.2,0.1,0.05,0) 
# 35

One Sample Mean Test for Non-Inferiority/Superiority

Description

Ho: margin \le delta Ha: margin > delta

if delta >0, the rejection of Null Hypothesis indicates the true mean is superior over the reference value mu0;

if delta <0, the rejection of the null hypothesis implies the true mean is non-inferior against the reference value mu0.

Usage

OneSampleMean.NIS(alpha, beta, sigma, margin, delta)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

OneSampleMean.NIS(0.05,0.2,1,0.5,-0.5)
# 7

One sample proportion test for equality

Description

Ho: p=p0

Ha: not equal

The test is finding whether there is a difference between the true rate of the test drug and reference value p0

Usage

OneSampleProportion.Equality(alpha, beta, p, differ)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.4.1.4<-OneSampleProportion.Equality(0.05,0.2,0.5,0.2)
Example.4.1.4

One sample proportion test for equivalence

Description

Ho: |p-p0| \ge margin

Ha: |p-p0| < margin

The proportion of response is equivalent to the reference p0 is the null hypothesis is rejected

Usage

OneSampleProportion.Equivalence(alpha, beta, p, delta, differ)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.4.1.4<-OneSampleProportion.Equivalence(0.05,0.2,0.6,0.05,.2)
Example.4.1.4

One sample proportion test for Non-inferiority/Superiority

Description

Ho: p-p0 \le margin

Ha: p-p0 > margin

if margin >0, the rejection of Null Hypothesis indicates the true rate is superior over the reference value p0;

if margin <0, the rejection of the null hypothesis implies the true rate is non-inferior against the reference value p0.

Usage

OneSampleProportion.NIS(alpha, beta, p, delta, differ)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.4.1.4<-OneSampleProportion.NIS(0.025,0.2,0.5,0.2,-0.1)
Example.4.1.4

One-Sided Tests with fixed effect sizes

Description

One-sided tests

Ho: \delta_j = 0

Ha: \delta_j > 0

Usage

OneSide.fixEffect(m, m1, delta, a1, r1, fdr)

Arguments

Details

alpha_star=r1*fdr/((m-m1)*(1-fdr)), which is the marginal type I error level for r1 true rejection with the FDR controlled at f.

beta_star=1-r1/m1, which is equal to 1-power.

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.12.2.1<-OneSide.fixEffect(m=4000,m1=40,delta=1,a1=0.5,r1=24,fdr=0.01)
Example.12.2.1
# n=68; n1=34=n2

One-Sided Tests with varying effect sizes

Description

One-sided tests

Ho: \delta_j = 0

Ha: \delta_j > 0

Usage

OneSide.varyEffect(s1, s2, m, m1, delta, a1, r1, fdr)

Arguments

Details

alpha_star=r1*fdr/((m-m1)*(1-fdr)), which is the marginal type I error level for r1 true rejection with the FDR controlled at f.

beta_star=1-r1/m1, which is equal to 1-power.

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

delta=c(rep(1,40/2),rep(1/2,40/2));

Example.12.2.2 <- OneSide.varyEffect(100,150,4000,40,delta,0.5,24,0.01)
Example.12.2.2
# n=148 s1<n<s2, h(s1)<0,h(s2)<0

One-way ANOVA pairwise comparison

Description

Ho: p_i=p_j Ha: not all equal

Usage

OneWayANOVA.PairwiseComparison(alpha, beta, tau, p1, p2, delta)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.4.4.2<-OneWayANOVA.PairwiseComparison(0.05,0.2,2,0.2,0.4,-0.2)
Example.4.4.2

Example.4.4.2<-OneWayANOVA.PairwiseComparison(0.05,0.2,2,0.2,0.5,-0.3)
Example.4.4.2

Pairwise Comparison for Multiple-Sample One-Way ANOVA

Description

Ho: \mu_i is equal to \mu_j Ha: \mu_i is not equal to \mu_j

The test is comparing the means among treatments. There are tau pair comparisons of interested. Adjusted the multiple comparison by Bonferroni method,

Usage

OneWayANOVA.pairwise(alpha, beta, tau, sigma, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Population Bioequivalence

Description

Consider 2 by 2 crossover design.

H0: lamda >= 0

Ha: lamda < 0

Usage

PBE(alpha, beta, sigma1.1, sigmatt, sigmatr, sigmabt, sigmabr, rho, a, delta, lamda)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.10.3<-PBE(0.05,0.2,0.2,sqrt(0.17),sqrt(0.17),0.4,0.4,0.75,1.74,0.00,-0.2966)
Example.10.3
# 12

Propensity Score ignoring strata

Description

Combining data across J strata. Still use weighted Mantel_Haenszel test.

Ho: p_{j1}=p_{j2},

Ha: p_{j2} q_{j1}/(p_{j1} q_{j2})=phi, which is not equal to 1

Usage

Propensity.Score.nostrata(alpha, beta, J, a, b, p1, phi)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

a=c(0.15,0.15,0.2,0.25,0.25);
b=c(0.4,0.4,0.5,0.6,0.6);
p1=c(0.5,0.6,0.7,0.8,0.9);

Example.15.2.3.2<-Propensity.Score.nostrata(alpha=0.05,beta=0.2,J=5,a,b,p1,phi=2)
Example.15.2.3.2
# 1151

Propensity Score with Stratas

Description

Using weighted Mantel_Haenszel test in propensity analysis with stratas.

Ho: p_{j1}=p_{j2},

Ha: p_{j2} q_{j1}/(p_{j1} q_{j2})=phi, which is not equal to 1

Usage

Propensity.Score.strata(alpha, beta, J, a, b, p1, phi)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

a=c(0.15,0.15,0.2,0.25,0.25);
b=c(0.4,0.4,0.5,0.6,0.6);
p1=c(0.5,0.6,0.7,0.8,0.9);

Example.15.2.3.1<-Propensity.Score.strata(alpha=0.05,beta=0.2,J=5,a,b,p1,phi=2)
Example.15.2.3.1
# 447

Quality of life

Description

Under the time series model, determine sample size based on normal approximation.

Usage

QOL(alpha, beta, c, epsilon)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.15.4.3<-QOL(0.05,0.1,0.5,0.25)
Example.15.4.3

Crossover Design in QT/QTc Studies with PK response as covariate

Description

Ho: \mu_1 -\mu_2 = 0

Ha: \mu_1 -\mu_2 = d

The test is finding the treatment difference in QT interval for crossover design. d is not equal to 0, which is the difference of clinically importance.

Usage

QT.PK.crossover(alpha, beta, pho, K, delta, gamma, v1, v2, tau1, tau2)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.15.1.4.2<-QT.PK.crossover(0.05,0.2,0.8,3,0.5,0.002,1,1,4,5)
Example.15.1.4.2
# 29

Parallel Group Design in QT/QTc Studies with PK response as covariate

Description

Ho: \mu_1 -\mu_2 = 0

Ha: \mu_1 -\mu_2 = d

The test is finding the treatment difference in QT interval. d is not equal to 0, which is the difference of clinically importance.

Usage

QT.PK.parallel(alpha, beta, pho, K, delta, v1, v2, tau1, tau2)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.15.1.4.1<-QT.PK.parallel(0.05,0.2,0.8,3,0.5,1,1,4,5)
Example.15.1.4.1
# 54

Crossover Design in QT/QTc Studies without covariates

Description

Ho: \mu_1 -\mu_2 = 0

Ha: \mu_1 -\mu_2 = d

The test is finding the treatment difference in QT interval for crossover design . d is not equal to 0, which is the difference of clinically importance.

Usage

QT.crossover(alpha, beta, pho, K, delta, gamma)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.15.1.3<-QT.crossover(0.05,0.2,0.8,3,0.5,0.002)
Example.15.1.3
# 29

Parallel Group Design in QT/QTc Studies without covariates

Description

Ho: \mu_1 -\mu_2 = 0

Ha: \mu_1 -\mu_2 = d

The test is finding the treatment difference in QT interval. d is not equal to 0, which is the difference of clinically importance.

Usage

QT.parallel(alpha, beta, pho, K, delta)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.15.1.2<-QT.parallel(0.05,0.2,0.8,3,0.5)
Example.15.1.2
# 54

Relative Risk in Parallel Design test for Equality

Description

Ho: OR=1

Ha: not equal to 1

Usage

RelativeRisk.Equality(alpha, beta, or, k, pt, pc)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.4.6.4<-RelativeRisk.Equality(0.05,0.2,2,1,0.4,0.25)
Example.4.6.4

Relative Risk in Parallel Design test for Equivalence

Description

Ho: |log(OR)| \ge margin

Ha: |log(OR)| < margin

Usage

RelativeRisk.Equivalence(alpha, beta, or, k, pt, pc, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.4.6.4<-RelativeRisk.Equivalence(0.05,0.2,2,1,0.25,0.25,.5)
Example.4.6.4

Relative Risk in Parallel Design test for Non-inferiority/Superiority

Description

Ho: OR \le margin

Ha: OR > margin

Usage

RelativeRisk.NIS(alpha, beta, or, k, pt, pc, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.4.6.4<-RelativeRisk.NIS(0.05,0.2,2,1,0.4,0.25,.2)
Example.4.6.4

Relative Risk in Crossover Design test for Equality

Description

Ho: log(OR)=0

Ha: not equal to 0

Usage

RelativeRiskCrossOver.Equality(alpha, beta, sigma, or)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Relative Risk in Crossover Design test for Equivalence

Description

Ho: |log(OR)| \ge margin

Ha: |log(OR)| < margin

Usage

RelativeRiskCrossOver.Equivalence(alpha, beta, sigma, or, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Relative Risk in Crossover Design test for Non-inferiority/Superiority

Description

Ho: log(OR) \le margin

Ha: log(OR) > margin

Usage

RelativeRiskCrossOver.NIS(alpha, beta, sigma, or, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Calculate the power for Sensitivity Index

Description

Ho: \mu_1 = \mu_2

Ha: \mu_1 is not equal to \mu_2

The test is finding the treatment difference in QT interval.

d is not equal to 0, which is the difference of clinically importance.

Usage

Sensitivity.Index(alpha, n, deltaT)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.15.5.1<-Sensitivity.Index(0.05,30,2.92)
Example.15.5.1
# power=0.805

Stuart-Maxwell Test

Description

Extention from McNemar test to r by r table (r>2).

Ho: p_{ij} = p_{ji} for all different i,j.

Ha: not equal

The test is finding whether there is a categorical shift from i pre-treatment to j post-treatment.

Usage

Stuart.Maxwell.Test(noncen, p.ij, p.ji, r)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Two Sample Crossover Design Test for Equality

Description

Ho: margin is equal to 0 Ha: margin is unequal to 0

The test is finding whether there is a difference between the mean responses of the test group and control group.

Usage

TwoSampleCrossOver.Equality(alpha, beta, sigma, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Two Sample Crossover Design Test for Equivalence

Description

Ho: |margin| \ge delta Ha: |margin| < delta

This test is whether the test drug is equivalent to the control in average if the null hypothesis is rejected at significant level alpha

Usage

TwoSampleCrossOver.Equivalence(alpha, beta, sigma, delta, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.3.3.4<-TwoSampleCrossOver.Equivalence(0.05,0.1,0.2,0.25,-0.1)
Example.3.3.4 # 8

Two Sample Crossover Design Test for Non-Inferiority/Superiority

Description

Ho: |margin| \ge delta Ha: |margin| < delta

if delta >0, the rejection of Null Hypothesis indicates the superiority of the test over the control;

if delta <0, the rejection of the null hypothesis implies the non-inferiority of the test against the control.

Usage

TwoSampleCrossOver.NIS(alpha, beta, sigma, delta, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.3.3.4<-TwoSampleCrossOver.NIS(0.05,0.2,0.2,-0.2,-0.1)
Example.3.3.4 # 13

Two Sample Mean Test for Equality

Description

H0: margin is equal to 0 Ha: margin is unequal to 0

The test is finding whether there is a difference between the mean responses of the test group and control group.

Usage

TwoSampleMean.Equality(alpha, beta, sigma, k, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.3.2.4<-TwoSampleMean.Equality(0.05,0.2,0.1,1,0.05)
Example.3.2.4 # 63

Two Sample Mean Test for Equivalence

Description

Ho: |margin| \ge delta Ha: |margin| < delta

This test is whether the test drug is equivalent to the control in average if the null hypothesis is rejected at significant level alpha

Usage

TwoSampleMean.Equivalence(alpha, beta, sigma, k, delta, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.3.2.4<-TwoSampleMean.Equivalence(0.1,0.1,0.1,1,0.05,0.01)
Example.3.2.4 #107

Two Sample Mean Test for Non-Inferiority/Superiority

Description

Ho: margin \le delta Ha: margin > delta

if delta >0, the rejection of Null Hypothesis indicates the superiority of the test over the control;

if delta <0, the rejection of the null hypothesis implies the non-inferiority of the test against the control.

Usage

TwoSampleMean.NIS(alpha, beta, sigma, k, delta, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.3.2.4<-TwoSampleMean.NIS(0.05,0.2,0.1,1,-0.05,0)
Example.3.2.4 # 50

  

Two sample proportion test for equality

Description

H0: p1=p2

Ha: not equal

The test is finding whether there is a difference between the mean response rates of the test drug and reference drug

Usage

TwoSampleProportion.Equality(alpha, beta, p1, p2, k)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.4.2.4<-TwoSampleProportion.Equality(0.05,0.2,0.65,0.85,1)
Example.4.2.4

Two sample proportion test for equivalence

Description

Ho: |p1-p2| \ge margin

Ha: |p1-p2| < margin

The proportion of response p1 is equivalent to the reference drug p2 is the null hypothesis is rejected

Usage

TwoSampleProportion.Equivalence(alpha, beta, p1, p2, k, delta, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.4.2.4<-TwoSampleProportion.Equivalence(0.05,0.2,0.75,0.8,1,0.2,0.05)
Example.4.2.4

Two sample proportion test for Non-Inferiority/Superiority

Description

Ho: p1-p2 \le margin Ha: p1-p2 > margin

if margin >0, the rejection of Null Hypothesis indicates the true rate p1 is superior over the reference value p2;

if margin <0, the rejection of the null hypothesis implies the true rate p1 is non-inferior against the reference value p2.

Usage

TwoSampleProportion.NIS(alpha, beta, p1, p2, k, delta, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.4.2.4<-TwoSampleProportion.NIS(0.05,0.2,0.65,0.85,1,0.2,0.05)
Example.4.2.4

Two sample proportion Crossover design test for equality

Description

H0: p2-p1 = 0 Ha: not equal to 0

Usage

TwoSampleSeqCrossOver.Equality(alpha, beta, sigma, sequence, delta)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.4.3.4<-TwoSampleSeqCrossOver.Equality(0.05,0.2,0.25,2,0.2)
Example.4.3.4

Two sample proportion Crossover design test for equivalence

Description

Ho: |p1-p2| \ge margin

Ha: |p1-p2| < margin

Usage

TwoSampleSeqCrossOver.Equivalence(alpha, beta, sigma, sequence, delta, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.4.3.4<-TwoSampleSeqCrossOver.Equivalence(0.05,0.2,0.25,2,0,0.2)
Example.4.3.4

Two sample proportion Crossover design for Non-inferiority/Superiority

Description

H0: p2-p1 <= margin

Ha: p2-p1 > margin

Usage

TwoSampleSeqCrossOver.NIS(alpha, beta, sigma, sequence, delta, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.4.3.4<-TwoSampleSeqCrossOver.NIS(0.05,0.2,0.25,2,0,-0.2)
Example.4.3.4

Test for two sample conditional data in exponential model for survival data

Description

unconditional versus conditional

Usage

TwoSampleSurvival.Conditional(alpha,beta,lam1,lam2,eta1,eta2,k,ttotal,taccrual,g1,g2)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Test for two sample equality in exponential model for survival data

Description

H0: the difference between the hazard rates of two samples is equal to

Ha: not equal to 0

The test is finding whether there is a difference between the hazard rates of the test drug and the reference drug.

Usage

TwoSampleSurvival.Equality(alpha, beta, lam1, lam2, k, ttotal, taccrual, gamma)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.7.2.4<-TwoSampleSurvival.Equality(0.05,0.2,1,2,1,3,1,0.00001)
Example.7.2.4

Test for two sample equivalence in exponential model for survival data

Description

margin=lamda1-lamda2, the true difference of hazard rates between control group lamda1 and a test drug group lamda2

H0: |margin| >= delta

Ha: |margin| < delta

This test is whether the test drug is equivalent to the control in average if the null hypothesis is rejected at significant level alpha

Usage

TwoSampleSurvival.Equivalence(alpha, beta, lam1, lam2, k, ttotal, taccrual, gamma, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.7.2.4<-TwoSampleSurvival.Equivalence(0.05,0.2,1,1,1,3,1,0.00001,0.5)
Example.7.2.4

Test for two sample Non-Inferiority/Superiority in exponential model for survival data

Description

margin=lamda1-lamda2, the true difference of hazard rates between control group lamda1 and a test drug group lamda2

H0: margin <= delta

Ha: margin > delta

if delta >0, the rejection of Null Hypothesis indicates the superiority of the test drug over the control;

if delta <0, the rejection of the null hypothesis implies the non-inferiority of the test test drug against the control.

Usage

TwoSampleSurvival.NIS(alpha, beta, lam1, lam2, k, ttotal, taccrual, gamma,margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.7.2.4<-TwoSampleSurvival.NIS(0.05,0.2,1,2,1,3,1,0.00001,0.2)
Example.7.2.4

Two-Sided Tests with fixed effect sizes

Description

Two-sided tests

Ho: \delta_j = 0

Ha: \delta_j is not equal to 0

Usage

TwoSide.fixEffect(m, m1, delta, a1, r1, fdr)

Arguments

Details

alpha_star=r1*fdr/((m-m1)*(1-fdr)), which is the marginal type I error level for r1 true rejection with the FDR controlled at f.

beta_star=1-r1/m1, which is equal to 1-power.

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.12.2.3<-TwoSide.fixEffect(m=4000,m1=40,delta=1,a1=0.5,r1=24,fdr=0.01)
Example.12.2.3
# n=73

Two-Sided Tests with varying effect sizes

Description

Two-sided tests

Ho: \delta_j = 0

Ha: \delta_j is not equal to 0

Usage

TwoSide.varyEffect(s1, s2, m, m1, delta, a1, r1, fdr)

Arguments

Details

alpha_star=r1*fdr/((m-m1)*(1-fdr)), which is the marginal type I error level for r1 true rejection with the FDR controlled at f.

beta_star=1-r1/m1, which is equal to 1-power.

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

delta=c(rep(1,40/2),rep(1/2,40/2));
Example.12.2.4<-TwoSide.varyEffect(s1=100,s2=200,m=4000,m1=40,delta=delta,a1=0.5,r1=24,fdr=0.01)
Example.12.2.4
# n=164 s1<n<s2, h(s1)<0,h(s2)<0

Composite Efficacy Measure(CEM) for Vaccine clinical trials.

Description

Let sij be the severity score associated with the jth case in the ith treatment group. \mu_i=mean(s_{ij}), \sigma^2_i=var(s_{ij}).

H0: pT=pC and muT=muC

Ha: pT is not equal to pC and muT is not equal to muC

Usage

Vaccine.CEM(alpha, beta, mu_t, mu_c, sigma_t, sigma_c, pt, pc)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.15.6.4<-Vaccine.CEM(0.05,0.2,0.2,0.3,sqrt(0.15),sqrt(0.15),0.1,0.2)
Example.15.6.4

The evaluation of vaccine efficacy with Extremely Low Disease Incidence(ELDI)

Description

If the disease incidence rate is extremely low, the number of cases in the vaccine group given the total number of cases is distributed as a binomial random variable with parameter theta.

Ho: \theta \ge \theta_{0}

Ha: \theta < \theta_{0}

Usage

Vaccine.ELDI(alpha, beta, theta0, theta, pt, pc)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.15.6.2<-Vaccine.ELDI(0.05,0.2,0.5,1/3,0.001,0.002)
Example.15.6.2
# 17837

Reduction in Disease Incidence(RDI) for Vaccine clinical trials.

Description

The test is to find whether the vaccine can prevent the disease or reduce the incidence of the disease in the target population. Usually use prospective, randomized, placebo-controlled trials.

Usage

Vaccine.RDI(alpha, d, pt, pc)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.15.6.1<-Vaccine.RDI(0.05,0.2,0.01,0.02)
Example.15.6.1
# 14214

In Vitro Bioequivalence

Description

Consider 2 by 2 crossover design. \zeta = \delta^2+sT^2+sR^2-thetaBE*max(\sigma_0^2,sR^2) . sT^2=\sigma_{BT}^2+\sigma_{WT}^2, sR^2=\sigma_{BR}^2+\sigma_{WR}^2

Ho: \zeta \ge 0

Ha: \zeta < 0

Usage

Vitro.BE(alpha, beta, delta, sigmaBT, sigmaBR, sigmaWT, sigmaWR, thetaBE)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.10.5<-Vitro.BE(0.05,0.2,0,0.5,0.5,0.5,0.5,1)
Example.10.5

# n=43 Vitro.BE reach 0

William Design test for equality

Description

Ho: \mu_{1}-\mu_{2}=0

Ha: not equal to 0

Usage

WilliamsDesign.Equality(alpha, beta, sigma, sequence, delta)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.4.5.4<-WilliamsDesign.Equality(0.05,0.2,0.75^2,6,0.2)
Example.4.5.4

Williams Design test for equivalence

Description

Ho: |\mu_2-\mu_1| \ge margin

Ha: |\mu_2-\mu_1| < margin

Usage

WilliamsDesign.Equivalence(alpha, beta, sigma, sequence, delta, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.4.5.4<-WilliamsDesign.Equivalence(0.05,0.2,0.75^2,6,0.2,0.3)
Example.4.5.4

Williams Design test for Non-inferiority/Superiority

Description

H0: \mu_1-\mu_2 \le margin

Ha: \mu_1-\mu_2 > margin

Usage

WilliamsDesign.NIS(alpha, beta, sigma, sequence, delta, margin)

Arguments

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Examples

Example.4.5.4<-WilliamsDesign.NIS(0.05,0.2,0.75^2,6,0.2,0.05)
Example.4.5.4

Test Goodness of Fit by Pearson's Test

Description

Test the goodness of fit and the primary study endpoint is non-binary categorical response. pk=nk/n, nk is the frequency count of the subjects with response value k. pk,0 is a reference value.

H0: pk=pk,0 for all k

Ha: not equal

Usage

gof.Pearson(alpha, beta, pk, pk0, r)

Arguments

Details

(*) is \chi^{2}_{r-1}(\chi^{2}_{\alpha, r-1}|noncen)=\beta

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003

Test Goodness of Fit by Pearson's Test for two-way table

Description

H0: pk=pk,0 for all k

Ha: not equal

Usage

gof.Pearson.twoway(alpha, beta, trt, ctl, r, c)

Arguments

Details

(*) is \chi^{2}_{r-1}(\chi^{2}_{\alpha, r-1}|noncen)=\beta

References

Chow SC, Shao J, Wang H. Sample Size Calculation in Clinical Research. New York: Marcel Dekker, 2003