Exposure-response estimate with a bootstrap sensitivity interval

Fits the partially linear exposure-response model with plr_crossfit (or any estimator with the same interface), then re-fits it on n_bootstrap 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

exposure_response_plr(
  data,
  outcome,
  exposure,
  confounders,
  n_bootstrap = 100L,
  random_state = 42L,
  estimator = plr_crossfit
)

Arguments

data

A data frame with one row per unit.

outcome, exposure, confounders

Column names: the outcome and the exposure (single strings) and the confounders (one or more strings).

n_bootstrap

Number of resamples, a non-negative whole number (default 100); at least 10 must succeed.

random_state

Seed for the resampling (default 42).

estimator

A function (data, outcome, treatment, covariates) returning a list with ate and se. The default is plr_crossfit; rmorie's morie_estimate_double_ml() has the same interface.

Value

A list with ate (the full-sample estimate), se_analytic (the estimator's standard error), se_bootstrap (the standard deviation of the replicates), ci_lower_bs and ci_upper_bs (the 95% percentile interval), n_bootstrap (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 estimator(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 se_bootstrap their standard deviation. Resampling uses random_state and restores R's own random stream afterwards. The cost is n_bootstrap + 1 estimator calls; with plr_crossfit 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 n_bootstrap 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.

See also

core_bootstrap_mean for a bootstrap of a mean.

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$x2 + rnorm(200)
r <- exposure_response_plr(d, outcome = "asthma", exposure = "exposure",
                           confounders = c("x1", "x2"), n_bootstrap = 20)
r$ate
#> [1] 0.2536464
c(r$ci_lower_bs, r$ci_upper_bs)
#> [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))$coefficients
  list(ate = cf[treatment, 1], se = cf[treatment, 2], method = "OLS")
}
exposure_response_plr(d, "asthma", "exposure", c("x1", "x2"),
                      n_bootstrap = 20, estimator = ols)$method
#> [1] "OLS + percentile bootstrap"

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