Hybrid Frequentist/Bayesian Power and Bayesian Power in Planning Clinical Trials

The normal theory of sample size calculation is discussed, including extensions to binomial and time-to-event outcomes, non-inferiority trials, and proof-of-concept trials with dual success criteria. Assurance is introduced to calculate the minimum sample size required to achieve a specific level of confidence in the trial's results. The connection between conditional and predictive power, power and assurance, and surety in sample sizing is explored.

Format: Hardback
Length: 188 pages
Publication date: 20 May 2022
Publisher: Taylor & Francis Ltd

A comprehensive exploration of the principles and applications of normal theory in the field of statistical analysis encompasses a wide range of topics. This theory, which is rooted in the principles of probability, plays a pivotal role in understanding the relationship between various statistical measures such as average power, expected power, predictive power, assurance, conditional Bayesian power, and Bayesian power. By delving into these concepts, researchers and practitioners gain valuable insights into the design and analysis of clinical trials, as well as other types of scientific studies.

One of the key extensions of normal theory involves its application to binomial and time-to-event outcomes, as well as non-inferiority trials. These extensions allow researchers to analyze and interpret data from these complex scenarios, enabling them to make informed decisions based on the evidence available.

Furthermore, the study of the upper bound on average power, assurance, and Bayesian power is an important area of research. This bound is derived from the prior probability of a positive treatment effect, and it provides a valuable tool for determining the minimum sample size required to achieve a certain level of statistical significance. By understanding this bound, researchers can optimize the design of their studies and ensure that they have sufficient power to detect meaningful differences between treatment groups.

In addition to its theoretical implications, normal theory has practical applications in the field of clinical trials. Assurance, a measure of the expected proportion of participants who will experience a positive treatment effect, is particularly useful in the development of new treatments and therapies. By conducting multiple trials and analyzing the data, researchers can gain confidence in the effectiveness of a treatment and determine its optimal dosage and duration.

Furthermore, the concept of conditional assurance can be applied to individual trials within a development program. This approach allows researchers to assess the certainty of a positive outcome for a particular trial based on the positive outcome of an earlier trial in the program or on the successful outcome of an interim analysis. This information can be used to inform decision-making regarding the continuation or discontinuation of a trial, as well as to allocate resources more efficiently.

Another important aspect of normal theory is the prior distribution of power and sample size. The choice of a prior distribution plays a critical role in determining the accuracy of power calculations and the reliability of the results. By understanding the properties of different prior distributions, researchers can select the most appropriate one for their study and improve the accuracy of their estimates.

In recent years, the basic approach to proof-of-concept trials with dual success criteria has been extended to include the investigation of the connection between conditional and predictive power at an interim analysis. This connection is important because it allows researchers to assess the effectiveness of a treatment early in the development process and make informed decisions regarding the continuation or discontinuation of a trial.

Furthermore, the introduction of the idea of surety in sample sizing of clinical trials based on the width of the confidence intervals for the treatment effect is a significant development. This approach takes into account the uncertainty associated with statistical estimates and aims to optimize the sample size to achieve a certain level of surety. By using this approach, researchers can reduce the risk of Type I and Type II errors and improve the accuracy of their conclusions.

In conclusion, normal theory is a powerful tool for statistical analysis that plays a crucial role in understanding and interpreting the relationship between various statistical measures and their applications in the field of clinical trials and other scientific studies. By extending the concepts of this theory to binomial, time-to-event outcomes, non-inferiority trials, and non-inferiority trials, researchers and practitioners gain valuable insights into the design and analysis of these studies. The study of the upper bound on average power, assurance, and Bayesian power provides a valuable tool for determining the minimum sample size required to achieve a certain level of statistical significance, while assurance is a measure of the expected proportion of participants who will experience a positive treatment effect. The conditional assurance approach can be applied to individual trials within a development program, and the prior distribution of power and sample size is an important aspect of ensuring the accuracy of power calculations and the reliability of the results. The extension of the basic approach to proof-of-concept trials with dual success criteria and the investigation of the connection between conditional and predictive power at an interim analysis are significant developments that improve the accuracy and reliability of clinical trial outcomes. Finally, the introduction of the idea of surety in sample sizing of clinical trials based on the width of the confidence intervals for the treatment effect is a significant development that aims to optimize the sample size and reduce the risk of Type I and Type II errors.

Dimension: 234 x 156 (mm)
ISBN-13: 9781032111292