getDesignPairedPropMcNemar {lrstat}R Documentation

Group Sequential Design for McNemar's Test for Paired Proportions

Description

Obtains the power given sample size or obtains the sample size given power for a group sequential design for McNemar's test for paired proportions.

Usage

getDesignPairedPropMcNemar(
  beta = NA_real_,
  n = NA_real_,
  pDiscordant = NA_real_,
  riskDiff = NA_real_,
  nullVariance = TRUE,
  rounding = TRUE,
  kMax = 1L,
  informationRates = NA_real_,
  efficacyStopping = NA_integer_,
  futilityStopping = NA_integer_,
  criticalValues = NA_real_,
  alpha = 0.025,
  typeAlphaSpending = "sfOF",
  parameterAlphaSpending = NA_real_,
  userAlphaSpending = NA_real_,
  futilityBounds = NA_real_,
  typeBetaSpending = "none",
  parameterBetaSpending = NA_real_,
  userBetaSpending = NA_real_,
  spendingTime = NA_real_
)

Arguments

beta

The type II error.

n

The total sample size.

pDiscordant

The proportion of discordant pairs (xi = pi01 + pi10).

riskDiff

The risk difference between the active and control treatments (delta = pi_t - pi_c = pi01 - pi10)

nullVariance

Whether to use the variance under the null or the variance under the alternative.

rounding

Whether to round up sample size. Defaults to 1 for sample size rounding.

kMax

The maximum number of stages.

informationRates

The information rates. Fixed prior to the trial. Defaults to (1:kMax) / kMax if left unspecified.

efficacyStopping

Indicators of whether efficacy stopping is allowed at each stage. Defaults to true if left unspecified.

futilityStopping

Indicators of whether futility stopping is allowed at each stage. Defaults to true if left unspecified.

criticalValues

Upper boundaries on the z-test statistic scale for stopping for efficacy.

alpha

The significance level. Defaults to 0.025.

typeAlphaSpending

The type of alpha spending. One of the following: "OF" for O'Brien-Fleming boundaries, "P" for Pocock boundaries, "WT" for Wang & Tsiatis boundaries, "sfOF" for O'Brien-Fleming type spending function, "sfP" for Pocock type spending function, "sfKD" for Kim & DeMets spending function, "sfHSD" for Hwang, Shi & DeCani spending function, "user" for user defined spending, and "none" for no early efficacy stopping. Defaults to "sfOF".

parameterAlphaSpending

The parameter value for the alpha spending. Corresponds to Delta for "WT", rho for "sfKD", and gamma for "sfHSD".

userAlphaSpending

The user defined alpha spending. Cumulative alpha spent up to each stage.

futilityBounds

Lower boundaries on the z-test statistic scale for stopping for futility at stages 1, ..., kMax-1. Defaults to rep(-6, kMax-1) if left unspecified. The futility bounds are non-binding for the calculation of critical values.

typeBetaSpending

The type of beta spending. One of the following: "sfOF" for O'Brien-Fleming type spending function, "sfP" for Pocock type spending function, "sfKD" for Kim & DeMets spending function, "sfHSD" for Hwang, Shi & DeCani spending function, "user" for user defined spending, and "none" for no early futility stopping. Defaults to "none".

parameterBetaSpending

The parameter value for the beta spending. Corresponds to rho for "sfKD", and gamma for "sfHSD".

userBetaSpending

The user defined beta spending. Cumulative beta spent up to each stage.

spendingTime

A vector of length kMax for the error spending time at each analysis. Defaults to missing, in which case, it is the same as informationRates.

Details

Consider a group sequential design for McNemar's test for paired proportions. The table below shows joint probabilities for each cell (\pi_{ij} where i is for control group and j is for experimental group), with marginal totals.

Experimental: No Response Experimental: Response Row Total
Control: No Response \pi_{00} \pi_{01} 1-\pi_c
Control: Response \pi_{10} \pi_{11} \pi_c
Column Total 1-\pi_t \pi_t 1

The parameters \pi_{01} and \pi_{10} are the discordant pairs (i.e., \pi_{01} + \pi_{10} = \xi) and the risk difference is \pi_{01} - \pi_{10} = \delta. The parameter \pi_t is the proportion of experimental group response, and \pi_c is the proportion of control group response. The parameter of interest is

\theta = \pi_t - \pi_c = \pi_{01} - \pi_{10} = \delta

The variance of \hat{\theta} can be obtained from the multinomial distribution as follows:

Var(\hat{\theta}) = \frac{1}{n} \{ \pi_{01}(1-\pi_{01}) + \pi_{10}(1-\pi_{10}) + 2\pi_{01}\pi_{10} \}

which can be simplified to

Var(\hat{\theta}) = \frac{1}{n} (\xi - \delta^2)

Here, n is the total number of treatment pairs. This is the unconditional variance, which is used for the overall design.

Value

An S3 class designPairedPropMcNemar object with three components:

Author(s)

Kaifeng Lu, kaifenglu@gmail.com

Examples


# Example 1: fixed design
(design1 <- getDesignPairedPropMcNemar(
  beta = 0.1, n = NA, pDiscordant = 0.16, riskDiff = 0.1,
  alpha = 0.025))

# Example 2: group sequential design
(design2 <- getDesignPairedPropMcNemar(
  beta = 0.1, n = NA, pDiscordant = 0.16, riskDiff = 0.1,
  alpha = 0.025, kMax = 3, typeAlphaSpending = "sfOF"))


[Package lrstat version 0.2.15 Index]