pba {PropScrRand}

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

x

A data frame of the covariate values of previously assigned units.

tr

A vector of treatment assignments (0 or 1) for previously assigned units.

newx

Data frame of covariate values of the new unit.

k

Balancing parameter.

global

Global target proportion to be treated.

previous

The output of a previous call to pba or pbaAgain

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

results

A list of results from the PBA procedure.

phat

The fitted propensity score for the new unit.

ptreat

The probability of assignment to the treatment group for the new unit.

newtr

Result of random assignment using ptreat.

input

A list of inputs to PBA procdure. Used in future calls to pbaAgain.

x

Input x.

tr

Input tr.

newx

Input newx.

k

Input k.

global

Input global.

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)