Generate Treatment Permutations

Description

Used within calls to pcr to generate a set of unique treatment permutations for randomization.

Usage

genPerms(n, n1, nPerms)

Arguments

Details

This function randomly samples nPerms of the choose(n, n1) possible treatment permutations. If nPerms > choose(n, n1), then all choose(n, n1) permutations are generated systematically. Also, in the case of 1-to-1 allocation, the complement treatment vectors are also produced, so the returned matrix has 2*nPerms permutations. Uniqueness is checked throughout and duplicate permutations disgarded.

Value

The result is an n1 x nPerms (or n1 x choose(n, n1) or n1 x 2*nPerms) matrix. Each column represents one treatment permutation, with the values in the column giving the index of the treated units.

Author(s)

Travis M. Loux

Examples

genPerms(n=50, n1=25, nPerms=500)
genPerms(n=50, n1=35, nPerms=500)

Compute Propensity Score Variance

Description

Given a data set and vector of indices for treated units, computes the variance of the propensity score fitted via logistic regression.

Usage

getVar(covs, tIndex)

Arguments

Value

Returns the variance of the fitted propensity scores.

Author(s)

Travis M. Loux

Propensity-Biased Allocation

Description

Performs propensity-biased allocation for assigning a new unit to treatment in a sequential design with two treatment levels (i.e., treatment and control).

Usage

pba(x, tr, newx, k = 1, global = 0.5)
pbaAgain(previous, newx, k = NA)

Arguments

Details

The function pba generates a treatment assignment for a new unit. The steps of the process include regressesing tr on x by logistic regression, computeing the fitted value of the new unit using covarate values in newx, and transforming the fitted propensity score into the probability of treatment by a call to piFunction using k and global as parameters. The balancing parameter k must be one of 0, Inf, or the ratio of two positive odd integers. Small values of k result in less restrictive randomization while larger values of k result in more forced balance. In particular, k = 0 is equivalent to pure randomization and k = Inf results in deterministic allocation. Finally, a treatment assignment for the new unit is generated via a Bernoulli trial with probability from piFunction.

The function pbaAgain takes as input the output from a previous call to pba or pbaAgain and runs pba for the new unit using the values of newx. If k = NA (the default), the value of k from previous is used; otherwise, the provided value of k is used. The parameter global is assumed to stay the same throughout the trial. The output of pbaAgain contains the same information as pba.

Value

Author(s)

Travis Loux

References

Loux, T.M. (2013) A simple, flexible, and effective covariate-adaptive treatment allocation procedure. Statistics in Medicine 32(22), 3775-3787. DOI: 10.1002/sim.5837

Examples

x0 = data.frame(matrix(rnorm(60), ncol=3))
t0 = rbinom(nrow(x0), size=1, prob=0.5)

x1 = data.frame(matrix(rnorm(3), ncol=3))
trial1 = pba(x=x0, tr=t0, newx=x1, k=Inf)

x2 = data.frame(matrix(rnorm(3), ncol=3))
trial2 = pbaAgain(previous=trial1, newx=x2)

x3 = data.frame(matrix(rnorm(3), ncol=3))
trial3 = pbaAgain(previous=trial2, newx=x3, k=5/3)

Propensity-Constrained Randomization

Description

Performs propensity-contstrained randomization on a given data set with measured covariates on all units.

Usage

pcr(x, nTreat, M, m)

Arguments

Details

Given the parameters, pcr generates M unique permutations by calling genPerms. For each permutation, the empirical propensity scores are computed and the variance returned by getVar. Finally, the m permutations with the smallest propensity score variance are found. The m permutations returned in best can then be used to perform randomization and randomization inference. We suggest M >= 10000 and m/M <= 0.10.

Value

Author(s)

Travis Loux

References

Loux, T.M. (2015) Randomization, matching, and propensity scores in the design and analysis of experimental studies with known covariates. Statistics in Medicine. 34(4), 558-570. DOI: 10.1002/sim.6361

Examples

# 1:1 allocation, M small
dat1 = data.frame(x1=rnorm(50),
                  x2=rnorm(50),
                  x3=sample(c('a','b','c'), size=50, replace=TRUE))
trial1 = pcr(x=dat1, nTreat=25, M=500, m=50)

# 1:1 allocation, M large
dat2 = data.frame(x1=rnorm(10),
                  x2=rnorm(10),
                  x3=sample(c('a','b','c'), size=10, replace=TRUE))
trial2 = pcr(x=dat2, nTreat=5, M=200, m=20)

# non-1:1 allocation, M small
dat3 = data.frame(x1=rnorm(50),
                  x2=rnorm(50),
                  x3=sample(c('a','b','c'), size=50, replace=TRUE))
trial3 = pcr(x=dat3, nTreat=35, M=200, m=20)

# non-1:1 allocation, M large
dat4 = data.frame(x1=rnorm(10),
                  x2=rnorm(10),
                  x3=sample(c('a','b','c'), size=10, replace=TRUE))
trial4 = pcr(x=dat4, nTreat=6, M=300, m=30)

Get PBA Treatment Probability

Description

Used within calls to pba and pbaAgain to obtain the probability a unit is assigned treatment given its fitted propensity score.

Usage

piFunction(fit, kparam, qparam)

Arguments

Details

The input kparam must be one of 0, Inf, or the ratio of two positive odd integers. Both fit and qparam must be between 0 and 1.

Value

A numeric object. In the conext of PBA, the probability of assignment to treatment for the current unit.

Author(s)

Travis M. Loux

Examples

piFunction(fit=0.6, kparam=1, qparam=0.5)
piFunction(fit=0.6, kparam=5, qparam=0.5)
piFunction(fit=0.6, kparam=1/5, qparam=0.5)

piFunction(fit=0.6, kparam=1, qparam=2/3)
piFunction(fit=0.6, kparam=5, qparam=2/3)
piFunction(fit=0.6, kparam=1/5, qparam=2/3)

Plots of piFunction

Description

Can be used to investigate the strength of balance forced by various values of the tuning parameter k.

Usage

plotpi(k, global = 0.5)
addpi(k, global = 0.5, ...)

Arguments

Details

The function plotpi creates a plot of treatment probability against fitted propensity score for values of k and global. The function addpi adds a curve for a new combination of k and global to an existing plot.

Author(s)

Travis M. Loux

Examples

plotpi(k=3, global=0.5)
addpi(k=5/3, lty=2, col='red')
plotpi(k=1/3, global=2/3)