Sensitivity Analysis

This function performs a line search over values of delta, the sensitivity parameter, in order to find (if it exists) delta*, the value of delta where the confidence interval no longer includes zero.

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

A list with three elements: sensitivity_plot, a ggplot object; sims_df, a data frame of bounds and confidence intervals at each delta; and p_star, a one-row data frame giving delta* when it exists and an explanatory character string when it does not.

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_plot

sens$p_star
#>   p value          label hjust vjust
#> 1 1     0 delta^'*' == 1   1.1   1.3