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New Adaptive Tables

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New Bayesian Tables

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New Base Tables

(Included in the* **Pro Tier*)

In the Spring 2021 nQuery Advanced 8.7 release, **5 new sample size tables have been added to the Pro tier of nQuery** covering various new adaptive designs.

**In this release the following areas are targeted for development:**

- Multi-Arm Multi-Stage Designs (MAMs) GSD
- Two Stage Phase II Designs
- Generalized MCP-Mod (Multiple Comparisons Procedure - Modelling)
- Group Sequential Designs

Adaptive designs, such as the group sequential design, have become widely used in clinical drug development. However, much of this development has been confined to the two-arm setting. A common situation in clinical trials is that in which an optimal treatment or dose has not been identified prior to the phase III trial. In this situation, it may be desirable to begin a Phase II trial (or longer Phase III trial) with several treatment arms and conduct interim analyses that will allow the dropping of less promising arms and potentially seamlessly move those arms into Phase III. This type of design is commonly named a multi-arm multi-stage design.

The Multi Arm Multi Stage (MAMs) group sequential design extends the common two-arm group sequential design to a design in which multiple treatment arms can be compared to a common control arm and allows the trial to be stopped for efficacy or futility based on the best performing arm. In addition, it can be shown that less effective arms may be dropped at interim analyses without affecting the Type I error.

MAMs designs provide the ability to assess more treatments in less time than could be done with a series of two-arm trials and can offer significantly smaller sample size requirements when compared to that required for the equivalent number of two-arm trials.

In this release, we have extended our MAMs Group Sequential designs to include an option for the proportions endpoint. This provides a familiar framework with which to conduct a MAMs design and explore the additional flexibility offered.

**The table added is as follows:**

- Multiple Arms Multiple Stage (MAMs) Group Sequential Design for Proportions

Phase II designs are often used to determine whether a new procedure or treatment is likely to meet a basic level of efficacy to warrant further development or evaluation. Phase IIa designs are focussed on the proof-of-concept part of Phase II trials. They aim to show the potential efficacy and safety of a proposed treatment. Two-stage designs are common to allow for flexibility to stop trials early for futility as Phase II is the most common failure point in drug evaluation. We have implemented two new two-stage Phase II designs in this release.

The first follows the method outlined in Bryant and Day (1995). As mentioned, often evaluation of toxicity is listed as a primary objective in Phase IIa trials. The Bryant and Day design is a two stage phase IIa design with a coprimary endpoint which allows one to evaluate both the efficacy and the toxicity of the drug or treatment within a single design.

In addition to this design, we have also implemented an adaptive response design based on the paper by Lin & Shih (2004). The main benefit of the method put forward by Lin and Shih over methods such as Simon's two-stage design, is the way in which the proportion of successes under which the alternative hypothesis is powered can be specified. This method allows the specification of two response proportions, the first a low or pessimistic value, and the second an optimistic or high value. This allows one to combat the uncertainty in the specification of the proportion of desirable results and so mitigates the risk of having a proportion which is too high, and so results in the study being underpowered, or a proportion which is too low, and so results in patient resources being unnecessarily wasted or the study taking an unnecessarily long time to complete.

**The tables added are as follows:**

- Two Stage Phase II Design for Response and Toxicity (Bryant and Day)
- Adaptive Response Two Stage Phase II Design (Lin & Shih's Design)

MCP-Mod (Multiple Comparisons Procedure - Modelling) is an increasingly popular statistical methodology for dose-finding Phase IIb trials. Since its development at Novartis, MCP-Mod promises to devise proof-of-concept and dose-ranging trials with greater evidence and data that can prove critical for Phase III clinical trial design.

Combining the robustness of multiple comparisons procedures with the flexibility of modelling, MCP-mod combines these methods to provide superior statistical evidence from Phase II trials with regards to dose selection with the FDA & EMA approving MCP-Mod as fit-for-purpose (FFP).

In this release, we have extended our MCP-Mod design to include the case where there are unequal standard deviations for each arm in the study.

**The table added is as follows:**

- Multiple Comparisons Procedure - Modelling for Continuous Outcome (Unequal Variance) (MCP-Mod)

Group sequential designs are a widely used type of adaptive trial in confirmatory Phase III clinical trials. Group sequential designs differ from a standard fixed term trial by allowing a trial to end early at pre-specified interim analyses for efficacy or futility. Group sequential designs achieve this by using a flexible error spending method which allows a set amount of the total Type I or Type II error at each interim analysis. The group sequential design allows the trialist the flexibility to end those trials early which otherwise would have led to another large cohort of subjects to be analysed unnecessarily.

Non-inferiority testing is used to test if a new treatment is non-inferior to a standard treatment by a pre-specified amount. This is a common objective in areas such as medical devices and generic drug development. This release sees one new design being implemented in this area.

**The table added is as follows:**

- Group Sequential Test for Non-inferiority of Mean Difference

**Phase II Multistage Designs**

- Two Stage Phase II Design for Response and Toxicity (Bryant and Day)

**Proportion > Two - Test**

- Multiple Arms Multiple Stage (MaMs) Group Sequential Design for Proportions

**Group Sequential Designs**

- Group Sequential Test for Non-inferiority of Mean Difference

**Means > Two - Test**

- Multiple Comparisons Procedure - Modelling for Continuous Outcome (Unequal Variance)

**Phase II Multistage Designs**

- Oncology Two Stage Phase IIA Design

To access the adaptive module you must have a **nQuery Pro Tier** subscription. If you do, then nQuery should automatically prompt you to update.

You can manually update nQuery Advanced by clicking **Help>Check for updates.**

**CLICK HERE FOR FULL DETAILS ABOUT UPDATING**

(Included in the* **Plus & Pro Tier*)

In the Spring 2021 nQuery Advanced 8.7 release, **2 new sample size tables have been added to the Plus Tier of nQuery.**

**Two main areas are targeted for development. These are:**

- Bayesian factors
- Consensus Based Intervals

Bayes factors can be described as the Bayesian equivalent of the p-value. The sample size is chosen to make it a priori probable that the Bayes factor is greater than a given cut-off of prespecificed size. Using Bayes factors allows evaluation of evidence in favor of a null hypothesis, as opposed to in frequentist settings where evidence can only be found in favor of the alternative hypothesis.

**The table added is as follows:**

- Bayesian Factor for One Mean

Consensus based intervals two highest posterior density (HPD) credible intervals for a binomial proportion to agree to within a prespecified distance. The two intervals arise from the use of two different prior densities, each following a beta distribution. This method is useful in situations where there are multiple prior opinions about the true proportion and we wish to incorporate an “enthusiastic” and “pessimistic” prior into our calculations.

**The table added is as follows:**

- Bayesian Consensus-Based Sample Size for One Proportion

**Means - One - Test**

- Bayesian Factor for One Mean

**Proportions One Confidence Interval**

- Bayesian Consensus-Based Sample Size for One Proportion

To access these tables, you must have a **nQuery Plus **or** nQuery Pro Tier** subscription.

**If you do, nQuery should automatically prompt you to update.**

You can manually update nQuery Advanced by clicking **Help>Check for updates.**

**CLICK HERE FOR FULL DETAILS ABOUT UPDATING**

(Included in all packages: *Base, Plus & Pro Tiers*)

In the Spring 2021 nQuery Advanced 8.7 release, **21 new sample size tables have been added** to nQuery. This release summary will provide an overview of which areas have been targeted along with the full list of tables added. The main areas targeted for development are as follows:

**Tests for Proportions****Survival/Time to Event Trials**

Proportions are a common type of data where the most common endpoint of interest is a dichotomous variable. Examples in clinical trials include the proportion of patients who experience a tumour regression. There are a wide variety of designs proposed for binary proportions ranging from exact to maximum likelihood to normal approximations.

Under this broad area of proportions we have added tables across the areas of inequality, equivalence and non-inferiority testing. The tables added under this general heading are as follows:

- Inequality Tests for One Proportion
- Non-Inferiority Test for Difference in Paired Proportions
- Non-Inferiority Test for Ratio of Paired Proportions
- Inequality Tests for Difference of Two Proportions
- Inequality Tests for Ratio of Two Proportions
- Inequality Tests for Odds Ratio of Two Proportions
- Equivalence Tests for Ratio of Two Proportions
- Equivalence Tests for Odds Ratio of Two Proportions

In addition to these more general tables we have also added some more specialised Proportions tables

**The additional tables added fall under the following categories:**

- Cross-over designs
- Reliability Demonstration Tests
- Shedding Studies

In a crossover design each subject receives all treatments at least once with the objective of measuring study differences among the treatments. “Crossover” comes from the most common two treatments case which is of interest here. Crossover designs are popular due to an expected increase in precision, since each subject effectively acts as their own control, and the concomitant reduction in study size but do have additional statistical and practical complications such as carry-over effects.

**The tables added are as follows:**

- Inequality Test for the Difference of Two Proportions in a 2x2 Crossover Design
- Inequality Test for the Odds Ratio of Two Proportions in a 2x2 Crossover Design
- Equivalence Test for the Difference of Two Proportions in a 2x2 Crossover Design
- Equivalence Test for the Odds Ratio of Two Proportions in a 2x2 Crossover Design
- Non-inferiority Test for the Difference of Two Proportions in a 2x2 Crossover Design
- Non-inferiority Test for the Odds Ratio of Two Proportions in a 2x2 Crossover Design

A reliability demonstration test is one which deals with the area of rare binomial events and tests the minimum required proportion of successes, known as the reliability, against a standard level. These tests are useful where a manufacturer will have to demonstrate that a certain product has met a goal of a certain reliability at a given time with a specific level of confidence.

- Test to Demonstrate Reliability for One Proportion
- Test to Demonstrate Reliability for One Proportion with Specified Adverse Events

Shedding studies relate to studies with a binomial outcome consisting of repeated binary measures with autocorrelation over time. This type of outcome is common in viral shedding studies, in which each individual's outcome is a proportion. However, these methods can be applied to any binomial outcome in a longitudinal assessment of an intermittent event.

**The tables added are as follows:**

- Test for Autocorrelated Proportion Cohort Design (Shedding Study)
- Test for Autocorrelated Proportion Crossover Design (Shedding Study)

Survival or Time-to-Event trials are trials in which the endpoint of interest is the time until a particular event occurs, for example death or tumour regression. Survival analysis is often encountered in areas such as oncology or cardiology. In contrast to studies with non-survival based endpoints, like continuous or binary endpoints for example, the statistical power of a time-to-event study is determined, not by the number of subjects in the study, but rather by the number of events which are observed and this requires additional flexibility when designing and analyzing such trials.

**The survival tables being added this release fall into the following categories:**

- Log-Rank test
- Piecewise Weighted Log-Rank Test for Delayed Effect
- Restricted Mean Survival Times

The log-rank test is one of the most common statistical tests used for the analysis of survival data. Its flexibility and interpretability provide useful insights into the comparable hazard rates in survival trials.

In this release one new table is being added for the log rank test. It allows for a constant accrual rate for the two sample log-rank test. Where it is assumed that both the event rates and the dropouts follow an exponential distribution. This additional option provides more flexibility in the area of the log-rank test.

**The table added is as follows:**

- Two Sample Log-Rank Test Assuming Constant Accrual, Exponential Rates, Dropouts

There is increasing interest in survival analysis for flexible models due to the increasing occurrence of non-proportional hazards in clinical trials in areas such as immunotherapy. The piecewise weighted log-rank test has been proposed as one potential method that allows a survival analysis to account for a delayed effect. This method splits the trial into two or more time periods which are weighted to create a better estimate of the overall effect by accounting for the different effect sizes expected during different time intervals.

In this release, the Analytic Power Calculation Method based on Generalised Piecewise Weighted Log-rank Test (APPLE+) method approach for determining the sample size for a weighted log-rank test for a delayed effect is added. This method is useful in detecting a difference between two hazard functions when there is a time-lag to treatment effect. This results in a delayed separation of the survival curves for the experimental and control groups, so the proportional hazard assumption no longer holds. This type of design is often encountered in immunotherapy trials when the immune system takes time to respond to the treatment.

In order to account for variations in the delayed onset of clinical effect between patients, the time for treatment to take effect occurs randomly between user-specified upper and lower time bounds. We assume that there is no treatment effect before this time and that the treatment is fully effective after this time. The calculation uses the APPLE+ (Analytic Power Calculation Method based on Generalised Piecewise Weighted Log-rank Test) method as described by Xu et al. (2018).

**The table added is as follows:**

- Generalized Piecewise Weighted Log-rank Test with random treatment time lag effect Survival Model (APPLE+ Method)

- Test to Demonstrate Reliability for One Proportion
- Test to Demonstrate Reliability for One Proportion with Specified Adverse Events
- Inequalty Tests for One Proportion

- Non-Inferiority Test for Difference in Paired Proportions
- Non-Inferiority Test for Ratio of Paired Proportions

- Inequality Test for the Difference of Two Proportions in a 2x2 Crossover Design
- Inequality Test for the Odds Ratio of Two Proportions in a 2x2 Crossover Design
- Test for Autocorrelated Proportion Cohort Design (Shedding Study)
- Test for Autocorrelated Proportion Crossover Design (Shedding Study)
- Inequality Tests for Difference of Two Proportions
- Inequality Tests for Ratio of Two Proportions
- Inequality Tests for Odds Ratio of Two Proportions

- Equivalence Test for the Difference of Two Proportions in a 2x2 Crossover Design
- Equivalence Test for the Odds Ratio of Two Proportions in a 2x2 Crossover Design
- Equivalence Tests for the Ratio of Two Proportions
- Equivalence Tests for the Odds Ratio of Two Proportions

- Non-inferiority Test for the Difference of Two Proportions in a 2x2 Crossover Design
- Non-inferiority Test for the Odds Ratio of Two Proportions in a 2x2 Crossover Design

- Two Sample Log-Rank Test Assuming Constant Accrual, Exponential Rates, Dropouts
- Generalised Piecewise Weighted Log-rank Test with Random Treatment Time Lag Effect Survival Model (APPLE+ Method)

- Non-Inferiority Test for the Difference of Two Restricted Mean Survival Times

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