| Title: | Propensity Score Methods for Assigning Treatment in Randomized Trials |
|---|---|
| Description: | Contains functions to run propensity-biased allocation to balance covariate distributions in sequential trials and propensity-constrained randomization to balance covariate distributions in trials with known baseline covariates at time of randomization. Currently only supports trials comparing two groups. |
| Authors: | Travis Loux |
| Maintainer: | Travis Loux <[email protected]> |
| License: | GPL-3 |
| Version: | 1.1.2 |
| Built: | 2025-03-03 04:02:13 UTC |
| Source: | https://github.com/tloux/propscrrand |
Used within calls to pcr to generate a set of unique treatment permutations for randomization.
genPerms(n, n1, nPerms)genPerms(n, n1, nPerms)
n |
Total number of units to be randomized. |
n1 |
Number of units to receive treatment. |
nPerms |
Number of permutations to generate. |
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.
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.
Travis M. Loux
genPerms(n=50, n1=25, nPerms=500) genPerms(n=50, n1=35, nPerms=500)genPerms(n=50, n1=25, nPerms=500) genPerms(n=50, n1=35, nPerms=500)
Given a data set and vector of indices for treated units, computes the variance of the propensity score fitted via logistic regression.
getVar(covs, tIndex)getVar(covs, tIndex)
covs |
A data frame of baseline covariates. |
tIndex |
A vector indicating which units are to receive treatment. |
Returns the variance of the fitted propensity scores.
Travis M. Loux
Performs propensity-biased allocation for assigning a new unit to treatment in a sequential design with two treatment levels (i.e., treatment and control).
pba(x, tr, newx, k = 1, global = 0.5) pbaAgain(previous, newx, k = NA)pba(x, tr, newx, k = 1, global = 0.5) pbaAgain(previous, newx, k = NA)
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 |
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.
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 |
input |
A list of inputs to PBA procdure. Used in future calls to |
x |
Input |
tr |
Input |
newx |
Input |
k |
Input |
global |
Input |
Travis Loux
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
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)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)
Performs propensity-contstrained randomization on a given data set with measured covariates on all units.
pcr(x, nTreat, M, m)pcr(x, nTreat, M, m)
x |
Data frame of covariates. |
nTreat |
Number of units to be treated. |
M |
Number of candidate permutations to create. |
m |
Number of permutations to keep. |
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.
treatments |
The (approximately) |
variance |
A vector of the propensity score variances for all |
cutoff |
The calculated |
best |
The column indices of the permutations in |
Travis Loux
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
# 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)# 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)
Used within calls to pba and pbaAgain to obtain the probability a unit is assigned treatment given its fitted propensity score.
piFunction(fit, kparam, qparam)piFunction(fit, kparam, qparam)
fit |
Fitted propensity score. |
kparam |
Balancing parameter. |
qparam |
Global target for proportion of units treated. |
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.
A numeric object. In the conext of PBA, the probability of assignment to treatment for the current unit.
Travis M. Loux
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)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)
Can be used to investigate the strength of balance forced by various values of the tuning parameter k.
plotpi(k, global = 0.5) addpi(k, global = 0.5, ...)plotpi(k, global = 0.5) addpi(k, global = 0.5, ...)
k |
Balancing parameter. |
global |
Global target for proportion of units treated. |
... |
Parameters in |
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.
Travis M. Loux
plotpi(k=3, global=0.5) addpi(k=5/3, lty=2, col='red') plotpi(k=1/3, global=2/3)plotpi(k=3, global=0.5) addpi(k=5/3, lty=2, col='red') plotpi(k=1/3, global=2/3)