Exposure-response estimate with a bootstrap sensitivity interval

Fits the partially linear exposure-response model with plrcf (or any estimator with the same interface), then re-fits it on nboot non-parametric resamples of the rows for a percentile interval (Efron and Tibshirani 1993, chapter 13). The bootstrap interval does not lean on the estimator's own standard error, so it is a check on it: when the two disagree, the analytic one should not be trusted alone.

Usage

exprspplr(data, y, expo, confs, nboot = 100L, rstate = 42L, estr = plrcf)

Arguments

data: A data frame with one row per unit.
y, expo, confs: Column names: the outcome and the exposure (single strings) and the confounders (one or more strings).
nboot: Number of resamples, a non-negative whole number (default 100); at least 10 must succeed.
rstate: Seed for the resampling (default 42).
estr: A function (data, outcome, treatment, covariates) returning a list with ate and se. The default is plrcf; rmorie's morie_estimate_double_ml() has the same interface.

Value

A list of class c("rmbl_plr_boot", "list") (its print method shows it as a box) with ate (the full-sample estimate), seana (the estimator's standard error), seboot (the standard deviation of the replicates), cilobs and ciupbs (the 95% percentile interval), nboot (the number of successful resamples) and method (the estimator's method with " + percentile bootstrap").

Details

Each resample draws nrow(data) rows with replacement and calls estr(resample, outcome, exposure, confounders); a resample on which the estimator fails is skipped, and the run stops if fewer than 10 succeed. The interval is the 2.5% and 97.5% type-7 quantiles of the replicate estimates, and seboot their standard deviation. Resampling uses rstate and restores R's own random stream afterwards. The cost is nboot + 1 estimator calls; with plrcf at n = 20000 and 100 resamples that is a few seconds. A progress bar on stderr follows the resamples when a person is watching (options(morie.progress = TRUE) outside an interactive session; options(morie.quiet = TRUE) silences it).

Refusals: column names that are not strings, an nboot that is not a single non-negative whole number, an estimator that is not a function, and the estimator's own errors on the full sample.

References

Efron, B. and Tibshirani, R. J. (1993). An Introduction to the Bootstrap. Chapman and Hall.

Examples

set.seed(1)
d <- data.frame(x1 = rnorm(200), x2 = rnorm(200))
d$exposure <- 20 + 2 * d$x1 + rnorm(200)
d$asthma <- 5 + 0.3 * d$exposure + d$x2 + rnorm(200)
r <- exprspplr(d, y = "asthma", expo = "exposure",
                           confs = c("x1", "x2"), nboot = 20)
r$ate
#> [1] 0.2536464
c(r$cilobs, r$ciupbs)
#> [1] 0.1365177 0.3476568

# Any estimator with the same interface: here an ordinary regression.
ols <- function(data, outcome, treatment, covariates) {
  f <- stats::reformulate(c(treatment, covariates), outcome)
  cf <- summary(stats::lm(f, data = data))$coefficients
  list(ate = cf[treatment, 1], se = cf[treatment, 2], method = "OLS")
}
exprspplr(d, "asthma", "exposure", c("x1", "x2"),
                      nboot = 20, estr = ols)$method
#> [1] "OLS + percentile bootstrap"

# Fewer than 10 resamples cannot give an interval.
try(exprspplr(d, "asthma", "exposure", c("x1", "x2"), nboot = 5))
#> Error : Only 5 successful bootstrap fits; need >=10. Inspect the model's convergence on your resamples.