Package 'medrobust'

Create sensitivity_region object from list

Description

Create sensitivity_region object from list

Usage

as_sensitivity_region(region_list)

Arguments

region_list

List with sn0_range, sp0_range, psi_sn_range, psi_sp_range

Value

sensitivity_region S7 object

Examples

as_sensitivity_region(list(
  sn0_range = c(0.80, 0.95), sp0_range = c(0.85, 0.99),
  psi_sn_range = c(1, 2), psi_sp_range = c(1, 1)
))

---

Convert partial identification bounds to a data frame

Description

as.data.frame() on a medrobust_bounds object (as returned by bound_ne) returns a one-row data frame of the bounds and fit summary, convenient for tabulating or combining results across analyses.

This is an S7 method for the base generic; call it as as.data.frame(bounds).

Arguments

x	A medrobust_bounds object.
...	Ignored.

Value

A one-row data.frame with columns NIE_lower, NIE_upper, NDE_lower, NDE_upper, NIE_width, NDE_width (upper minus lower), effect_scale, misclassified_variable, n_compatible, n_evaluated, and falsified_proportion. If the object carries bootstrap results, it also has percentile-interval columns for each bound endpoint (NIE_lower_ci_lower, NIE_lower_ci_upper, ..., NDE_upper_ci_upper) plus bootstrap_method and bootstrap_n_reps. Analytic (Imbens-Manski) intervals are not included; use x@analytic_ci.

See Also

bound_ne, medrobust_bounds

---

Convert a sensitivity region to a list

Description

as.list() on a sensitivity region object (as returned by sensitivity_region) returns its four parameter ranges as a plain named list, the same shape accepted by the sensitivity_region argument of bound_ne.

This is an S7 method for the base generic; call it as as.list(region).

Arguments

x	A sensitivity region object created by sensitivity_region.
...	Ignored.

Value

A named list with elements sn0_range, sp0_range, psi_sn_range, and psi_sp_range, each a length-2 numeric vector c(lower, upper).

See Also

sensitivity_region, bound_ne

---

Bootstrap Results Class

Description

Stores bootstrap inference results for partial identification bounds.

Usage

bootstrap_results(
  method = character(0),
  n_reps = integer(0),
  n_failed = 0L,
  confidence_level = integer(0),
  nie_lower_ci = integer(0),
  nie_upper_ci = integer(0),
  nde_lower_ci = integer(0),
  nde_upper_ci = integer(0),
  boot_nie_lower = integer(0),
  boot_nie_upper = integer(0),
  boot_nde_lower = integer(0),
  boot_nde_upper = integer(0),
  z0 = NULL,
  acceleration = NULL
)

Arguments

method	Character: "percentile" or "bca"
n_reps	Number of bootstrap replications
n_failed	Number of failed bootstrap samples
confidence_level	Confidence level (e.g., 0.95)
nie_lower_ci	Confidence interval for NIE lower bound
nie_upper_ci	Confidence interval for NIE upper bound
nde_lower_ci	Confidence interval for NDE lower bound
nde_upper_ci	Confidence interval for NDE upper bound
boot_nie_lower	Bootstrap samples for NIE lower bound
boot_nie_upper	Bootstrap samples for NIE upper bound
boot_nde_lower	Bootstrap samples for NDE lower bound
boot_nde_upper	Bootstrap samples for NDE upper bound
z0	BCa bias-correction parameter
acceleration	BCa acceleration parameter

Value

An S7 object of class bootstrap_results holding bootstrap confidence intervals and the replicate samples for the lower and upper bound endpoints of the natural direct and indirect effects.

---

Compute Width of Bootstrap Distribution

Description

Compute the mean, median, and range of bound widths from bootstrap samples.

Usage

bootstrap_width_summary(bootstrap_results, effect = "NIE")

Arguments

bootstrap_results	The bootstrap_results property of a bound_ne fit with bootstrap = TRUE, or the list returned by compute_bootstrap_ci()
effect	Character string: "NIE" or "NDE"

Value

List with width statistics

---

Confidence intervals for partial-identification bounds (Imbens-Manski)

Description

Computes a confidence interval for the partial-identification set returned by bound_ne(). The raw estimated bound $[\hat L, \hat U]$ is consistent but is not a confidence set: when the identified set is narrow relative to the sampling uncertainty of its endpoints, it under-covers the true effect at small samples. bound_ci() widens the endpoints by their standard errors using the Imbens & Manski (2004) construction, restoring approximately nominal coverage of the true effect.

Usage

bound_ci(
  bounds,
  data,
  exposure,
  mediator,
  outcome,
  confounders,
  misclassified_variable = c("exposure", "mediator"),
  n_boot = 200L,
  level = 0.95,
  seed = NULL
)

Arguments

bounds	A fitted medrobust_bounds object from bound_ne().
data	The data frame passed to bound_ne().
exposure, mediator, outcome, confounders	Column names, as in bound_ne().
misclassified_variable	Either "exposure" or "mediator"; selects the recovery used to evaluate the effect at a single sensitivity parameter.
n_boot	Number of resamples for the endpoint standard errors (default 200).
level	Confidence level (default 0.95).
seed	Optional integer seed for reproducibility.

Details

Endpoint standard errors are obtained by re-evaluating the effect at the fixed minimizing/maximizing sensitivity parameter on resampled data (one evaluation per resample, with no grid search), which is far cheaper than a full bootstrap of the whole grid.

Value

A named list with elements NIE and NDE, each a numeric vector with lower, upper (the point bounds), se_lower, se_upper (endpoint SEs), and ci_lower, ci_upper (the Imbens-Manski confidence interval).

References

Imbens, G. W. and Manski, C. F. (2004). Confidence Intervals for Partially Identified Parameters. Econometrica, 72(6), 1845-1857.

See Also

bound_ne()

Examples

sim <- simulate_dm_data(
  n = 2000,
  true_params = list(beta_AM = log(2.5), theta_AY = log(1.5), theta_MY = log(2.5)),
  dm_params = list(sn0 = 0.9, sp0 = 0.9, psi_sn = 1, psi_sp = 1),
  misclass_type = "mediator", confounders = 1, seed = 1
)
bounds <- bound_ne(
  data = sim@observed, exposure = "A", mediator = "M_star", outcome = "Y",
  confounders = "C1", misclassified_variable = "mediator",
  sensitivity_region = list(
    sn0_range = c(0.80, 0.99), sp0_range = c(0.80, 0.99),
    psi_sn_range = c(0.8, 1.5), psi_sp_range = c(0.8, 1.5)
  ),
  n_grid = 10, verbose = FALSE
)

# Widen the raw bounds [L, U] into Imbens-Manski confidence intervals
ci <- bound_ci(
  bounds, data = sim@observed, exposure = "A", mediator = "M_star",
  outcome = "Y", confounders = "C1", misclassified_variable = "mediator",
  n_boot = 50, seed = 1
)
ci$NDE

---

Partial Identification Bounds for Natural Effects Under Differential Misclassification

Description

Computes partial identification bounds for the Natural Direct Effect (NDE) and Natural Indirect Effect (NIE) when either the exposure or mediator is subject to differential misclassification. The method does not require validation data.

Usage

bound_ne(
  data,
  exposure,
  mediator,
  outcome,
  confounders = NULL,
  misclassified_variable = c("exposure", "mediator"),
  sensitivity_region = NULL,
  n_grid = 50,
  effect_scale = c("OR", "RR", "RD"),
  confidence_level = 0.95,
  ci_method = c("none", "analytic"),
  ci_n_boot = 200L,
  bootstrap = FALSE,
  bootstrap_reps = 1000,
  bootstrap_method = c("percentile", "bca"),
  parallel = FALSE,
  n_cores = NULL,
  cache = FALSE,
  cache_dir = NULL,
  verbose = TRUE,
  stratify_by = NULL,
  use_adaptive_grid = TRUE,
  grid_method = c("lhs", "auto", "regular", "adaptive", "sobol", "binary")
)

Arguments

data	A data frame containing the observed variables.
exposure	Character string. Name of the exposure variable (A or A*).
mediator	Character string. Name of the mediator variable (M or M*).
outcome	Character string. Name of the outcome variable (Y).
confounders	Character vector. Names of confounding variables.
misclassified_variable	Character string. Either "exposure" or "mediator" to indicate which variable is subject to misclassification.
sensitivity_region	A named list defining the sensitivity region Theta_Psi. Should contain: sn0_range, sp0_range, psi_sn_range, psi_sp_range. Each element should be a numeric vector of length 2 giving the minimum and maximum values. If NULL, default ranges are used.
n_grid	Integer. Number of grid points per parameter dimension. Default is 50.
effect_scale	Character string. Scale for reporting effects: "OR" (odds ratio), "RR" (risk ratio), or "RD" (risk difference). Default is "OR".
confidence_level	Numeric. Confidence level for confidence intervals. Default is 0.95.
ci_method	Character. "none" (default) or "analytic". If "analytic", attaches Imbens-Manski confidence intervals (see bound_ci()) to the result's @analytic_ci slot.
ci_n_boot	Integer. Resamples for the analytic CI endpoint SEs. Default 200.
bootstrap	Logical. Whether to compute bootstrap confidence intervals. Default is FALSE.
bootstrap_reps	Integer. Number of bootstrap replicates if bootstrap=TRUE. Default is 1000.
bootstrap_method	Character string. Bootstrap CI method: "percentile" (default) or "bca" (bias-corrected and accelerated). The percentile method is faster and adequate for most applications. BCa provides second-order accurate intervals but requires jackknife estimation, which is computationally intensive for large datasets.
parallel	Logical. Whether to use parallel processing. Default is FALSE.
n_cores	Integer. Number of cores for parallel processing. If NULL, uses detectCores() - 1. Default is NULL.
cache	Logical. Whether to cache intermediate results. Default is FALSE.
cache_dir	Character string. Directory for cache files. If NULL, uses temp directory.
verbose	Logical. Whether to print progress messages. Default is TRUE.
stratify_by	Character vector. Additional variables to stratify by (advanced use).
use_adaptive_grid	Logical. Whether to use adaptive grid refinement for large grids (n_grid >= 20). This dramatically reduces computation time by focusing on compatible regions. Default is TRUE.
grid_method	Character string specifying grid search algorithm: "lhs" (default): Latin Hypercube Sampling - space-filling design that reduces evaluations by 99% while maintaining broad coverage. Best for most applications (McKay et al., 1979). "auto": Automatically selects best method based on a 16-point probe of the parameter space. "regular": Exhaustive regular grid (n_grid^4 evaluations). Use for exact bounds when computational budget allows. "sobol": Sobol low-discrepancy sequences (Sobol, 1967). Similar to LHS but better for high-dimensional problems. "adaptive": Two-stage coarse-to-fine refinement. Effective when falsification rate is high. "binary": Binary search on parameter boundaries. Efficient when compatibility is monotonic in parameters.

Details

This function implements the partial identification approach described in Tofighi, D. (2025). The method derives bounds on causal mediation effects by specifying a plausible range for misclassification parameters and using testable implications to rule out empirically inconsistent values.

The sensitivity region Theta_Psi is defined by four parameters:

• sn0: Baseline sensitivity (probability of correct classification when Y=0)

• sp0: Baseline specificity

• psi_sn: Differential sensitivity parameter (odds ratio)

• psi_sp: Differential specificity parameter (odds ratio)

Non-differential misclassification corresponds to psi_sn = psi_sp = 1.

Value

An object of class medrobust_bounds containing:

NIE_lower	Lower bound for Natural Indirect Effect
NIE_upper	Upper bound for Natural Indirect Effect
NDE_lower	Lower bound for Natural Direct Effect
NDE_upper	Upper bound for Natural Direct Effect
compatible_sets	Data frame of compatible parameter sets
falsified_proportion	Proportion of sensitivity region falsified
effect_scale	Scale used for reporting
n_evaluated	Number of parameter sets evaluated
evaluated_sets	Every evaluated parameter set with a logical compatible column; see extract_falsified_region
n_compatible	Number of compatible parameter sets
computation_time	Time taken for computation
call	Original function call
data_summary	Summary statistics of the data
bootstrap_results	Bootstrap results if bootstrap=TRUE

References

Tofighi, D. (2025). Partial Identification of Causal Mediation Effects Under Differential Misclassification. Biostatistics.

McKay, M. D., Beckman, R. J., & Conover, W. J. (1979). A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21(2), 239-245.

Sobol', I. M. (1967). On the distribution of points in a cube and the approximate evaluation of integrals. USSR Computational Mathematics and Mathematical Physics, 7(4), 86-112.

See Also

check_compatibility, sensitivity_plot, falsification_summary

Examples

# Simulate data with a known mediator-misclassification mechanism
sim <- simulate_dm_data(
  n = 8000,
  true_params = list(beta_AM = log(2.5), theta_AY = log(1.5), theta_MY = log(2.5)),
  dm_params = list(sn0 = 0.9, sp0 = 0.9, psi_sn = 1, psi_sp = 1),
  misclass_type = "mediator", confounders = 1, seed = 1
)

# Sensitivity region containing the (here non-differential) truth
sens_region <- list(
  sn0_range = c(0.80, 0.99),
  sp0_range = c(0.80, 0.99),
  psi_sn_range = c(0.8, 1.5),
  psi_sp_range = c(0.8, 1.5)
)

# Compute partial-identification bounds for mediator misclassification.
# The raw bound [L, U] is consistent but is NOT a confidence set; at finite n
# it can under-cover the truth, so we add Imbens-Manski confidence intervals
# in the same fit via ci_method = "analytic".
set.seed(1)
bounds <- bound_ne(
  data = sim@observed,
  exposure = "A",
  mediator = "M_star",
  outcome = "Y",
  confounders = "C1",
  misclassified_variable = "mediator",
  sensitivity_region = sens_region,
  n_grid = 10,
  ci_method = "analytic", ci_n_boot = 50
)

# View results
print(bounds)
summary(bounds)
bounds@analytic_ci$NDE   # raw [L, U] plus Imbens-Manski confidence interval

# Visualize
sensitivity_plot(bounds, param = "psi_sn")

---

Check Compatibility of Misclassification Parameters

Description

Tests whether a specific set of misclassification parameters is compatible with the observed data by checking testable implications. Returns detailed diagnostics about which constraints are satisfied or violated.

Usage

check_compatibility(
  data,
  exposure,
  mediator,
  outcome,
  confounders = NULL,
  psi,
  misclassified_variable = c("exposure", "mediator"),
  return_details = TRUE,
  tolerance = 1e-06
)

Arguments

data	Data frame containing the observed variables
exposure	Character string. Name of exposure variable
mediator	Character string. Name of mediator variable
outcome	Character string. Name of outcome variable
confounders	Character vector. Names of confounding variables
psi	Named list containing misclassification parameters: sn0: Baseline sensitivity sp0: Baseline specificity psi_sn: Differential sensitivity (odds ratio) psi_sp: Differential specificity (odds ratio)
misclassified_variable	Character string. Either "exposure" or "mediator"
return_details	Logical. If TRUE, returns detailed stratum-level diagnostics. Default is TRUE.
tolerance	Numeric. Tolerance for numerical precision when checking constraints. Default is 1e-6. On the mediator path, bound_ne applies the same constraints with no tolerance, so this function is the more lenient of the two there: a psi whose implied probabilities fall outside [0, 1] by less than tolerance is reported compatible here but rejected by bound_ne().

Details

This function implements the testable implications derived in Propositions 4.1 and 5.1 of the paper. For mediator misclassification, it checks whether the observed data can be explained by any true causal parameters given the specified misclassification mechanism. For exposure misclassification, it checks the likelihood ratio constraints on observed probabilities.

The function is useful for:

• Testing specific hypotheses about misclassification parameters

• Understanding which constraints are most informative

• Debugging sensitivity analyses

• Generating diagnostic plots

Value

A list with class compatibility_test containing:

compatible	Logical. TRUE if parameters are compatible
psi	The tested parameter set
n_constraints_total	Total number of testable constraints
n_constraints_satisfied	Number of satisfied constraints
n_constraints_violated	Number of violated constraints
violated_constraints	Data frame of violated constraints (if any)
implied_probabilities	Solved true probabilities (if compatible)
stratum_details	Stratum-level diagnostics (if return_details=TRUE)

See Also

bound_ne, falsification_summary

Examples

data("heals_data")

# Test non-differential misclassification with high accuracy
test_ndm <- check_compatibility(
  data = heals_data,
  exposure = "A_star",
  mediator = "M",
  outcome = "Y",
  confounders = c("age", "male", "smoking", "bmi"),
  psi = list(sn0 = 0.90, sp0 = 0.90, psi_sn = 1.0, psi_sp = 1.0),
  misclassified_variable = "exposure"
)

print(test_ndm)

# Test strong differential misclassification
test_strong_dm <- check_compatibility(
  data = heals_data,
  exposure = "A_star",
  mediator = "M",
  outcome = "Y",
  confounders = c("age", "male", "smoking", "bmi"),
  psi = list(sn0 = 0.85, sp0 = 0.85, psi_sn = 3.0, psi_sp = 1.0),
  misclassified_variable = "exposure"
)

print(test_strong_dm)

---

Compare Bounds Across Multiple Analyses

Description

Compare partial identification bounds from multiple analyses (e.g., different sensitivity regions, different datasets, different assumptions).

Usage

compare_bounds(bounds_list, labels = NULL)

Arguments

bounds_list	A named list of medrobust_bounds objects.
labels	Optional character vector of labels for each analysis. If NULL, uses names from bounds_list.

Value

A data frame comparing the bounds, and optionally a plot.

Examples

# Compare bounds under different sensitivity assumptions
sim <- simulate_dm_data(
  n = 500,
  true_params = list(beta_AM = log(2.5), theta_AY = log(1.5), theta_MY = log(2.5)),
  dm_params = list(sn0 = 0.9, sp0 = 0.9, psi_sn = 1, psi_sp = 1),
  misclass_type = "mediator", confounders = 1, seed = 1
)
args0 <- list(
  data = sim@observed, exposure = "A", mediator = "M_star", outcome = "Y",
  confounders = "C1", misclassified_variable = "mediator", n_grid = 10
)
set.seed(1)
bounds1 <- do.call(bound_ne, c(args0, list(sensitivity_region = list(
  sn0_range = c(0.82, 0.97), sp0_range = c(0.82, 0.97),
  psi_sn_range = c(0.85, 1.3), psi_sp_range = c(0.85, 1.3)))))
bounds2 <- do.call(bound_ne, c(args0, list(sensitivity_region = list(
  sn0_range = c(0.80, 0.99), sp0_range = c(0.80, 0.99),
  psi_sn_range = c(0.8, 1.5), psi_sp_range = c(0.8, 1.5)))))

comparison <- compare_bounds(
  list(conservative = bounds1, liberal = bounds2)
)
print(comparison)

---

Compatibility Test Class

Description

S7 class for storing results of compatibility tests for specific misclassification parameter values.

Arguments

compatible	Logical indicating if parameters are compatible with data
psi	List of misclassification parameters tested
sn1	Sensitivity when Y=1 (implied from psi)
sp1	Specificity when Y=1 (implied from psi)
n_constraints_total	Total number of testable constraints
n_constraints_satisfied	Number of constraints satisfied
n_constraints_violated	Number of constraints violated
violated_constraints	Data frame with details of violated constraints
implied_probabilities	List of implied probability distributions, or NULL when the data are incompatible with psi
stratum_details	List with stratum-specific details, or NULL when they were not requested or the test exited before any stratum was checked
misclassified_variable	Character: "exposure" or "mediator"
reason	Character describing reason for incompatibility (if any)

Value

An S7 object of class compatibility_test holding the outcome of the data-compatibility (falsification) test, including the satisfied and violated testable constraints.

---

Compute Standard Errors for Bounds

Description

Estimate standard errors for the lower and upper bounds using the bootstrap distribution.

Usage

compute_bound_se(bootstrap_results)

Arguments

bootstrap_results

The bootstrap_results property of a bound_ne fit with bootstrap = TRUE, or the list returned by compute_bootstrap_ci()

Value

Named vector of standard errors

---

Extract Compatible Parameter Sets

Description

Extract the compatible parameter sets from a bounds analysis.

Usage

extract_bounds(bounds_object)

Arguments

bounds_object

An object of class medrobust_bounds

Value

A data frame containing compatible parameter sets

Examples

sim <- simulate_dm_data(
  n = 2000,
  true_params = list(beta_AM = log(2.5), theta_AY = log(1.5), theta_MY = log(2.5)),
  dm_params = list(sn0 = 0.9, sp0 = 0.9, psi_sn = 1, psi_sp = 1),
  misclass_type = "mediator", confounders = 1, seed = 1
)
bounds <- bound_ne(
  data = sim@observed, exposure = "A", mediator = "M_star", outcome = "Y",
  confounders = "C1", misclassified_variable = "mediator",
  sensitivity_region = list(
    sn0_range = c(0.80, 0.99), sp0_range = c(0.80, 0.99),
    psi_sn_range = c(0.8, 1.5), psi_sp_range = c(0.8, 1.5)
  ),
  n_grid = 10, verbose = FALSE
)
head(extract_bounds(bounds))

---

Extract Falsified Region

Description

Extract the parameter sets that the grid search evaluated and the data falsified. Works for every grid_method, because bound_ne records each evaluated set with its verdict.

Usage

extract_falsified_region(bounds_object)

Arguments

bounds_object

An object of class medrobust_bounds

Value

A data frame with columns sn0, sp0, psi_sn and psi_sp, one row per falsified parameter set.

---

Summarize Falsification Results

Description

Provides a detailed summary of which regions of the sensitivity parameter space are empirically falsified by the data. Helps understand which assumptions about misclassification are most constrained by the observed data.

Usage

falsification_summary(
  bounds_object,
  by_parameter = TRUE,
  n_bins = 10,
  plot = TRUE
)

Arguments

bounds_object	An object of class medrobust_bounds returned by bound_ne
by_parameter	Logical. If TRUE, breaks down falsification by each parameter dimension. Default is TRUE.
n_bins	Integer. Number of bins for discretizing parameters when computing falsification rates. Default is 10.
plot	Logical. If TRUE, generates visualization of falsification patterns. Default is TRUE.

Details

This function uses every parameter set bound_ne() evaluated (its evaluated_sets property) to show which regions of the sensitivity space are ruled out by the testable implications. The falsification rate of a bin is the share of the sets evaluated in that bin that the data falsified; a bin in which no set was evaluated has rate NA. High falsification rates indicate that the data are informative about that particular parameter.

The falsification analysis is useful for:

• Understanding which misclassification assumptions are most constrained

• Identifying whether bounds are wide due to weak data vs. wide sensitivity region

• Guiding choice of sensitivity parameters for future studies

• Assessing whether additional data would meaningfully narrow bounds

Value

A list of class falsification_summary containing:

overall	Overall falsification rate
by_parameter	Parameter-specific falsification rates (if by_parameter=TRUE)
joint_falsification	2D falsification patterns
most_constrained	Parameters that are most falsified
least_constrained	Parameters that are least falsified
plot	ggplot2 object (if plot=TRUE)

See Also

bound_ne, check_compatibility

Examples

# Compute bounds first (see ?bound_ne)
sim <- simulate_dm_data(
  n = 8000,
  true_params = list(beta_AM = log(2.5), theta_AY = log(1.5), theta_MY = log(2.5)),
  dm_params = list(sn0 = 0.9, sp0 = 0.9, psi_sn = 1, psi_sp = 1),
  misclass_type = "mediator", confounders = 1, seed = 1
)
set.seed(1)
bounds <- bound_ne(
  data = sim@observed, exposure = "A", mediator = "M_star", outcome = "Y",
  confounders = "C1", misclassified_variable = "mediator",
  sensitivity_region = list(
    sn0_range = c(0.80, 0.99), sp0_range = c(0.80, 0.99),
    psi_sn_range = c(0.8, 1.5), psi_sp_range = c(0.8, 1.5)
  ),
  n_grid = 10
)

falsif <- falsification_summary(bounds)
print(falsif)

# View falsification plot
falsif@plot

---

Format Effect Estimate for Reporting

Description

Format an effect estimate as a string for tables/reports.

Usage

format_effect(estimate, effect_scale = "OR", digits = 2, ci = NULL)

Arguments

estimate	Numeric effect estimate (or bounds)
effect_scale	Character string: "OR", "RR", or "RD"
digits	Integer: number of decimal places
ci	Optional: confidence interval (length 2 vector)

Value

Character string

Examples

format_effect(1.48)
format_effect(1.48, ci = c(1.21, 1.81))   # point estimate with a CI
format_effect(c(1.12, 1.37))              # bounds [L, U]
format_effect(0.031, effect_scale = "RD", digits = 3)

---

Gestational Hypertension as a Differentially Misclassified Binary Mediator

Description

A random sample of U.S. live births used to illustrate partial-identification bounds when a binary mediator is differentially misclassified, without validation data. The mediator—gestational hypertension as recorded on the birth certificate—is a textbook differentially misclassified variable: its birth-certificate sensitivity is poor and reporting accuracy plausibly depends on the outcome (preterm birth). This is the substantive triad analyzed by the closest prior point-identification method (Hochstedler Webb and Wells, 2025).

Usage

gesthtn

Format

A data frame with 5,000 observations and 4 binary variables:

A

Binary. Advanced maternal age (1 = age >= 35 years, 0 = age < 35).

M_star

Binary. Recorded (surrogate) gestational hypertension from the birth certificate (1 = Yes, 0 = No). A misclassified measurement of the true mediator; the true status is not observed.

Y

Binary. Preterm birth (1 = gestational age < 37 weeks, 0 = term).

C1

Binary. Parity (1 = one or more prior live births, 0 = none).

Details

## Source data A fixed-seed (20260614) random sample of 5,000 from 3,662,426 complete cases in the 2021 U.S. National Center for Health Statistics (NCHS) Natality (birth-certificate) file, public-domain U.S.-government data obtained via the NBER mirror. Variables were derived as above from mager, rf_ghype, combgest, and priorlive; see system.file("scripts", "prepare_gesthtn.R", package = "medrobust").

## Misclassification Validation of the 2003 revised birth certificate against the medical record (Dietz et al., 2015) found the gestational-hypertension item to have poor sensitivity (< 70%) and excellent specificity (> 90%); differential (outcome-dependent) sensitivity is plausible. These motivate a sensitivity region with baseline sensitivity in roughly [0.50, 0.70], specificity in [0.90, 0.99], and a differential-sensitivity odds ratio at or above 1.

Source

NCHS Natality 2021 (U.S. birth certificates), via the NBER mirror https://data.nber.org/nvss/natality/csv/2021/natality2021us.csv. Misclassification context: Dietz et al. (2015), Public Health Reports 130(1):60-70, doi:10.1177/003335491513000108. Prior art on this application: Hochstedler Webb and Wells (2025), Statistical Methods in Medical Research 34(5):1037-1059, doi:10.1177/09622802251316970.

Examples

data("gesthtn")
table(gesthtn$M_star, gesthtn$Y)

# Partial-identification bounds for the (differentially misclassified) mediator;
# see ?bound_ne and the article
# https://data-wise.github.io/medrobust/articles/gesthtn-bounds.html
region <- sensitivity_region(
  sn0_range = c(0.50, 0.70), sp0_range = c(0.90, 0.99),
  psi_sn_range = c(1.0, 3.0), psi_sp_range = c(1.0, 1.0)
)

---

Synthetic HEALS Data with Differential Measurement Error

Description

A synthetic dataset based on the Health Effects of Arsenic Longitudinal Study (HEALS) that demonstrates differential measurement error in exposure assessment. The dataset includes both observed (misclassified) and true (ground truth) arsenic exposure, allowing for validation of sensitivity analysis methods.

Usage

heals_data

Format

A data frame with 450 observations and 9 variables:

id

Integer. Unique subject identifier (1 to 450).

Y

Binary. Cardiovascular disease status (0 = Absent, 1 = Present).

M

Binary. Elevated inflammation marker (sVCAM-1) (0 = Low, 1 = High).

A_star

Binary. Self-reported arsenic exposure (0 = No, 1 = Yes). Subject to severe differential recall bias.

A_true

Binary. True arsenic exposure status (0 = No, 1 = Yes). Included for validation; not available in real studies.

age

Numeric. Age in years (range: 18-75, mean ~42.8).

male

Binary. Sex (0 = Female, 1 = Male).

smoking

Binary. Ever smoker status (0 = Never, 1 = Ever).

bmi

Numeric. Body mass index in kg/m² (mean ~19.7).

Details

## Data Generation The data were generated to mimic the HEALS cohort using published effect sizes and demographic profiles from:

• Ahsan et al. (2006) - Baseline demographics

• Chen et al. (2007) - Arsenic-inflammation relationship

• Argos et al. (2010) - Arsenic-CVD relationship (HR ~ 1.92)

## Measurement Error Model Differential misclassification was introduced with:

• Cases (Y=1): Sensitivity = 0.90, Specificity = 0.55 (over-reporting)

• Controls (Y=0): Sensitivity = 0.60, Specificity = 0.90

This creates severe recall bias where CVD cases over-report arsenic exposure, inflating the naive effect estimate by approximately 70

## True vs. Naive Effects

• True Natural Direct Effect: OR ~ 1.68

• Naive NDE (using A_star): OR ~ 2.85

• Bias amplification: ~70

Source

Synthetic data generated using methods described in the article "Synthetic HEALS Data: Ground Truth with Differential Measurement Error" on the package website: https://data-wise.github.io/medrobust/articles/heals-synthetic-data.html.

Examples

# Load the data
data("heals_data")
str(heals_data)

# Examine prevalence
table(heals_data$A_star, heals_data$Y)

# Compare naive vs. true effect
naive_mod <- glm(Y ~ A_star + M + age + male + smoking + bmi,
                 data = heals_data, family = binomial)
true_mod <- glm(Y ~ A_true + M + age + male + smoking + bmi,
                data = heals_data, family = binomial)

cat("Naive NDE:", round(exp(coef(naive_mod)["A_star"]), 2), "\n")
cat("True NDE:", round(exp(coef(true_mod)["A_true"]), 2), "\n")

# To compute partial-identification bounds for the (potentially
# misclassified) exposure A_star, pass this data to bound_ne();
# see ?bound_ne for a complete, runnable example.

---

Medrobust Bounds Class

Description

S7 class for storing partial identification bounds for natural direct and indirect effects under differential misclassification.

Arguments

NIE_lower	Lower bound for Natural Indirect Effect
NIE_upper	Upper bound for Natural Indirect Effect
NDE_lower	Lower bound for Natural Direct Effect
NDE_upper	Upper bound for Natural Direct Effect
compatible_sets	Data frame of parameter sets compatible with data
n_compatible	Number of compatible parameter sets
n_evaluated	Total number of parameter sets evaluated
falsified_proportion	Proportion of parameter space falsified
effect_scale	Character: "OR", "RR", or "RD"
misclassified_variable	Character: "exposure" or "mediator"
sensitivity_region	Sensitivity region specification
naive_estimates	List of naive effect estimates
bootstrap_results	Bootstrap inference results (if computed)
data_summary	Summary statistics from the data
evaluated_sets	Data frame of every parameter set the grid search evaluated (sn0, sp0, psi_sn, psi_sp) with a logical compatible column; NULL when no search ran
call	The function call that created this object

Value

An S7 object of class medrobust_bounds containing the partial identification bounds for the natural direct and indirect effects, the parameter sets compatible with the data, and the associated inference and diagnostic summaries.

---

Create Falsification Summary Object

Description

Low-level constructor for falsification_summary S7 objects. Most users should use the falsification_summary() function which analyzes bounds.

Usage

new_falsification_summary(
  overall,
  n_evaluated,
  n_compatible,
  n_falsified,
  by_parameter = NULL,
  joint_falsification = NULL,
  most_constrained = character(0),
  least_constrained = character(0),
  plot = NULL
)

Arguments

overall	Overall falsification rate
n_evaluated	Number of parameter sets evaluated
n_compatible	Number of compatible parameter sets
n_falsified	Number of falsified parameter sets
by_parameter	Parameter-specific falsification (optional)
joint_falsification	Joint falsification patterns (optional)
most_constrained	Most constrained parameters (optional)
least_constrained	Least constrained parameters (optional)
plot	ggplot2 object (optional)

Value

A falsification_summary S7 object

Examples

new_falsification_summary(
  overall = 0.25, n_evaluated = 100L, n_compatible = 75L, n_falsified = 25L
)

---

Physical Inactivity as a Differentially Misclassified Binary Exposure

Description

A pooled sample of U.S. adults from NHANES used to illustrate partial-identification bounds when a binary exposure is differentially misclassified, without validation data. The exposure—self-reported physical inactivity—is a textbook differentially misclassified variable: it has no biomarker, relies on participant recall and report, and reporting accuracy plausibly depends on health status (and thus on the outcome). The mediator, laboratory-measured systemic inflammation (hs-CRP), is by contrast measured without error. nhanes_pa is the exposure-side mirror image of gesthtn (which misclassifies the mediator), completing the mediator/exposure symmetry of the package's worked examples.

Usage

nhanes_pa

Format

A data frame with approximately 9,906 observations and 6 binary variables (every column is an integer in {0, 1}):

A_star

Binary. Self-reported physical inactivity (1 = inactive, 0 = active). A misclassified (surrogate) measurement of the true exposure; "inactive" means leisure-time aerobic activity below the 2018 Physical Activity Guidelines threshold of 150 moderate-equivalent minutes per week (vigorous minutes counted double). The true activity status is not observed.

M

Binary. Elevated systemic inflammation, hs-CRP >= 3 mg/L (1 = elevated, 0 = not). Laboratory-measured, treated as error-free.

Y

Binary. Prevalent cardiovascular disease (1 = any of coronary heart disease, angina, myocardial infarction, or stroke; 0 = none).

C1

Binary. Older age (1 = age >= 50 years, 0 = age < 50).

C2

Binary. Female sex (1 = female, 0 = male).

C3

Binary. Obesity (1 = BMI >= 30, 0 = BMI < 30).

Details

## Source data Pooled NHANES 2015–2016 (_I) and 2017–2018 (_J) cycles, adults aged 20 and older, restricted to complete cases on the six modeled binaries. Unlike gesthtn (a fixed-seed random sample drawn from millions of births), nhanes_pa ships the full complete-case sample with no random sampling: the data are tiny (six binary columns), and the complete-case construction is deterministic, so the dataset is reproducible by construction with no seed. The eight C1 x C2 x C3 strata are well-populated (each roughly 843–1,588), which keeps bound_ne(confounders = c("C1", "C2", "C3")) feasible across the differential-sensitivity sweep. Variables were derived from the PAQ (physical-activity questionnaire), HSCRP (high-sensitivity C-reactive protein), MCQ (medical conditions), DEMO (demographics), and BMX (body measures) files; see system.file("scripts", "prepare_nhanes_pa.R", package = "medrobust").

## Misclassification The misclassified variable here is a self-reported exposure in a cross-sectional survey, so the relevant mechanism is differential reporting: sensitivity and specificity for self-reported inactivity may depend on the prevalent outcome (e.g., respondents with cardiovascular disease may report activity differently from healthy respondents). This is outcome-dependent reporting error, not case-control recall bias—there is no retrospective recall of past exposure conditional on diagnosis. With no validation data, an analyst can posit plausible accuracy (e.g., baseline sensitivity and specificity each in [0.80, 0.95]) and sweep a differential-sensitivity odds ratio ($\psi_{Sn}$) at or above 1 to probe robustness.

Source

CDC National Health and Nutrition Examination Survey (NHANES), public-domain U.S.-government data for cycles 2015–2016 and 2017–2018, obtained via the nhanesA package (https://cran.r-project.org/package=nhanesA). Survey home: https://www.cdc.gov/nchs/nhanes/. Activity threshold: 2018 Physical Activity Guidelines for Americans (150 moderate-equivalent min/week).

Examples

data("nhanes_pa")
table(A_star = nhanes_pa$A_star, Y = nhanes_pa$Y)

# Partial-identification bounds for the (differentially misclassified) exposure;
# see ?bound_ne and the article
# https://data-wise.github.io/medrobust/articles/nhanes_pa-bounds.html
region <- sensitivity_region(
  sn0_range = c(0.80, 0.95), sp0_range = c(0.80, 0.95),
  psi_sn_range = c(1.0, 2.0), psi_sp_range = c(1.0, 1.0)
)

---

Plot Bootstrap Distribution

Description

Visualize the bootstrap distribution of bounds.

Usage

plot_bootstrap_distribution(
  bootstrap_results,
  effect = "NIE",
  original_bounds = NULL
)

Arguments

bootstrap_results	The bootstrap_results property of a bound_ne fit with bootstrap = TRUE, or the list returned by compute_bootstrap_ci()
effect	Character string: "NIE" or "NDE"
original_bounds	Original bound estimates (optional)

Value

ggplot2 object

---

Power Analysis for Partial Identification Bounds

Description

Conducts simulation-based power analysis to determine the sample size needed to achieve a target bound width or to rule out the null hypothesis with high probability.

Usage

power_analysis(
  true_params,
  dm_params,
  sensitivity_region,
  misclass_type = c("exposure", "mediator"),
  sample_sizes = seq(100, 1000, by = 100),
  target_width = NULL,
  target_power = 0.8,
  alpha = 0.05,
  effect = c("NIE", "NDE"),
  n_sim = 100,
  n_grid = 30,
  confounders = 1,
  parallel = TRUE,
  n_cores = NULL,
  verbose = TRUE,
  seed = 12345
)

Arguments

true_params	Named list of true causal parameters (see simulate_dm_data)
dm_params	Named list of misclassification parameters
sensitivity_region	Named list defining Theta_Psi for bound_ne
misclass_type	Character string. "exposure" or "mediator"
sample_sizes	Integer vector. Sample sizes to evaluate. Default is seq(100, 1000, by = 100).
target_width	Numeric. Target bound width. If specified, finds minimum sample size to achieve this width with high probability. Default is NULL.
target_power	Numeric. Target power for rejecting null. Default is 0.80.
alpha	Numeric. Significance level. Default is 0.05.
effect	Character string. Which effect to power for: "NIE" or "NDE". Default is "NIE".
n_sim	Integer. Number of simulation replicates per sample size. Default is 100.
n_grid	Integer. Grid resolution for bound_ne. Default is 30.
confounders	Integer. Number of confounders. Default is 1.
parallel	Logical. Use parallel processing? Default is TRUE.
n_cores	Integer. Number of cores. Default is NULL (auto-detect).
verbose	Logical. Print progress? Default is TRUE.
seed	Integer. Random seed. Default is 12345.

Value

An S7 object of class power_analysis_result containing:

power_curve	Data frame with power by sample size
true_effect	True effect value
target_power	Target power level
target_width	Target bound width (if specified)
recommended_n_power	Recommended sample size for target power
recommended_n_width	Recommended sample size for target width
simulation_params	Parameters used for simulation

See Also

simulate_dm_data, bound_ne

Examples

# A power analysis runs many bootstrap-bound replications across several
# sample sizes, so it is computationally intensive; it is wrapped in
# \dontrun{} to keep checks fast. Reduce sample_sizes / n_sim to run quickly.
## Not run: 
# Power analysis for exposure DM with moderate effects
power_result <- power_analysis(
  true_params = list(beta_AM = 0.405, theta_AY = 0.405, theta_MY = 0.405),
  dm_params = list(sn0 = 0.85, sp0 = 0.85, psi_sn = 1.5, psi_sp = 1.0),
  sensitivity_region = list(
    sn0_range = c(0.80, 0.90),
    sp0_range = c(0.80, 0.90),
    psi_sn_range = c(1.0, 2.0),
    psi_sp_range = c(1.0, 1.0)
  ),
  misclass_type = "exposure",
  sample_sizes = c(200, 400, 600, 800, 1000),
  target_width = 0.3,
  target_power = 0.80,
  n_sim = 100
)

print(power_result)
plot(power_result)

## End(Not run)

---

Power Analysis Result Class

Description

S7 class for storing power analysis results for partial identification bounds.

Arguments

power_curve	Data frame with power and width by sample size
true_effect	True effect value used in simulations
target_power	Target power level for sample size recommendations
target_width	Target bound width for sample size recommendations
recommended_n_power	Recommended sample size to achieve target power
recommended_n_width	Recommended sample size to achieve target width
simulation_params	List of simulation parameters used

Value

An S7 object of class power_analysis_result holding the power and bound-width curves across sample sizes and the recommended sample sizes for the target power and width.

---

Print Method for compatibility_test

Description

Prints a formatted report of a falsification test returned by check_compatibility. This is an S7 method for the base generic; call it as print(x).

Arguments

x	An object of class compatibility_test.
...	Additional arguments (currently unused).

Value

Invisibly returns the input object.

See Also

check_compatibility, summary.compatibility_test

---

Create Sensitivity Analysis Plots

Description

Generate publication-quality visualizations of partial identification bounds as a function of sensitivity parameters.

Usage

sensitivity_plot(
  bounds_object,
  param = "psi_sn",
  effect = c("both", "NIE", "NDE"),
  plot_type = c("bounds", "heatmap", "contour"),
  show_naive = TRUE,
  show_null = TRUE,
  color_scheme = "default",
  theme = "bw",
  ...
)

Arguments

bounds_object	An object of class medrobust_bounds returned by bound_ne.
param	Character vector specifying which parameter(s) to plot on the x-axis. Options: "psi_sn", "psi_sp", "sn0", "sp0". Can specify multiple for faceted plots.
effect	Character string: "NIE", "NDE", or "both" (default).
plot_type	Character string specifying plot type: "bounds" (default): Line plot showing upper and lower bounds "heatmap": 2D heatmap of bound width (requires two parameters) "contour": Contour plot of bounds (requires two parameters)
show_naive	Logical indicating whether to overlay the naive estimate (assuming no misclassification). Default is TRUE.
show_null	Logical indicating whether to show horizontal line at null value (effect = 1 for OR/RR, effect = 0 for RD). Default is TRUE.
color_scheme	Character string specifying color palette: "default", "viridis", "colorblind", "grayscale".
theme	Character string for ggplot2 theme: "bw" (default), "minimal", "classic", "void".
...	Additional arguments passed to ggplot2 functions.

Details

The function creates different plot types to visualize sensitivity analysis:

Bounds plot: Shows how the lower and upper bounds vary as a function of one sensitivity parameter, with other parameters held fixed or averaged.

Heatmap: Shows the width of the identification region (upper - lower) as a function of two sensitivity parameters simultaneously.

Contour plot: Shows contour lines of the bounds in 2D parameter space.

Value

A ggplot2 object that can be further customized or saved.

Examples

# Compute bounds to plot (see ?bound_ne)
sim <- simulate_dm_data(
  n = 8000,
  true_params = list(beta_AM = log(2.5), theta_AY = log(1.5), theta_MY = log(2.5)),
  dm_params = list(sn0 = 0.9, sp0 = 0.9, psi_sn = 1, psi_sp = 1),
  misclass_type = "mediator", confounders = 1, seed = 1
)
set.seed(1)
bounds <- bound_ne(
  data = sim@observed, exposure = "A", mediator = "M_star", outcome = "Y",
  confounders = "C1", misclassified_variable = "mediator",
  sensitivity_region = list(
    sn0_range = c(0.80, 0.99), sp0_range = c(0.80, 0.99),
    psi_sn_range = c(0.8, 1.5), psi_sp_range = c(0.8, 1.5)
  ),
  n_grid = 10
)

# Basic bounds plot
sensitivity_plot(bounds, param = "psi_sn", effect = "NIE")

# Show both effects
sensitivity_plot(bounds, param = "psi_sn", effect = "both")

# Customize the returned ggplot object
p <- sensitivity_plot(bounds, param = "psi_sn") +
  ggplot2::labs(title = "My Custom Title") +
  ggplot2::theme(legend.position = "bottom")
p

---

Create Sensitivity Region

Description

Constructor for sensitivity_region S7 objects. Issues a warning if the region may be non-informative (Sn + Sp <= 1).

Usage

sensitivity_region(sn0_range, sp0_range, psi_sn_range, psi_sp_range)

Arguments

sn0_range	Numeric vector of length 2: [min, max] for baseline sensitivity
sp0_range	Numeric vector of length 2: [min, max] for baseline specificity
psi_sn_range	Numeric vector of length 2: [min, max] for sensitivity OR
psi_sp_range	Numeric vector of length 2: [min, max] for specificity OR

Value

A sensitivity_region S7 object

Examples

region <- sensitivity_region(
  sn0_range = c(0.80, 0.95), sp0_range = c(0.85, 0.99),
  psi_sn_range = c(1, 2), psi_sp_range = c(1, 1)
)
region

---

Simulate Data with Differential Misclassification

Description

Generates synthetic data with known differential misclassification for power analysis, methods validation, and simulation studies. Allows control over true causal parameters and misclassification mechanisms.

Usage

simulate_dm_data(
  n = 500,
  true_params = list(beta_AM = 0.405, theta_AY = 0.405, theta_MY = 0.405),
  dm_params = list(sn0 = 0.85, sp0 = 0.85, psi_sn = 1.5, psi_sp = 1),
  misclass_type = c("exposure", "mediator"),
  confounders = 1,
  confounder_params = list(type = "binary", effect_on_A = 0.3, effect_on_M = 0.3,
    effect_on_Y = 0.3),
  effect_modification = FALSE,
  interaction_coef = 0,
  seed = NULL,
  return_truth = TRUE,
  return_params = TRUE
)

Arguments

n	Integer. Sample size. Default is 500.
true_params	Named list of true causal parameters: beta_AM: Effect of A on M (log-odds scale) theta_AY: Direct effect of A on Y (log-odds scale) theta_MY: Effect of M on Y (log-odds scale) baseline_M: Baseline probability of M when A=0 (optional) baseline_Y: Baseline probability of Y when A=0, M=0 (optional)
dm_params	Named list of misclassification parameters: sn0: Baseline sensitivity (Y=0) sp0: Baseline specificity (Y=0) psi_sn: Differential sensitivity (odds ratio) psi_sp: Differential specificity (odds ratio)
misclass_type	Character string. Either "exposure" or "mediator" to indicate which variable is misclassified. Default is "exposure".
confounders	Integer. Number of confounding variables to include. Default is 1. Set to 0 for no confounders.
confounder_params	Named list controlling confounder generation: type: "binary" or "continuous". Default is "binary". effect_on_A: Effect size on exposure (log-odds). Default is 0.3. effect_on_M: Effect size on mediator (log-odds). Default is 0.3. effect_on_Y: Effect size on outcome (log-odds). Default is 0.3.
effect_modification	Logical. Should there be effect modification (interaction between A and M on Y)? Default is FALSE.
interaction_coef	Numeric. Interaction coefficient if effect_modification=TRUE. Default is 0.
seed	Integer. Random seed for reproducibility. If NULL, no seed is set.
return_truth	Logical. Should true (unobserved) values be returned? Default is TRUE.
return_params	Logical. Should true causal effects be calculated and returned? Default is TRUE.

Value

An S7 object of class simulated_dm_data containing:

observed	Data frame with observed (potentially misclassified) variables
truth	Data frame with true (unobserved) values (if return_truth=TRUE)
true_effects	List of true causal effects (if return_params=TRUE)
generation_params	Parameters used for data generation
misclassification_applied	Summary of applied misclassification

See Also

bound_ne, power_analysis

Examples

# Basic simulation with moderate effects and mild DM
sim_data <- simulate_dm_data(
  n = 500,
  true_params = list(
    beta_AM = 0.405,   # OR = 1.5
    theta_AY = 0.405,  # OR = 1.5
    theta_MY = 0.405   # OR = 1.5
  ),
  dm_params = list(
    sn0 = 0.85,
    sp0 = 0.85,
    psi_sn = 1.5,
    psi_sp = 1.0
  ),
  misclass_type = "exposure",
  seed = 12345
)

# Use in analysis
set.seed(1)
bounds <- bound_ne(
  data = sim_data@observed,
  exposure = "A_star",
  mediator = "M",
  outcome = "Y",
  confounders = "C1",
  misclassified_variable = "exposure",
  sensitivity_region = list(
    sn0_range = c(0.80, 0.90),
    sp0_range = c(0.80, 0.90),
    psi_sn_range = c(1.0, 2.0),
    psi_sp_range = c(1.0, 1.0)
  ),
  n_grid = 10
)

---

Simulated Data with Differential Misclassification Class

Description

S7 class for storing simulated data with known differential misclassification, used for power analysis and methods validation.

Arguments

observed	Data frame with observed (potentially misclassified) variables
truth	Data frame with true (unobserved) values
true_effects	List of true causal effects
generation_params	List of parameters used to generate the data
misclassification_applied	List of misclassification parameters applied

Value

An S7 object of class simulated_dm_data holding the simulated observed data together with the true (unobserved) values, the true causal effects, and the data-generating parameters.

---

Summary Method for compatibility_test

Description

Prints a detailed summary of a falsification test returned by check_compatibility. This is an S7 method for the base generic; call it as summary(object).

Arguments

object	An object of class compatibility_test.
...	Additional arguments (currently unused).

Value

Invisibly returns the input object.

See Also

check_compatibility, print.compatibility_test

---

Test Multiple Hypotheses

Description

Test multiple hypotheses about misclassification parameters simultaneously.

Usage

test_multiple_hypotheses(
  data,
  exposure,
  mediator,
  outcome,
  confounders,
  psi_list,
  misclassified_variable
)

Arguments

data	Data frame
exposure	Character string
mediator	Character string
outcome	Character string
confounders	Character vector
psi_list	List of parameter sets to test, each a list with sn0, sp0, psi_sn and psi_sp. Names label the rows of the result; unnamed entries are labeled H1, H2, ... by position.
misclassified_variable	Character string

Value

Data frame with test results for each hypothesis

Examples

sim <- simulate_dm_data(
  n = 2000,
  true_params = list(beta_AM = log(2.5), theta_AY = log(1.5), theta_MY = log(2.5)),
  dm_params = list(sn0 = 0.9, sp0 = 0.9, psi_sn = 1, psi_sp = 1),
  misclass_type = "mediator", confounders = 1, seed = 1
)

# psi_list must be named: the names label the rows of the result
test_multiple_hypotheses(
  data = sim@observed, exposure = "A", mediator = "M_star", outcome = "Y",
  confounders = "C1", misclassified_variable = "mediator",
  psi_list = list(
    accurate = list(sn0 = 0.9, sp0 = 0.9, psi_sn = 1, psi_sp = 1),
    poor     = list(sn0 = 0.6, sp0 = 0.6, psi_sn = 1, psi_sp = 1)
  )
)

---