Maximum information designs

Expressions to determine the sample size N needed to provide power 1-beta to detect a difference between groups, say delta, involve other nuisance parameters, such as the variance of the observations for a test or means, or the control group probability for a test of proportions or the control group hazard rate for a logrank test of event-times. Designs where N is fixed are called maximum N or duration designs because the sample size and required duration of the study can be fixed, or estimated. However, such designs are expected, but not guaranteed, to provide the desired level of power to detect the specified difference delta at the study end because the true or estimated values of the nuisance parameters are unknown. Thus, the actual information to be accrued and the associated level of power are random variables with sample variation.

Expressions are developed to determine the amount of information needed to provide the desired level of power, regardless of the values of the nuisance parameters.

The amount of information (I) in the observed data is readily quantified and can often be expressed as the inverse of the variance of the test statistic. Also, the total amount of information required to provide the desired level of power 1-beta to detect a difference delta with a test at level alpha is readily determined, designated as Ialpha,beta,delta. Under a maximum information design, the study is continued until the required total amount of information is accrued, or I = Ialpha,beta,delta. In this case, the sample size or duration are random variables, but each can be estimated under various projections about the underlying parameters (variance, probability, hazard) in advance. The implementation of a maximum information design for two and multiple group trials is described for a test of means, proportions and event-times using the logrank test. Application to other methods of analysis is described.

A maximum information design provides greater assurance that the desired level of power will be attained. However, the exact study duration is unknown. Issues related to the implementation of such a design are discussed.