sensitivityIxJ (version 0.1.5)

sampling.score.sen.IxJ: Monte Carlo Score Test Sensitivity Analysis for I by J Tables

Description

This function implements a sampling-based approach to sensitivity analysis for score tests in I by J contingency tables under the generic bias model. It uses Sequential Importance Sampling (SIS) from Eisinger and Chen (2017) to approximate p-values when exact computation is infeasible due to large reference set

Usage

sampling.score.sen.IxJ(
  obs.table,
  gamma,
  delta,
  row = "treatment",
  mc.iteration = 5000,
  treatment.scores,
  outcome.scores,
  verbose = FALSE
)

Value

A list containing:

rct.prob

Estimated probability under RCT (all u-allocations zero)

max.prob

Maximum estimated probability across all u-allocations

maximizer

The u-allocation vector yielding max.prob

obs.stat

Observed test statistic value

obs.table

The input observed table

gamma

Extracted gamma value from the generic bias model

delta

delta vector

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. Must have a monotone trend for ordinal tests.

row

A string indicating whether rows represent "outcome" or "treatment". Must be either "outcome" or "treatment". Default is "treatment".

mc.iteration

Integer specifying the number of Monte Carlo iterations for each u-allocation. Higher values increase accuracy but require more computation time. Default is 5000.

treatment.scores

A numeric vector specifying 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 scores for each outcome level. Must have the same length as the number of outcomes and exhibit a monotone trend.

verbose

Logical flag indicating whether to print progress messages during computation. Default is FALSE.

Details

The function uses importance sampling to estimate p-values for score tests when both treatments and outcomes are ordinal. The score test statistic is computed as the sum of products of cell counts with their corresponding treatment and outcome scores.

The u-space is automatically constructed to respect the ordinal nature of the data, focusing on allocations that assign bias to higher outcome levels first (assuming an increasing trend in outcome scores).

Unlike exact methods, this function provides Monte Carlo estimates that converge to true values as mc.iteration increases. Results may vary slightly between runs unless the random seed is fixed.

References

Eisinger, R. D., & Chen, Y. (2017). Sampling for Conditional Inference on Contingency Tables. Journal of Computational and Graphical Statistics, 26(1), 79–87.

See Also

exact.score.sen.IxJ for exact computation when feasible, sampling.general.sen.IxJ for general test statistics.

Examples

# \donttest{
# Binary outcome example
obs.table <- matrix(c(15, 10, 5, 20), ncol = 2, byrow = TRUE)
result <- sampling.score.sen.IxJ(obs.table = obs.table,
                                 gamma = 0.5,
                                 delta = c(0, 1),
                                 treatment.scores = c(0, 1),
                                 outcome.scores = c(0, 1),
                                 mc.iteration = 5000)
# }