**Futility Analysis In Clinical Trials** – Sample Sizes for Group Sequential Testing in PASS PASS contains procedures for power analysis and sample size calculations for many different one-sample and two-sample cases. The group sequencing tools in PASS are easy to use and validated for accuracy. To learn more about group series testing in PASS, we recommend downloading and installing the free trial version of the software. Click here to learn more about group sequential analysis and sample size reestimation in . Jump to:

Introduction The various group sequential sample calculation procedures in PASS allow you to study power and sample size for an ever-expanding list of scenarios:

## Futility Analysis In Clinical Trials

Either of these procedures can be used to determine the power, sample size, and/or limits for the corresponding group sequential test. Efficiency and/or futility limits can be generated for one- and two-tailed testing. The distance between the stairs can be the same or specified to size. Individual stages can also be skipped. Limits can be calculated from popular alpha and beta cost functions (O’Brien-Fleming Analog, Pocock Analog, Hwang-Shih-DeCani Gamma family, linear) or custom cost functions, or limits can be entered directly if desired. Vanity limits can be mandatory or optional. Corresponding P-value limits are given for each limit statistic. Alpha and/or Beta spend in each phase will be reported. Border plots are also produced. Each procedure is used as a planning tool to determine sample size and initial limits. Scene data, as acquired, can be evaluated using the companion group analysis procedure in Statistical Analysis and Graphics software. The accompanying procedure also allows for sample size reassessment and updated limits for current information. In this procedure, simulation can be used to analyze boundary crossing probabilities based on the current scene results. An example of a group series limit plot produced in these procedures is shown below. Overview of a cohort sequential study There are three basic phases of a cohort sequential (interim) study:

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Design Phase – Determine Number of Subjects To begin the group sequential testing process, an initial calculation must be made to determine sample size and target information when the final phase (maximum information) is reached. The sample size calculation requires the specification of the following:

The calculation of the design phase is performed in the PASS group sequence procedures. The PASS software allows the user to easily sample a range of effect size parameters (means, standard deviations, proportions, risk percentages) as these are not always known in advance. The resulting sample size from the sample size calculation also allows for the calculation of the maximum information, which is the total information of the study when the final stage is reached. Based on the maximum information, the target information and the target sample size of each stage can be calculated. In particular, this allows the user to have a target sample size for the first stage. Group Sequential Analysis Phase group sequential analysis consists of a series of phases where a decision is made at each phase to stop or continue. This analysis can be performed using the accompanying (analytical) procedure for this sample size procedure, in. First Intermediate Phase The design phase yields the intended number of test subjects for the first phase. The study begins and response data is collected for subjects, toward the target number of subjects in the first phase, until a decision is made to perform analysis on the existing data. The analysis at this point is called the first stage. Unless the number of subjects in the first phase is consistent with the design goal for the first phase, the calculated information in the first phase will not exactly match the design information for the first phase. In addition, the trial parameter estimates will rarely, if ever, match the parameters used in the calculation of the design information, and thus the calculated information in the first stage will differ from the design information. In general, the calculated information does not differ too much from the design information, but in any case the analysis of the spending function group order is well suited to make appropriate adjustments for any differences. The information of the first stage is divided by the maximum information to obtain the information ratio (or information fraction) of stage one. This information ratio is used in conjunction with the spending function(s) to determine the alpha and/or beta spend at that stage. In turn, the limits of stage one, corresponding to the information ratio, are calculated. A Z (or t) statistic is calculated from the raw data values. The stage one stat is compared to each of the stage one limits. If any of the limits are breached, the study will generally be stopped (non-binding vanity limits may be an exception). If none of the boundaries are crossed, the investigation moves on to the next stage. If none of the limits are exceeded, it may also be useful to explore the conditional strength or stopping probabilities of future phases using the procedure. Conditional power and stopping probabilities are based on the user-specified assumed actual difference. Second and other intermediate stages (if reached) Since the information ratio of the first stage is not equal to the design information ratio, a designation must be made at that point as the target information of the second stage. There are two options available in the procedure. One option is to focus on the information ratio of the original design. For example, if the original design ratios of a four stage design are 0.25, 0.50, 0.75, 1.0 and the observed ratio of stage one is 0.22, the researcher may still choose to second stage to aim for 0.50, even though this now requires additional information accumulation of 0.28 (proportion). The goals of the third and fourth legs would also remain 0.75 and 1.0. A second option is to adjust the target information proportionally to the remaining ratios. For this option, if the design ratios 0.25, 0.50, 0.75, 1.0 and 0.22 are observed, the remaining 0.78 will be distributed evenly among the remaining phases. In this example, the remaining target ratios become 0.48, 0.74, 1.0. For both options, once target information for the next stage is determined, revised target sample sizes are obtained (in the procedure), and the study continues until a decision is made to perform the next interim analysis on the cumulative response data. In the same way as in the first phase, the information ratio of the current phase is used with the spending function to determine alpha and/or beta spend in the current phase. The current scene boundaries are then calculated. The z statistic is calculated and compared to the limits and a decision is made to stop or continue. If a limit is exceeded, the study is usually stopped. If none of the boundaries are crossed, the investigation moves on to the next stage. Again, if no limit is exceeded, conditional power and stopping probabilities can be considered based on a choice of the assumed actual difference. The study continues from phase to phase until the study is stopped for crossing a limit, or until the final phase is reached. Final Stage (if reached) The Final Stage (if achieved) is similar to all Intermediate Stages, with some exceptions. For all temporary analyses, the decision is made to stop before the border crossing, or to continue to the next leg. At the final stage, only the decision of effectiveness or futility can be made. Another complication of the final phase, which does not apply to the temporary phases, is the calculation of the maximum information. In the final stage, the current information should become the maximum information, because the cost functions require that the ratio of information should be 1.0 at the final representation. If the current information in the final phase is less than the maximum design information, the scenario is sometimes described as under-running. Similarly, if the current information in the final stage is greater than the maximum design information, the result can be called overshoot. For both undershoot and overshoot, the adjustment mechanism is the same and is described in the Technical Details section, under Information and General Information. Apart from these two exceptions, the final phase analysis is performed in the same way as the intermediate analyses. The remaining alpha and beta to spend are used to calculate the limits for the final stage. If the test is a one-tailed test, the final phase limit is a single value. The z-statistic of the last phase is calculated from the sample ratios of the complete data of each group. The z statistic is compared to the limit and a decision is made about effectiveness or futility. Reporting Phase Once a group sequential boundary has been crossed and the decision to stop has been made, the need to properly summarize and communicate the study results remains. Some or all of the following may be reported:

Boundary Graph Showing the Boundary Exceeded The Boundary Graph provides a helpful visual summary of the process leading up to the reported study decision. Adjusted Confidence Interval and Estimation of the Difference in Ratio Due to the bias introduced in the group sequential analysis process, the raw confidence interval of the difference in ratios should not be used. An adjusted confidence interval should

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