Methods and Applications of Sample Size Calculation and Recalculation in Clinical Trials

Part I Basics

1 Introduction

1.1 Background and outline

1.2 Examples

1.2.1 The ChroPac trial

1.2.2 The Parkinson trial

1.3 General considerations when calculating sample sizes

2 Statistical test and sample size calculation

2.1 The main principle of statistical testing

Part II Sample size calculation

3 Comparison of two groups for normally distributed outcomes and test for difference or superiority

3.1 Background and notation

3.2 z-test

3.3 t-test

3.4 Analysis of covariance

3.5 Bayesian approach

3.5.1 Background

3.5.2 Methods

4 Comparison of two groups for continuous and ordered categorical outcomes and test for difference or superiority

4.1 Background and notation

4.2 Continuous outcomes

4.3 Ordered categorical outcomes

4.3.1 Assumption-free approach

4.3.2 Assuming proportional odds

5 Comparison of two groups for binary outcomes and test for difference and superiority

5.2 Asymptotic tests

5.2.1 Difference of rates as effect measure

5.2.3 Odds ratio as effect measure

5.2.4 Logistic regression

5.3.1 Background

5.3.2 Fisher-Boschloo test

6 Comparison of two groups for time-to-event outcomes and test for differences or superiority

6.1 Background and notation

6.1.1 Time-to-event data

6.1.2 Sample size calculation for time-to-event data

6.2 Exponentially distributed time-to-event data

6.3 Time-to-event data with proportional hazards

6.3.1 Approach of Schoenfeld

6.3.2 Approach of Freedman

7 Comparison of more than two groups and test for difference

7.1 Background and notation

7.2 Normally distributed outcomes

7.3 C