sentrip {triplesmatch}

Sensitivity analysis for a triples match in an observational study

Description

This function parallels [sensitivityfull::senfm()] for full matches. However, this function does not force the scores used for the test to be Huber's M-statistic. Instead, scores should be calculated ahead of time and then entered here. Performs either a randomization test or the corresponding Rosenbaum sensitivity analysis.

Usage

sentrip(scores, treated1, gamma = 1, alternative = "greater")

Arguments

scores

A matrix of scores. Rows correspond to matched triples and the three columns correspond to the three units in the match. The first unit is the one treated unit if 'treated1 == TRUE' or the one control unit if 'treated1 == FALSE'. The other two columns contain the remaining two units in the match. These are control units if 'treated1 == TRUE' or treated units if 'treated1 == FALSE'. This can easily be created from the triples match using the [formattrip()] function with 'type == "wide"'

treated1

A logical vector with length equal to the number of triples. 'TRUE' if there is only one treated unit in the matched triple; 'FALSE' if there are two treated units and only one control unit. This can easily be created from the triples match using the [formattrip()] function with 'type == "wide"'

gamma

The sensitivity parameter \Gamma \geq 1. Setting \Gamma = 1 performs a randomization test that assumes ignorable treatment assignment given the matched triples

alternative

One of 'greater', 'less' or 'both'. 'greater' implies the alternative hypothesis is that the treatment has a positive effect on the scores, 'less' implies the alternative hypothesis is that the treatment has a negative effect on the scores, and 'both' conducts a two-sided hypothesis test

Value

Named list with 5 elements: 'pval' is the upper bound on the one or two-sided P-value depending on 'alternative', 'deviate' is the deviate that was compared to the Normal distribution to produce pval, 'statistic' is the value of the statistic that is the sum of scores among treated units, 'expectation' is the maximum expectation of this statistic for the given \Gamma, and 'variance' is the maximum variance of this statistic among treatment assignments that achieve the maximum expectation

See Also

sensitivityfull::senfm for more details, especially for the interpretation of the 'expectation' and 'variance' components of the output and relevant references.

formattrip for easily creating inputs to this function.

Examples

# Generate some data
set.seed(246)
n <- 30
x <- rnorm(n, 0, 3)
nt <- floor(n * 0.5)
nc <- n - nt
z <- c(rep(1, nt), rep(0, nc))
# Create a distance matrix, everything in one stratum
dist <- dist_mahal(data.frame(x = x), z, rep(1, n))[[1]]
# Create the triples match
triplesm <- triples_st(cost = dist, z = z, solver = "rlemon")
# Create an outcome
y <- 1:40
# Give the outcome some random unit names
names(y) <- sample(1:40)
# Reformat the triples match
ywide <- formattrip(m = triplesm, y = y, type = "wide")
# Turn the outcome into scores, in this case aberrant ranks
ab <- aberrantscores(ywide$ymat, 15, cutoff_dir = "less", tau = 0, treated1 = NULL)
# Conduct a one-sided hypothesis test with a bias of gamma = 1.25
sentrip(scores = ab, treated1 = ywide$treated1, gamma = 1.25, alternative = "greater")