Non-inferiority Tests with Variable Margins

Description

This package was developed to give the control quantile non-inferiority test described in Fay and Follmann (2015), and the function to calculate that test is nicqTest. Some competitors to that test are some tests described in Rohmel and Kieser (2013): brkTest, fmecTest, and fmecExact.

Details

Author(s)

Michael P. Fay

Maintainer: Michael P. Fay <mfay@niaid.nih.gov>

References

Fay, MP and Follmann DA (2016). Non-inferiority Tests for Anti-Infective Drugs using Control Group Quantiles. Clinical Trials. 13(6): 632-640.

Rohmel, J and Kieser, M (2013). Investigations on non-inferiority–the Food and Drug Administration draft guidance on treatments for nosocomial pneumonia as a case for exact tests for binomial proportions. Statistics in Medicine. 32: 2335-2348.

See Also

nicqTest

Arguments for Algorithm Control for brkTest.

Description

Function that gives a list.

Usage

brkControl(alpha = 0.025, alphastar = 0.001, ngrid = 1000)

Arguments

Value

a list with values names the same as the arguments.

See Also

brkTest

Barnard-Rohmel-Kieser Test

Description

A variable margin difference in proportion test for non-inferiority. The test is based on Barnard's test.

Usage

brkTest(x1, n1, x2, n2, threshold = 0.2, delta = 0.1, control = brkControl())

Arguments

Details

This test is labeled T4 in Rohmel and Keiser (2013).

Value

a list of class brk, with elements:

Author(s)

Michael P. Fay

References

Rohmel, J, and Kieser, M (2013). "Investigations on non-inferiority - - the Food and Drug Administration draft guidance on treatments for nosocomial pneumonia as a case for exact tests for binomial proportions" Statistics in Medicine 32:2335-2348.

See Also

See Also nicqTest, ~~~

Examples

x<-brkTest(3,8,0,6)
x
x$FullResults$PVALUES

Get power from brkTest).

Description

Power under an alternative F1 and F2 relationship, represented by a F2=g(F1).

Usage

findPowerR(R, g, psearch = (0:1000)/1000)

Arguments

Odds Ratio/Difference Non-inferiority tests

Description

Rohmel and Keier (2013) developed these non-inferioirty tests with variable margins. One margin function, NiM3, has the variable margin measuring a constant difference in proportions (0.10 in paper) after a threshold (0.20 proportion in the control group), or tests for differences defined in terms of a constant odds ratio (1.71 in paper) at values less than the threshold. The fmecTest with type='max' gives the maximum of two p-values, either a difference in proportions test (one-sided asymptotic method of Farrington and Manning, 1990) or an odds ratio test (one-sided Fisher's exact). This test is NiM3/T2 in Rohmel and Keier (2013). We also provide an exact version of this test with fmecExact, denoted NiM3/T3 in Rohmel and Keier (2013). When type='switch' the tests are like T1 of Rohmel and Keier (2013).

Usage

fmecTest(x1, n1, x2, n2, threshold = 0.2, delta = 0.1,
    alternative = c("less","greater"), 
    type = c("max", "switch"))

fmecExact(x1, n1, x2, n2, threshold = 0.2, delta = 0.1, 
    alternative = c("less", "greater"), 
    type = c("max", "switch"), ngrid = 1000)

Arguments

Details

For details see Rohmel and Keier (2013, Section 3). These functions only use NiM3.

Value

a list of class 'htest':

Author(s)

Michael P. Fay

References

Farrington, CP and Manning G (1990). "Test statistics and sample size formulae for comparative binomial trials with null hypothesis of non-zero risk difference or non-unit relative risk" Statistics in Medicine 9:1447-1454.

Rohmel, J, and Kieser, M (2013). "Investigations on non-inferiority - - the Food and Drug Administration draft guidance on treatments for nosocomial pneumonia as a case for exact tests for binomial proportions" Statistics in Medicine 32:2335-2348.

See Also

nicqTest

Examples

fmecTest(6,10,2,12,alternative="less",type="max")
fmecExact(6,10,2,12,alternative="less",type="max")

Internal functions used for tests from Rohmel and Kieser ( fmecTest, fmecExact, and brkTest).

Description

Not to be called directly.

Usage

brkCalc(n1, n2, threshold, delta, g = nimDiffOR, 
    alpha = 0.025, alphastar = 0.001, ngrid = 1000)

EC(X1, X2, M1, M2, or = 1.71, alternative = c("less", "greater", "two.sided"))

FarrMann(X1, X2, M1, M2, delta0, 
    alternative = c("less", "greater", "two.sided"), 
    fudgeDigits = 8)

findPower(ir, jr, n1, n2, psearch, qsearch)

getfij(n1, n2, p, q)

getieje(ir, jr)

getij(R)

getPossibleR(ie, je, n1, n2, decreasei = TRUE, increasej = TRUE)
getpadd(i, j, n1, n2, psearch, qsearch)
getR(i, j, n1, n2)

Details

Fill in details later. For now see code.

Internal functions for nicqTest.

Description

Usually not directly called, called by nicqTest.

Usage

getfx2(i, n1, n2, g, slowint = FALSE, mint = 100, interr = 10^-3)
nicqCalc(X2T1i,g,i0,n1,n2,delta0=.10,q0=.20,
    conf.int=TRUE,
    conf.level=0.95,
    conf.sided=c("two.sided","one.sided"), alternative="less",
    control=nicqControl())

nicqGetpvalue(X2T1i,n1,n2,g,i0,alternative="less",
control=nicqControl())

Arguments

Details

The function getfx2 gets probability mass function for x2=number of failures in the test group at or before the ith failure in the control group. Uses very simple numeric integration (slowint=FALSE) that just adds mint trapazoids (rectangles with triangle tops).

Value

vector of probabilities for all possible x2 values, forced to sum to 1.

Get i that maiximizes power when F1=F2 for a specified g function

Description

Usually not directly called, called by nicqTest.

Usage

getimaxpower(n1, n2, g, alpha = 0.05, rdig = 5, maxprop=1, alt="less", ...)

Arguments

Value

the i value

Function that returns a list of algorithm controls for nicq

Description

Controls for numeric integration, etc. Mostly used in getfx2 that is called by nicqTest.

Defined as a function instead of a list, so sanity checks can be built in (but none have been included yet).

Usage

nicqControl(rdig = 5, slowint = FALSE, mint = 100, 
    interr = 10^-3,  epsilon=10^(-4), alpha = 0.025,
    tau.conf.level=0.95)

Arguments

Value

a list with each argument as a named value

See Also

nicqTest

Non-inferiority control quantile test

Description

Tests for a difference in proportion of failures between test and control by the time the qth quantile of the contol group has failed. Uses a variable margin function, and the time of the qth quantile of the control group is unknown.

If the cumulative distributions for the two groups are F1 (control) and F2 (test), then we are interested in the difference: delta=F2(t0)-F1(t0), where F1(t0)=q. Note F1,F2 are unknown and non-parametric, and t0 is unknown. In this case, using a constant delta does not give practical non-inferiority margins, therefore we use a variable margin function, so that we test (when alternative='less') H0: F2(t) >= g(F1(t)) versus H1: F2(t) < g(F1(t)) for all t.

The test also works for other types of continuous responses besides time to failure (see details), but the help description uses time to failure for brevity.

Usage

nicqTest(x,delta0,q,g=nimDiffOR,yc=NULL,nc=NULL,nt=NULL,
    ic="prop",
    z=NULL,status=NULL,ties=c("cons","approx"),
    alternative=c("less","greater"),
    conf.level=0.95,
    conf.int=TRUE,
    conf.sided=c("two.sided","one.sided"), 
    gname=NULL,
    control=nicqControl())

Arguments

Details

The data may be entered in 3 different formats, and the first argument x changes depending on which format. When z is given then x is the vector of failure times from both groups and z gives the group membership of each of those failures. If there is right censoring this may be given using status, and the nicq function will make sure that the censoring happens late enough so that the test can still be calculated. When yc is given then x is a vector of failure times in the test group and yc are the failure times in the control group. When ic is an integer, then x represents the number of failure times that have occurred in the test group at or before the time of the icth failure in the control group. In this last format only nc (number in control group) and nt (number in the test group) must be given.

The confidence interval is calculated on the difference, F2(t0)-F1(t0), where t0 is unknonwn and defined so that F1(t0)=q, with q given.

The responses can be any numeric values, as long as the difference, F2(t0)- F1(t0), is of interest.

For more details see Fay and Follmann (2015).

The confidence intervals for the qth quantile of the control is calculated using the bpcp function followed by the quantile.kmciLR from the bpcp R package.

Value

An nicq object which inherits from htest class (the print method for is slightly different). A list with elements:

warning

Since 'two.sided' alternatives are not allowed, the p-values may not match the confidence intervals in the usual way if conf.sided='two.sided' (the default). Consider the example below, with alternative='less' and delta0=0.10. The p-value is 0.04, so we might expect that the upper limit of the 95 percent confidence limit would be less than 0.10, but this is not so because conf.sided='two.sided' and we are using the two-sided confidence interval and p is greater than 0.05/2=0.025.

Author(s)

Michael P. Fay (mfay@niaid.nih.gov)

References

Fay, MP and Follmann DA (2016). Non-inferiority Tests for Anti-Infective Drugs using Control Group Quantiles. Clinical Trials. 13(6): 632-640.

Examples

## if you know that q=0.20 and there are no ties then ic=q*nc=40 
nicqTest(66,g=nimDiffOR,delta0=.1,q=.2,nc=200,nt=300,ic=40,conf.int=FALSE)
## examples with confidence intervals may be slower: see
##  demo(nicqTest.examples)

Variable margin functions

Description

For testing the alternative F2(t)< g(F1(t)). We give several built-in choices for the function g. All functions must be defined in terms of delta and q, where F1(t0)=q and t0 is defined implicitly, and delta = F2(t0) - g(F1(t0)).

Usage

nimDiffOR(p, delta = 0.1, q = 0.2)
nimOR(p, delta=0.1, q=0.2)
nimDiff(p,delta=.1, q=NULL)

Arguments

Details

The functions are defined in terms of delta and q so that the function can change as a function of delta and we can use the function to get confidence intervals for delta (defined in terms of q, since q=F1(t0) which defines t0).

Functions should handle vectors of F1(t) values, and the output is a vector of the same length. The results should be between 0 and 1.

The function nimDiffOR gives the minimum of the difference (defined by delta) or the odds ratio (defined in terms of q and delta) when delta>0, and the maximum when delta<0.

For plots of the functions see Fay and Follmann (2015).

Value

a vector of values g(F1(t)).

References

Fay, MP and Follmann DA (2016). Non-inferiority Tests for Anti-Infective Drugs using Control Group Quantiles. (to appear in Clinical Trials).

See Also

nicqTest

Examples

## notice that the second values, F1(t)=0.20=q, 
## all equal 
##  q+delta=0.30
nimDiff(c(1:9)/10)
nimOR(c(1:9)/10)
nimDiffOR(c(1:9)/10)
## for delta<0, take max of difference and odds ratio
nimDiffOR(c(1:9)/10,delta=-.1)

Power or Sample Size for Non-inferiority Control Quantile Test

Description

Function gives power (if n1=NULL) or sample size (if power=NULL). Assumes no ties.

Usage

powerNicqTest(n1 = NULL, n2 = NULL, power = NULL, 
    sig.level = 0.025, n2.over.n1 = 1, q = 0.2, 
    delta0 = 0.1, alternative = c("less", "greater"), 
    gnull = nimDiffOR, galt = function(x){x}, 
    minn=5, maxn = 10^5, ...)

Arguments

Details

The function either calculates the power (if n1=NULL) or calculates n1 and n2 (if power=NULL). In the latter case, we use uniroot.integer to find the smallest n1 that gives power at least as large as the given power [with n2 defined as ceiling(n2.over.n1*n1)].

Value

a power.htest object. A list with elements:

See Also

nicqTest

Examples

# to calculate power, leave power=NULL and supply n1 and n2
powerNicqTest(n1=200,n2=300)
# or supply n1 and n2.over.n1
powerNicqTest(n1=200,n2.over.n1=3/2)
## to calculate n1 and n2, supply power
## find minimum n1 that have power greater than 0.80
## takes 13 iterations to find n1=346
## so do not run it here
#powerNicqTest(power=.80,print.steps=TRUE)

Print Method for brk or nicq Object.

Description

For brk did not use print.htest because the p-values are just bounds for some values (e.g., p greater than 0.025). So I needed to print the results differently.

For nicq, uses print.htest except for $estimates has some special printing instructions since there may be some extra confidence intervals on the control quantile of interest.

Usage

## S3 method for class 'brk'
print(x, digits = getOption("digits"), prefix = "\t", ...)

## S3 method for class 'nicq'
print(x, ...)

Arguments

Value

Does not print out FullResults list because it is generally too large.