check.overlap function

Check propensity score overlap

Results in a plot to check whether the propensity score has adequate overlap between treatment groups

check.overlap(
  x,
  trt,
  propensity.func,
  type = c("histogram", "density", "both"),
  bins = 50L,
  alpha = ifelse(type == "both", 0.35, 0.5)
)

Arguments

• x: The design matrix (not including intercept term)
• trt: treatment vector with each element equal to a 0 or a 1, with 1 indicating treatment status is active.
• propensity.func: function that inputs the design matrix x and the treatment vector trt and outputs the propensity score, ie Pr(trt = 1 | X = x). Function should take two arguments 1) x and 2) trt. See example below. For a randomized controlled trial this can simply be a function that returns a constant equal to the proportion of patients assigned to the treatment group, i.e.: propensity.func = function(x, trt) 0.5.
• type: Type of plot to create. Options are either a histogram (type = "histogram") for each treatment group, a density (type = "density") for each treatment group, or to plot both a density and histogram (type = "code")
• bins: integer number of bins for histograms when type = "histogram"
• alpha: value between 0 and 1 indicating transparency level (1 for solid, 0 for fully transparent)

Examples

library(personalized)

set.seed(123)
n.obs  <- 250
n.vars <- 15
x <- matrix(rnorm(n.obs * n.vars, sd = 3), n.obs, n.vars)

# simulate non-randomized treatment
xbetat   <- 0.25 + 0.5 * x[,11] - 0.5 * x[,12]
trt.prob <- exp(xbetat) / (1 + exp(xbetat))
trt01    <- rbinom(n.obs, 1, prob = trt.prob)

# create function for fitting propensity score model
prop.func <- function(x, trt)
{
    # fit propensity score model
    propens.model <- cv.glmnet(y = trt,
                               x = x, family = "binomial")
    pi.x <- predict(propens.model, s = "lambda.min",
                    newx = x, type = "response")[,1]
    pi.x
}

check.overlap(x = x,
              trt = trt01,
              propensity.func = prop.func)

# now add density plot with histogram
check.overlap(x = x,
              trt = trt01,
              type = "both",
              propensity.func = prop.func)

# simulated non-randomized treatment with multiple levels
xbetat_1   <- 0.15 + 0.5 * x[,9] - 0.25 * x[,12]
xbetat_2   <- 0.15 - 0.5 * x[,11] + 0.25 * x[,15]
trt.1.prob <- exp(xbetat_1) / (1 + exp(xbetat_1) + exp(xbetat_2))
trt.2.prob <- exp(xbetat_2) / (1 + exp(xbetat_1) + exp(xbetat_2))
trt.3.prob <- 1 - (trt.1.prob + trt.2.prob)
prob.mat <- cbind(trt.1.prob, trt.2.prob, trt.3.prob)
trt    <- apply(prob.mat, 1, function(rr) rmultinom(1, 1, prob = rr))
trt    <- apply(trt, 2, function(rr) which(rr == 1))

# use multinomial logistic regression model with lasso penalty for propensity
propensity.multinom.lasso <- function(x, trt)
{
    if (!is.factor(trt)) trt <- as.factor(trt)
    gfit <- cv.glmnet(y = trt, x = x, family = "multinomial")

    # predict returns a matrix of probabilities:
    # one column for each treatment level
    propens <- drop(predict(gfit, newx = x, type = "response", s = "lambda.min",
                            nfolds = 5, alpha = 0))

    # return the probability corresponding to the
    # treatment that was observed
    probs <- propens[,match(levels(trt), colnames(propens))]

    probs
}

check.overlap(x = x,
              trt = trt,
              type = "histogram",
              propensity.func = propensity.multinom.lasso)