# products: Classical Trial Design with ExpDesign Studio

Classical Trial Studio is one of the components in ExpDesign Studio. It can also be used as stand-alone software. Over 100 sample size calculation methods have been implemented in Classical Trial Studio.

## Example 1: Designing a Non-inferiority Trial with Survival End Point

It becomes more and more popular to design a non-inferiority than superiority oncology trial. The objective of this kind of trial is typically stated as testing the effectiveness of ABC (the experiment drug) through a non-inferiority trial with XYZ as the active control. Here is an example: A trial design group is designing a phase III clinical trial for a potential oncology drug, ABC. The study drug ABC will be combined with an approved drug XYZ as second line therapy in patients with Multiple Myeloma. The combined treatment will be compared with XYZ alone for the effectiveness in prolonging patients' survival time. It is estimated that the median survival time is 8 months (hazard rate = 0.0866) for XYZ only and 9 months (hazard rate = 0.0693) for the combined treatment group. The duration of patient enrollment is anticipated to be 15 months with total trial duration of 30 months. Assume the non-inferiority margin for the difference in hazard rate is 0.02. Using ExpDesign Studio, we learned that a sample size 290 patients will allow us to detect the difference at a level of significance 0.025 and with a power of 80%. ExpDesign will also generate the report for the trial design with or without the power curve.

## Example 2: Calculating sample size based on prognostic model with continuous and right-censored data from DNA microarrays

DNA microarrays are arrays that simultaneously provide information about expression levels of thousands of genes and are consequently finding wide use in biomedical research. Hsieh and Lavori proposed this method for planning sample size based on number of events. Note that we are assuming that the log ratio or log intensities are based on logarithms to the base 2, so a one-unit change in x represents a twofold change. To control the number of false positives and the false negatives, the type-I and type-II error rates are usually not to exceed 0.001 and 0.05, respectively.

## List of Sample Size Calculation Methods Available in ExpDesign Studio

There are more than 100 sample calculation methods for balanced designs and more than 40 methods for unbalanced designs. The sample size calculation methods are categorized using three letters as follows.

*One/Paired Sample Hypothesis Test for Mean (OHM)*

Sign Test for median difference - one or paired sample

Wilcoxon Sum Rank test - one sample

Test for Ho: (µ_{0}, s_{0}) vs. Ha: (µ_{a}, s_{a}) - large sample

One-sample t-test

One-sample t-test with finite population adjustment

Paired-sample t-test

Paired-sample t-test with finite population adjustment

One way repeated measures ANOVA

One way repeated measures contrast

One sample multiple-Test for zero means

*One/Paired Sample Hypothesis Test for Proportion (OHP)*

One sample exact test for proportion using binomial distribution

McNemar's test for a paired sample

Chi-square test (normal approximation) for one sample proportion

Chi-square test (normal approximation) for one sample proportion - adjusted for finite population

*One/Paired Sample Hypothesis Test for Others (OHO)*

Test for Bloch-Kraemer intraclass Kappa coefficient (binary outcome)

Test for Bloch-Kraemer intraclass Kappa coefficient (binary outcome) with Kraemer's Z-transformation

Test Ho: correlation from zero -- one group with Fisher's arctan transformation

Test Ho: regression coefficient = zero -- Fisher's arctan transformation

Logistic regression on x for binary outcome

Logistic regression on x for binary outcome with covariates

Linear regression, test for Ho: correlation coefficient =0

Multiple linear regression, test for Ho: multiple correlation R =0

Multiple regression, test 0 increase in R^{2} due to B covariates added to the prior model with A covariates

Linear regression y=a+bx, test Ho: b=b0, vs, Ha: b<>b0

Kendall's Test of Independence

*Paired Sample Equivalence Test for Mean (PEM)*

Paired t test for equivalence of means

*Paired Sample Equivalence Test for Proportion (PEP)*

Paired response: equivalence of p_{1} and p_{2} (large sample)

*One Sample Confidence Interval for Mean (OPM)*

One sample mean CI - Lin's z-method (large sample)

One sample mean CI with finite sample size adjustment (large sample)

Paired sample mean CI - a special case of Lin's z-method (large sample)

Paired sample mean CI with finite sample size adjustment (large sample)

Confidence Interval for repeated measures contrast

One sample confidence interval for mean based on t-statistic

Paired sample confidence interval for mean difference based on t-statistic

*One Sample Confidence Interval for Proportion (OPP)*

Confidence interval for proportion (large n)

Confidence interval for odds ratio for paired proportions -- case-control study (large n)

Confidence interval for probability of observing a rare event

Confidence interval for proportion -- adjusted for finite population (large n)

*One Sample Confidence Interval for Others (OPO)*

Confidence interval for correlation coefficient

Linear regression y=a+bx, confidence interval for b

Confidence interval for Bloch-Kraemer intraclass Kappa coefficient for binary outcome

*Two-Sample Hypothesis Test for Mean (THM)*

Two-sample t-Test

Mann-Whitney U/Wilcoxon two-sample test

Two-sample z-test (large sample or population variance known)

2x2 Crossover study

One way repeated measures ANOVA for two groups

Test for treatment mean difference with 2x2 crossover design

Two-sample z-test for treatment mean difference

Two-sample multiple-test for mean differences

Comparing expression profiles among predefined classes using DNA microarrays

*Two-Sample Hypothesis Test for Proportion (THP)*

Arcsine method (non-countinuity Correction) for two large groups (n P_{1}>10, n P_{2}>10)

Arcsine method (with countinuity Correction) for two large groups (n P_{1}>10, n P_{2}>10)

Poisson method for two sample proportions (nP_{1}<10, nP_{2}<10)

Asymptotic z-method considering variance difference

Pearson's Chi-square test (Kramer/Greenhouse, Casagrande improved)- large sample

Snedecor's Method for normal but heterogeneous samples

Lachin's test for treatment by time interaction (two-time points repeated measures for 2 groups)

Mantel-Haenszel test for odds ratio with k strata (large sample)

Whitehead proportional odds ratio model with k categories and two treatments (logistic regression)

Chi-square test (normal approximation) for two-sample proportion with k categories (equal cells)

Mantel-Haenszel test for odds ratio with k strata -Nam-method

Repeated measures for two group proportions

*Two-Sample Hypothesis Test for Others (THO)*

Test for mean survival time with exponential distribution (no censored data -Cox's F-test)

Test for mean survival time with exponential distribution (Gehan-Wilcoxon, Mantel-Haenszel)

Pasternack-Gilbert method: exponential survival distribution - no censoring

Exponential survival distribution with uniform patient enrollment rate over time T

Exponential survival distribution with uniform patient enrollment rate over time T_{0} and a follow-up period

Test interaction in a model with exponential survival function -- equal size in each cell (2 strata)

Test interaction in a model with exponential survival function -- most conservative (k strata)

LogRank test for survival analysis - balanced design

Exponential survival distribution with uniform patient enrollment rate over time T_{0}, a follow-up period and dropouts

Exponential survival distribution with a Bernoulli confounding variable (uniform patient enrollment rate and a follow-up period)

Test two correlation coefficients -- Fisher's arctan transformation

Linear regression y_{1}=a_{1}+b_{1}x, y_{2}=a_{2}+b_{2}x, Test Ho: b_{1}=b_{2}, vs. Ha: b_{1}<>b_{2}.

*Two-Sample Equivalence Test for Mean (TEM)*

Equivalence of two means (two-sample t-Test)

Two one-sided t-tests for equivalence - parallel design (using exact bivariate t distribution)

Two one-sided t-tests for equivalence based on ratio of means - parallel design (using exact bivariate t distribution)

Two one-sided t-tests for equivalence based on ratio of two means - crossover design (using exact bivariate t distribution)

Two one-sided t-tests for equivalence based on mean ratio for lognormal data - parallel design (using exact bivariate t distribution)

Schuirmann-Chow's two one-sided t-tests for equivalence

Test for Bioequivalence with high-order crossover design-- Balamm design (4-sequence, 2-period), (2-sequence, 3-period), (2-sequence, 4-period), (4-sequence, 4-period)

*Two-Sample Equivalence Test for Proportion (TEP)*

Lin z-method

Makuch_Simon z method

One-sided test for equivalence

Equivalence test for two proportions using bivariate t-distribution (large n)

*Two-Sample Equivalence Test for Survival (TEO)*

Non-inferiority test (Chow) - exponential distribution with uniform enrollment rate and a follow-up period

Equivalence Test using bivariate-t - exponential distribution with uniform enrollment rate and a follow-up period

*Two-Sample Confidence Interval for Mean (TCM)*

Confidence interval for difference of two means (large sample)

*Two-Sample Confidence Interval for Proportion (TCP)*

Confidence interval for difference in two group proportions (large n)

Confidence interval for difference in two group proportions with minimum total size (large n)

Confidence interval for ln(odds ratio) - unmatched case-control study(large n)

*Two-Sample Confidence Interval for Others (TCO)*

Linear regression y_{1}=a_{1}+b_{1}x, y_{2}=a_{2}+b_{2}x, confidence interval for b_{1}-b_{2}

*Multi-Sample Hypothesis Test for Mean (MHM)*

ANOVA with Latin Square design

One-way ANOVA for parallel groups

One-way Contrast between means

Two-way analysis of variance with interaction term

Two-way analysis of variance without interaction

One-way random block design

Three-way layout random block design with Interaction

Test all k means equal with over all Type I error controlled at alpha level

*Multi-Sample Hypothesis Test for Proportions (MHP)*

Chi-square test for equal proportions in M groups in K categories

*Multi-Sample Hypothesis Test for Others (MHO)*
One-way repeated measures contrast - for dose-response relationship

William's test for minimum effective dose

Cochran-Armitage test for linear/monotonic trend (dose response)

Prognostic model with continuous and right-censored data from DNA microarrays

*Multi-Sample Confidence Interval for Others (MCO)*

Confidence interval for one-way contrasts (large sample)