Sensitivity Analysis

Searches over delta, the sensitivity parameter of estimator_ds_sens, for delta*: the smallest value at which the confidence interval starts to include zero. A delta* near zero means the finding rests on assuming away nearly all of the missingness; a delta* near one means it survives almost any amount. Returns the search, a plot of it, and delta* itself, which is NA when the interval already includes zero under ignorability.

Usage

sensitivity_ds(
  Y,
  Z,
  R1,
  Attempt,
  R2,
  minY,
  maxY,
  sims = 100,
  strata = NULL,
  alpha = 0.05,
  data
)

Arguments

Y

The (unquoted) outcome variable, or a formula outcome ~ treatment. Must be numeric.

Z

The (unquoted) assignment indicator variable. Must be numeric and take values 0 or 1. Ignored when Y is a formula.

R1

The initial sample response indicator: unquoted column name, or a quoted string column name when using the formula interface. Must be numeric and take values 0 or 1.

Attempt

The follow-up attempt indicator: unquoted column name, or quoted string. Must be numeric and take values 0 or 1.

R2

The follow-up response indicator: unquoted column name, or quoted string. Must be numeric and take values 0 or 1.

minY

The minimum possible value of the outcome (Y) variable.

maxY

The maximum possible value of the outcome (Y) variable.

sims

Number of values of delta at which to evaluate the bounds. Defaults to 100.

strata

Stratification variable: unquoted column name or a quoted string column name.

alpha

The desired significance level. 0.05 by default.

data

A dataframe. Must be given by name: data is the last argument, so passing it positionally assigns it to another argument.

Value

An object of class "attrition_sensitivity": a list with three elements, sensitivity_plot, a ggplot object; sims_df, a data frame of bounds and confidence intervals at each value of delta; and delta_star, a single number giving delta*, or NA when no delta* exists, which happens when the confidence interval already contains zero at delta = 0. Printing reports delta*; tidy() returns sims_df.

References

Coppock, Alexander, Alan S. Gerber, Donald P. Green, and Holger L. Kern (2017). Combining Double Sampling and Bounds to Address Nonignorable Missing Outcomes in Randomized Experiments. Political Analysis 25(2):188-206. doi:10.1017/pan.2016.6

Examples

set.seed(343)
N <- 1000
Y_0 <- sample(1:5, N, replace = TRUE, prob = c(0.1, 0.3, 0.3, 0.2, 0.1))
Y_1 <- sample(1:5, N, replace = TRUE, prob = c(0.1, 0.1, 0.4, 0.3, 0.1))
Z <- rbinom(N, 1, 0.5)
Y_star <- Z * Y_1 + (1 - Z) * Y_0
R1 <- rbinom(N, 1, prob = 0.7 + 0.1 * Z)
Y <- Y_star
Y[R1 == 0] <- NA

# Follow up intensively with a random half of the initial non-responders
Attempt <- rep(0, N)
Attempt[R1 == 0] <- rbinom(sum(R1 == 0), 1, 0.5)
R2 <- rep(0, N)
R2[Attempt == 1] <- rbinom(sum(Attempt == 1), 1, 0.9)
Y[Attempt == 1 & R2 == 1] <- Y_star[Attempt == 1 & R2 == 1]
df <- data.frame(Y, Z, R1, Attempt, R2)

sens <- sensitivity_ds(Y, Z, R1, Attempt, R2, minY = 1, maxY = 5,
                       sims = 20, data = df)
sens
#> Sensitivity analysis on Y
#> delta* = 1.000: the 95% confidence interval first includes zero when
#>   ignorability is dropped for 100.0% of the follow-up nonrespondents.
#> Components: sensitivity_plot, sims_df (20 values of delta), delta_star
sens$sensitivity_plot

sens$delta_star
#> [1] 1