Analyze Binary Data Using Beta-Binomial Model

Perform analysis for efficacy using a Beta(\(\alpha\), \(\beta\)) prior to compute the posterior probability that the experimental treatment is better than the control treatment care. The analysis assumes a Bayesian model and uses posterior probabilities for decision-making:

• Efficacy: If \(Pr(\pi_{Exp} > \pi_{Ctrl} | \text{data}) > \text{Upper Cutoff Efficacy}\), declare efficacy.

• Futility: If \(Pr(\pi_{Exp} > \pi_{Ctrl} | \text{data}) < \text{Lower Cutoff Futility}\), declare futility.

• At final analysis (FA): Declare efficacy or futility based on the posterior probability.

When simulating under the null case, setting \(dLowerCutoffForFutility = 0\) provides the false-positive rate for the non-binding futility rule. Setting \(dLowerCutoffForFutility > 0\) provides the operating characteristics (OC) of the binding futility rule, as the rule is always followed.

Usage

AnalyzeBinaryUsingBetaBinomial(
  SimData,
  DesignParam,
  LookInfo = NULL,
  UserParam = NULL
)

Arguments

SimData

A data frame containing the data generated in the current simulation.

DesignParam

A list of input parameters necessary to compute the test statistic and perform the test. Variables should be accessed using names (e.g., DesignParam$Alpha).

LookInfo

A list of input parameters related to multiple looks in group sequential designs. Variables should be accessed by names (e.g., LookInfo$NumLooks). Important variables include:

• LookInfo$NumLooks: Integer, number of looks in the study.

• LookInfo$CurrLookIndex: Integer, current look index (starting from 1).

• LookInfo$CumEvents: Vector, cumulative number of events at each look.

• LookInfo$RejType: Code representing rejection types. Possible values include:

• Efficacy Only:

  • 0: 1-Sided Efficacy Upper.

  • 2: 1-Sided Efficacy Lower.

• Futility Only:

  • 1: 1-Sided Futility Upper.

  • 3: 1-Sided Futility Lower.

• Efficacy and Futility:

  • 4: 1-Sided Efficacy Upper and Futility Lower.

  • 5: 1-Sided Efficacy Lower and Futility Upper.

UserParam

A list of user-defined parameters. Must contain the following named elements:

dAlphaCtrl

Prior alpha parameter for control treatment (prior successes).

dBetaCtrl

Prior beta parameter for control treatment (prior failures).

dAlphaExp

Prior alpha parameter for experimental treatment (prior successes).

dBetaExp

Prior beta parameter for experimental treatment (prior failures).

dUpperCutoffEfficacy

Upper cutoff (0,1) for efficacy check. Above this value declares efficacy.

dLowerCutoffForFutility

Lower cutoff (0,1) for futility check. Below this value declares futility.

If not specified, a Beta(1, 1) prior is used for both control and experimental treatments.

Value

A list containing the following elements:

TestStat

A double representing the computed test statistic.

Decision

Required integer value indicating the decision made:

0

No boundary crossed (neither efficacy nor futility).

1

Lower efficacy boundary crossed.

2

Upper efficacy boundary crossed.

3

Futility boundary crossed.

4

Equivalence boundary crossed.

ErrorCode

Optional integer value:

0

No error.

> 0

Non-fatal error; current simulation is aborted but subsequent simulations continue.

< 0

Fatal error; no further simulations are attempted.

Delta

Estimated difference between experimental and control treatments.