Package 'TrialSize'

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 <[email protected]>

Vicky Qian Wu <[email protected]>

Harry G. Zhang (Quality check)

Shein-Chung Chow

maintainer: Vicky Qian Wu <[email protected]>

References

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

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Description

Ho: $\mu_1 = \mu_2$

Ha: $\mu_1$ is not equal to $\mu_2$