psmatch {psBayesborrow}

Propensity score matching

Description

Propensity score matching is implemented to select external controls who are more relevant to patients in the current trial with respect to covariates of interest.

Usage

psmatch(
  formula, data, n.EC,
  method.psest="glm", method.pslink="logit",
  method.whomatch, method.matching, method.psorder, n.boot=100)

Arguments

formula

Object of class formula, which is a symbolic description of the propensity score model to be fitted. The dependent variable must be named study. The explanatory variables only include covariates of interest, which must be specified in the form of linear combination.

data

Data frame, which must contain variables named study for study indicator (0 for external control, and 1 for current trial) and treat for treatment indicator (0 for concurrent and external control, and 1 for treatment).

n.EC

Number of patients in external control to be selected, which must be smaller than the number of patients in external control pool.

method.psest

Method of estimating the propensity score. Allowable options include, for example, "glm" for generalized linear model (e.g., logistic regression); "gam" for generalized additive model; "gbm" for generalized boosted model; "lasso" for lasso regression; "rpart" for classification tree. The default value is method.psest="glm".

method.pslink

Link function used in estimating the propensity score. Allowable options depend on the specific method.psest value specified. The default value is method.pslink="logit", which, along with method.psest="glm", identifies the default method as logistic regression.

method.whomatch

Options of who to match. Allowable options include conc.contl for matching concurrent control to external control pool; conc.treat for matching treatment to external control pool; conc.all for matching treatment plus concurrent control to external control pool; treat2contl for matching treatment to concurrent control plus external control pool.

method.matching

Propensity score matching method. Allowable options include "optimal" for optimal matching; "nearest" for nearest neighbor matching without replacement; "med.optimal" for equally splitting patients in the current trial and taking the median of each subset, followed by 1:1 optimal matching; "med.nearest" for equally splitting patients in the current trial and taking the median of each subset, followed by 1:1 nearest neighbor matching without replacement; "km.optimal" for k-means clustering of patients in the current trial, followed by 1:1 optimal matching; "km.nearest" for k-means clustering of patients in the current trial, followed by 1:1 nearest neighbor matching without replacement; "cm.optimal" for fuzzy c-means clustering of patients in the current trial, followed by 1:1 optimal matching; "cm.nearest" for fuzzy c-means of patients in the current trial, followed by 1:1 nearest neighbor matching without replacement; "boot.optimal" for bootstrap sampling from patients in the current trial, followed by 1:1 optimal matching; "boot.nearest" for bootstrap sampling from patient in the current trial, followed by 1:1 nearest neighbor matching without replacement.

method.psorder

Order that the matching takes place when a nearest neighbor matching is used. Allowable options include "largest", where matching takes place in descending order of propensity score; "smallest", where matching takes place in ascending order of propensity score; "random", where matching takes place in a random order; "data", where matching takes place based on the order of units in the data. The matching order must be specified when using the nearest neighbor matching.

n.boot

Number of bootstrap sampling, which must be specified when method.matching="boot.optimal" or method.matching="boot.nearest". The default value is n.boot=100.

Details

The propensity score is defined as the conditional probability of having been included in the current trial given observed covariates. There are four options applicable for to whom the patients in external control pool are matched, including (i) concurrent control versus external control pool ("conc.contl"), (ii) treatment versus external control pool ("conc.treat"), (iii) treatment plus concurrent control versus external control pool ("conc.all"), and (iv) treatment versus concurrent control plus external control pool ("treat2contl"). Along with method.whomatch="conc.contl", two 1:1 matching methods are applicable: (1) optimal matching ("optimal"), and (2) nearest neighbor matching without caliper ("nearest"). Along with method.whomatch="conc.treat" or method.whomatch="conc.all", ten matching methods are applicable: (1) optimal matching, where 1:1 matching is first done, followed by random sampling ("optimal"), (2) nearest neighbor matching, where caliper is tuned iteratively to obtain the fixed number of external controls ("nearest"), (3) equally splitting patients in the current trial and taking the median of each subset, followed by 1:1 optimal matching ("medm.optimal"), (4) equally splitting patients in the current trial and taking the median of each subset, followed by 1:1 nearest neighbor matching matching ("med.nearest"), (5) k-means clustering of patients in the current trial, followed by 1:1 optimal matching ("km.optimal"), (6) k-means clustering of patients in the current trial, followed by 1:1 nearest neighbor matching ("km.nearest"), (7) fuzzy c-means clustering of patients in the current trial, followed by 1:1 optimal matching ("cm.optimal"), (8) fuzzy c-means of patients in the current trial, followed by 1:1 nearest neighbor matching ("cm.nearest"), (9) bootstrap sampling from patients in the current trial, followed by 1:1 optimal matching ("boot.nearest"), and (10) bootstrap sampling from patient in the current trial, followed by 1:1 nearest neighbor matching ("boot.nearest"). Along with method.whomatch="treat2contl", two matching methods are applicable: (1) optimal matching, followed by random sampling ("optimal"), and (2) nearest neighbor matching, where caliper is tuned iteratively to obtain the fixed number of external controls ("nearest").

Value

The psmatch returns a list containing the following objects:

subjid.EC

Vector of subject ID of external control.

data.ps

Data frame with estimated propensity score.

References

Austin PC. A comparison of 12 algorithms for matching on the propensity score. Statistics in Medicine 2014; 33:1057-1069.

Lin J, Gamalo-Siebers M, Tiwari R. Propensity score matched augmented controls in randomized clinical trials: A case study. Pharmaceutical Statistics 2018; 17:629-647.

Lin J, Gamalo-Siebers M, Tiwari R. Propensity-score-based priors for Bayesian augmented control design. Pharmaceutical Statistics 2019; 18:223-238.

Rosenbaum PR. Optimal matching for observational studies. Journal of the American Statistical Association 1989; 84:1024-1032.

Sawamoto R, Oba K, Matsuyama Y. Bayesian adaptive randomization design incorporating propensity score-matched historical controls. Pharmaceutical Statistics 2022; 21:1074-1089.

Examples

n.CT       <- 100
n.CC       <- 50
nevent.C   <- 100
n.ECp      <- 1000
nevent.ECp <- 800
accrual    <- 16

out.mevent.CT <- 6
out.mevent.CC <- 6
driftHR       <- 1

cov.C <- list(list(dist="norm",mean=0,sd=1,lab="cov1"),
              list(dist="binom",prob=0.4,lab="cov2"))

cov.cor.C <- rbind(c(  1,0.1),
                   c(0.1,  1))

cov.EC <- list(list(dist="norm",mean=0,sd=1,lab="cov1"),
               list(dist="binom",prob=0.4,lab="cov2"))

cov.cor.EC <- rbind(c(  1,0.1),
                    c(0.1,  1))

cov.effect <- c(0.1,0.1)

indata <- trial.simulation.t2e(
  n.CT=n.CT, n.CC=n.CC, nevent.C=nevent.C,
  n.ECp=n.ECp, nevent.ECp=nevent.ECp, accrual=accrual,
  out.mevent.CT, out.mevent.CC, driftHR,
  cov.C=cov.C, cov.cor.C=cov.cor.C,
  cov.EC=cov.EC, cov.cor.EC=cov.cor.EC, cov.effect=cov.effect)

n.EC <- 50

method.whomatch <- "conc.treat"
method.matching <- "optimal"
method.psorder  <- NULL

psmatch(
  study~cov1+cov2, data=indata, n.EC=n.EC,
  method.whomatch=method.whomatch, method.matching=method.matching,
  method.psorder=method.psorder)