APPENDIX B Sample-Size Calculation Methods: Classical Design

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1 APPENDIX B Sample-Size Calculation Methods: Classical Design One/Paired - Sample Hypothesis Test for the Mean Sign test for median difference for a paired sample Wilcoxon signed - rank test for one or a paired sample Test for H 0 : (u 0, σ 0 ) versus H a : (u a, σ a ) large sample One-sample t-test One-sample t-test: finite population Paired-sample t-test Paired-sample t-test (finite population) One - way repeated measures ANOVA One - way repeated measures contrast One - sample multiple test for zero means One/Paired - Sample Hypothesis Test for Proportion McNemar s test for a paired sample Chi - square test for one sample proportion Chi - square test for one sample proportion: finite population One - sample exact test for proportion using binomial distribution One/Paired - Sample Hypothesis Test for Others Kendall s test of independence Test H 0 : correlation = zero using Fisher s arctan transformation Test H 0 : regression coefficient = zero using arctan transformation Classical and Adaptive Clinical Trial Designs Using ExpDesign Studio, By Mark Chang Copyright 2008 John Wiley & Sons, Inc. 235

2 236 APPENDIX B: SAMPLE-SIZE CALCULATION METHODS Logistic regression on x for a binary outcome Logistic regression on x for a binary outcome with covariates Linear regression; test for H 0 : correlation coefficient = 0 Multiple linear regression; test for H 0 : multiple correlation R = 0 Multiple regression; test zero increase in R 2 due to extra B covariates Linear regression y = a + bx ; test H 0 : b = b 0 vs. H a : b b 0 Test for Bloch Kraemer intraclass κ coefficient Test for Bloch Kraemer intraclass κ using Z-transformation Paired - Sample Equivalence Test for the Mean Paired t test for equivalence of means Paired - Sample Equivalence Test for Proportion Paired response: equivalence of p 1 and p 2 (large sample) One - Sample Confidence Interval for the Mean One-sample mean confidence method One-sample mean confidence interval method: finite population Paired-sample mean confidence interval method: large sample Paired-sample mean confidence interval method: finite population Confidence interval for repeated measures contrast One-sample confidence interval for a mean based on the t-statistic Paired mean confidence interval based on the t-statistic One - Sample Confidence Interval for Proportion Confidence interval for a proportion: large n Confidence interval for an odds ratio for paired proportions: large n Confidence interval for the probability of observing a rare event One - Sample Confidence Interval for Others Confidence interval for a correlation coefficient Linear regression y = a + bx, confidence interval for b Confidence interval for Bloch Kraemer intraclass κ

3 APPENDIX B: SAMPLE-SIZE CALCULATION METHODS 237 Two - Sample Hypothesis Test for the Mean Two-sample t-test Mann Whitney U /Wilcoxon rank - sum test for two samples Two-sample z - test: large sample or population variance known 2 2 crossover study One - way repeated measures ANOVA for two groups Test for a treatment mean difference with a 2 2 crossover design Two-sample z - test for treatment mean difference Two-sample multiple test for mean differences Comparing DNA expression profiles among predefined classes Donner s method for mean difference using cluster randomization Two - Sample Hypothesis Test for Proportion Asymptotic z - method considering variance difference Pearson s chi - square test: Kramer Greenhouse Lachin s test for two treatments by two-time-point interactions Mantel Haenszel test for an odds ratio with k strata: large sample Whitehead logistic model for two groups with k categories Chi-square test for a two-sample proportion with k categories Mantel Haenszel test for an odds ratio with k strata: continuity correction Repeated measures for two proportions Donner s method for proportion difference using cluster randomization Fisher s exact test Two - Sample Hypothesis Test for Others Exponential survival distribution with uniform patient enrollment Exponential survival distribution with uniform enrollment rate and follow-up Test interaction in a model with an exponential survival function: two strata Test interaction in a model with an exponential survival function: k strata Log - rank test for survival analysis Exponential survival distribution with a uniform enrollment, follow - up, and dropouts Exponential survival distribution with a Bernoulli confounding variable

4 238 APPENDIX B: SAMPLE-SIZE CALCULATION METHODS Testing two correlation coefficients using Fisher s arctan transformation Linear regression y 1 = a 1 + b 1 x, y 2 = a 2 + b 2 x ; test H 0 : b 1 = b 2 Two - Sample Equivalence Test for the Mean Two one - sided t - tests for equivalence: parallel design (bivariate t ) Two one-sided t - tests for equivalence based on a ratio of means: parallel design (bivariate t ) Two one-sided t - tests for equivalence based on a ratio of two means: crossover design (bivariate t ) Two one-sided t - tests for equivalence based on a mean ratio for lognormal data: parallel design (bivariate t ) Schuirmann Chow s two one - sided t-tests for equivalence Noninferiority test for means based on a one - sided two - sample t-test Two - Sample Equivalence Test for Proportion Equivalence test for two proportions: large n One - sided noninferiority test for two proportions Equivalence test for two proportions using the bivariate t-distribution (large n ) Two - Sample Equivalence Test for Survival Noninferiority test for survival with uniform accrual and follow - up Equivalence test for survival with uniform accrual and follow - up Two - Sample Confidence Interval for the Mean Confidence interval for the difference of two means: large sample Two - Sample Confidence Interval for Proportion Confidence interval for the difference in two proportions: large n Confidence interval for proportional difference with minimum total size Confidence interval for ln(odds ratio): unmatched case control study Two - Sample Confidence Interval for Others Multisample Hypothesis Test for the Mean ANOVA with Latin square design One - way ANOVA for parallel groups

5 APPENDIX B: SAMPLE-SIZE CALCULATION METHODS 239 Contrast test for m means: dose response Two - way ANOVA with an interaction term Two - way ANOVA without interaction One-way random block design William s test for minimum effective dose Multisample Hypothesis Test for Proportion Chi - square test for equal proportions in m groups Chi-square test for m sample proportions with k categories One - way contrast between proportions Cochran Armitage test for linear/monotonic trend: dose response Multisample Hypothesis Test for Others Prognostic model with right - censored data from DNA microarrays Test for all k equal survival means with overall type I error control One - way contrast test for survival with uniform accrual and follow - up Multisample Confidence Interval for Others Confidence interval for one - way contrast: large sample