exact.score.sen.IxJ: Exact Sensitivity Analysis for Sum Score (Ordinal) Tests in I by J Tables

Description

This function computes exact p-values for score-based sensitivity analysis in I by J contingency tables under the generic bias model. It is specifically designed for ordinal data where both treatment levels and outcomes have a natural ordering, and tests for trend using assigned scores.

Usage

exact.score.sen.IxJ(
  obs.table,
  gamma,
  delta,
  row = "treatment",
  verbose = FALSE,
  treatment.scores,
  outcome.scores
)

Value

A list containing:

rct.prob: Probability under Randomized Controlled Trial (RCT) with u_allocation set to zero.
max.prob: Maximum probability found across all allocations in u_space.
maximizer: The u_allocation vector that yields max.prob.
gamma: Extracted gamma value from the generic bias model.
delta: The delta vector
obs.stat: The observed test statistic based on the observed table and the assigned scores.
obs.table: The observed table.

Arguments

obs.table: A matrix or table object representing the observed contingency table.
gamma: A nonnegative scalar.
delta: A binary vector with no more than two unique values, corresponding to treatment levels. The length must match the number of treatments (rows of obs.table if row = "treatment", or columns if row = "outcome"). Must have a monotone trend matching the treatment ordering.
row: A string indicating whether rows represent "outcome" or "treatment". Must be either "outcome" or "treatment". Default is "treatment".
verbose: A logical flag indicating whether to print progress messages. Default is FALSE.
treatment.scores: A numeric vector specifying the scores for each treatment level. Must have the same length as the number of treatments and exhibit a monotone trend.
outcome.scores: A numeric vector specifying the scores for each outcome level. Must have the same length as the number of outcomes and exhibit a monotone trend.

Details

The score test assumes both treatments and outcomes are ordinal with monotone trends. The test statistic is computed as the sum of products of cell counts with their corresponding treatment and outcome scores. The function automatically generates an appropriate u-space for score tests, focusing on allocations that respect the ordinal nature of the data.

Examples

Run this code

# \donttest{
## Example 1: Binary outcome table (2 by 2)
obs.table <- matrix(c(12, 18, 17, 3), ncol = 2, byrow = TRUE,
                   dimnames = list(treatment = c("control", "treated"),
                                  outcome = c("failure", "success")))

# Perform score-based sensitivity analysis
result_2x2 <- exact.score.sen.IxJ(obs.table = obs.table,
                                  gamma = 0.5,
                                  delta = c(0, 1),
                                  treatment.scores = c(0, 1),
                                  outcome.scores = c(0, 1))
result_2x2

## Example 2: Three-level ordinal outcome (3 by 3)
obs.table <- matrix(c(12, 18, 17, 3, 12, 25, 0, 3, 4),
                   ncol = 3, byrow = FALSE,
                   dimnames = list(treatment = c("low", "medium", "high"),
                                  outcome = c("poor", "fair", "good")))

# Test for trend with ordinal scores
result_3x3 <- exact.score.sen.IxJ(obs.table = obs.table,
                                  gamma = 0.5,
                                  delta = c(0, 1, 1),
                                  treatment.scores = c(0, 1, 2),
                                  outcome.scores = c(1, 2, 3))
result_3x3
# }