A function that returns a permuted vector according to a matrix and permutation vector.

Description

A function that returns a permuted vector according to a matrix and permutation vector.

Usage

apply_permutation_to_matrix(M, p)

Arguments

Value

a length n vector with ith entry corresponding to the i, p_i entry in M

Examples

mat <- matrix(1:9, nrow = 3, ncol = 3)
perm <- c(2, 1, 3)
permuted <- apply_permutation_to_matrix(M = mat, p = perm)

Separable algorithm for threshold attributable effect in a sensitivity analysis with at most one over-exposed unit in each matched set. For a greater than alternative, finds the 'a' matched sets that most decrease the mean and/or variance.

Description

Separable algorithm for threshold attributable effect in a sensitivity analysis with at most one over-exposed unit in each matched set. For a greater than alternative, finds the 'a' matched sets that most decrease the mean and/or variance.

Usage

binary_thresh_attribute(
  Z,
  Q,
  index,
  gamma,
  thresh = 0,
  a = 1,
  trans = identity,
  mc = 50000
)

Arguments

Value

Either "reject" if the value a is deemed not plausible/compatible, "feasible" if the value a is deemed so, else a list containing a p-value and dataframe of matched sets that have contribution to the test statistic sorted in order of smallest mean reduction followed by smallest variance reduction.

Examples

# Load the data
data <- lead_crime
# Solve by the separable algorithm
solution <- binary_thresh_attribute(data$log_lead, data$complain, data$matched_sets,
gamma = 0, thresh = log(3.5), a = 5, trans = identity)

A helper that takes a gurobi model object outputted from dose_attributable_general or dose_thresh_attributable_one_sided and changes the Delta parameter. Saves computation time by directly editing the constraint involving Delta without having to reinitialize the other constraints that are kept the same. Outputs a list analogous to output from dose_attributable_general or dose_thresh_attributable_one_sided.

Description

A helper that takes a gurobi model object outputted from dose_attributable_general or dose_thresh_attributable_one_sided and changes the Delta parameter. Saves computation time by directly editing the constraint involving Delta without having to reinitialize the other constraints that are kept the same. Outputs a list analogous to output from dose_attributable_general or dose_thresh_attributable_one_sided.

Usage

change_Delta(model, Delta, direction = "equal", TT)

Arguments

Value

A gurobi model and solution.

Asymptotic sensitivity analysis for weak nulls with continuous exposures assuming constant effects across matched sets.

Description

Asymptotic sensitivity analysis for weak nulls with continuous exposures assuming constant effects across matched sets.

Usage

constant_effects_test(
  Z,
  R,
  index,
  gamma = 0,
  theta = 0,
  X = NA,
  estimand_function = extract_OLS,
  gamma_star_vec = NULL
)

Arguments

Value

A list containing the deviate, one-sided p-value, observed value of the test statistic in each matched set, and conservative standard deviation estimate.

Examples

 # Load the data
data <- lead_bmd
# prepare data
threshold <- log(0.74675)
match_info = data |> dplyr::group_by(matched_sets) |>
dplyr::summarise(below = sum(log_lead < threshold) > 0, disc = var(log_lead) > 0,
above = sum(log_lead > threshold) > 0)
below_indices <- match_info$matched_sets[match_info$below]
disc_indices <- match_info$matched_sets[match_info$disc]
above_indices <- match_info$matched_sets[match_info$above]
# outcome analysis using the stochastic intervention statistic, weak null
below_nbp <- data |> dplyr::filter(matched_sets %in% below_indices & matched_sets
%in% disc_indices)
above_below <- below_nbp |> dplyr::filter(matched_sets %in% above_indices)
extract_below_threshold_vs_baseline_function <- function(z, r) {
  extract_below_threshold_vs_baseline(z, r, threshold)
}
# one-sided test that estimand defined by estimand_function is 0 at gamma = 0
result <- constant_effects_test(Z = above_below$log_lead,
R = above_below$lumbar_spine_bmd,
index = above_below$matched_sets, gamma = 0, theta = 0,
estimand_function = extract_below_threshold_vs_baseline_function)

Computes deviation from uniform distribution in total variation distance for a given amount of unmeasured confounding and a greater than alternative with a binary outcome.

Description

Computes deviation from uniform distribution in total variation distance for a given amount of unmeasured confounding and a greater than alternative with a binary outcome.

Usage

dev_TV(Z, Q, index, gamma, direct = "upper")

Arguments

Value

A vector of length equaling the number of matched sets consisting of the TV distance from the uniform for each matched set at gamma level of unmeasured confounding for the worst-case.

Examples

# Load the data
data <- lead_crime
# compute total variation distances.
total_variation <- dev_TV(data$log_lead, data$complain,
data$matched_sets, gamma = log(1.5))

Inference for general attributable effects in sensitivity analysis with continuous exposures and binary outcomes. Gurobi must be installed to use this function.

Description

Inference for general attributable effects in sensitivity analysis with continuous exposures and binary outcomes. Gurobi must be installed to use this function.

Usage

dose_attributable_general(
  Z,
  Q,
  index,
  gamma,
  alpha = 0.05,
  monotone = TRUE,
  Delta,
  sign = "positive",
  trans = identity,
  direction = "equal",
  M = 10000,
  eps = 0.01,
  alternative = "both",
  mv_threshold = NA,
  baseline = 0,
  relax = FALSE,
  feasible = TRUE,
  MIPgap = 0.01,
  WorkLimit = 1000,
  OutputFlag = 0
)

Arguments

Value

A list containing the following:

Examples

# To run the following example, Gurobi must be installed.
# Load the data
data <- lead_crime
# Make a threshold at log(3.5) transformation function.
above = function(Z) { return(Z > log(3.5)) }
# Solve the mixed-integer program.

solution = tryCatch(dose_attributable_general(data$log_lead,
data$complain, data$matched_sets, gamma=log(1),
alpha = 0.1, monotone = TRUE, trans = above,
Delta = 5, direction = "less", M = 10000, eps = 0.0001,
alternative = "upper", relax = FALSE, feasible = FALSE),
error = function(e) NULL
  )

Sharp null monte-carlo sensitivity analysis for continuous exposures and binary outcomes.

Description

Sharp null monte-carlo sensitivity analysis for continuous exposures and binary outcomes.

Usage

dose_sensitivity_mc_gen(
  Z,
  Q,
  index,
  mc,
  gamma,
  weights = NA,
  obsT = NULL,
  trans = identity,
  direct = "upper",
  seed = 1,
  verbose = FALSE
)

Arguments

Value

A list containing two objects:

Examples

# Load the data
data <- lead_crime
# Make a threshold at log(3.5) transformation function.
above = function(Z) { return(Z > log(3.5)) }
# Conduct randomization test.
solution <- dose_sensitivity_mc_gen(data$log_lead, data$complain, data$matched_sets,
mc = 250, gamma = 0, trans = above)

Inference for threshold attributable effects in sensitivity analysis with continuous exposures and binary outcomes. Gurobi must be installed to use this function.

Description

Inference for threshold attributable effects in sensitivity analysis with continuous exposures and binary outcomes. Gurobi must be installed to use this function.

Usage

dose_thresh_attributable_one_sided(
  Z,
  Q,
  index,
  gamma,
  alpha = 0.05,
  monotone = TRUE,
  Delta,
  sign = "positive",
  direction = "equal",
  threshold = 0,
  M = 10000,
  eps = 0.01,
  mv_threshold = NA,
  baseline = 0,
  relax = FALSE,
  feasible = TRUE,
  MIPgap = 0.01,
  WorkLimit = 1000,
  OutputFlag = 0
)

Arguments

Value

A list containing the following:

Examples

# To run the following example, Gurobi must be installed.
# Load the data
data <- lead_crime
# Solve the mixed-integer program.

solution = tryCatch(dose_thresh_attributable_one_sided(data$log_lead,
data$complain, data$matched_sets,
gamma=log(1), alpha = 0.1, monotone = TRUE, Delta = 5,
 direction = "less", threshold = log(3.5),M = 10000,
 eps = 0.0001,relax = FALSE, feasible = FALSE),
    error = function(e) NULL
 )

A function that returns the coefficient from regressing an outcome vector on a dose vector.

Description

A function that returns the coefficient from regressing an outcome vector on a dose vector.

Usage

extract_OLS(z, r)

Arguments

Value

the OLS regression coefficient from regressing r on z.

Examples

# dose vector
dose <- c(0, 0.1, 0.4)
# outcome vector
outcome <- c(1, 1.1, 1.5)
beta <- extract_OLS(z = dose, r = outcome)

Compute average of outcomes above dose threshold minus average of outcomes.

Description

Compute average of outcomes above dose threshold minus average of outcomes.

Usage

extract_above_threshold_vs_baseline(z, r, threshold)

Arguments

Value

the average of the outcomes with dose z above threshold c minus the average of the outcomes r.

Examples

# dose vector
dose <- c(0, 0.1, 0.4)
# outcome vector
outcome <- c(1, 1.1, 1.5)
theta <- extract_above_threshold_vs_baseline(z = dose, r = outcome, threshold = 0.3)

Compute average of outcomes below dose threshold minus average of outcomes.

Description

Compute average of outcomes below dose threshold minus average of outcomes.

Usage

extract_below_threshold_vs_baseline(z, r, threshold)

Arguments

Value

the average of the outcomes with dose z below threshold c minus the average of the outcomes r.

Examples

# dose vector
dose <- c(0, 0.1, 0.4)
# outcome vector
outcome <- c(1, 1.1, 1.5)
theta <- extract_below_threshold_vs_baseline(z = dose, r = outcome, threshold = 0.3)

Compute largest dose outcome minus average of other outcomes.

Description

Compute largest dose outcome minus average of other outcomes.

Usage

extract_max_vs_baseline(z, r)

Arguments

Value

the outcome r corresponding to the largest dose z minus the average of the outcomes r.

Examples

# dose vector
dose <- c(0, 0.1, 0.4)
# outcome vector
outcome <- c(1, 1.1, 1.5)
theta <- extract_max_vs_baseline(z = dose, r = outcome)

Compute smallest dose outcome minus average of other outcomes.

Description

Compute smallest dose outcome minus average of other outcomes.

Usage

extract_min_vs_baseline(z, r)

Arguments

Value

the outcome r corresponding to the smallest dose z minus the average of the outcomes r.

Examples

# dose vector
dose <- c(0, 0.1, 0.4)
# outcome vector
outcome <- c(1, 1.1, 1.5)
theta <- extract_min_vs_baseline(z = dose, r = outcome)

Compute weighted sum of outcomes.

Description

Compute weighted sum of outcomes.

Usage

extract_stochastic_intervention(z, r, s)

Arguments

Value

the inner product of s and r

Examples

# dose vector
dose <- c(0, 0.1, 0.4)
# outcome vector
outcome <- c(1, 1.1, 1.5)
# weight vector
weight = c(0.3, 0.4, 0.3)
theta <- extract_stochastic_intervention(z = dose, r = outcome, s = weight)

Compute difference in average outcomes above and below a dose threshold.

Description

Compute difference in average outcomes above and below a dose threshold.

Usage

extract_threshold_effect(z, r, threshold)

Arguments

Value

the average of the outcomes with dose z above threshold c minus the average of the outcomes with dose z below the threshold c.

Examples

# dose vector
dose <- c(0, 0.1, 0.4)
# outcome vector
outcome <- c(1, 1.1, 1.5)
theta <- extract_threshold_effect(z = dose, r = outcome, threshold = 0.3)

Function factory for extract_threshold_effect.

Description

Function factory for extract_threshold_effect.

Usage

extract_threshold_effect_function(threshold = 0)

Arguments

Value

A function that corresponds to extract_threshold_effect with the given threshold

Examples

threshold_function <- extract_threshold_effect_function(threshold = 0.3)

Matched lead bone mineral density dataset

Description

A matched, trimmed dataset of lead exposure and lumbar bone mineral density. The data comes from NHANES 2011-18. There are 711 matched sets.

Usage

lead_bmd

Format

lead_bmd

A data frame with 1,436 rows and 23 columns:

log_lead

The log of lead exposure level measured in micrograms per deciliter.

lumbar_spine_bmd

Bone mineral density in the lumbar spine in g/cm^2

matched_sets

Matched set membership.

...

Source

https://wwwn.cdc.gov/nchs/nhanes/default.aspx

Matched lead crime dataset

Description

A matched, trimmed dataset of early life lead exposure and juvenile delinquency from a public dataset. There are 2007 matched sets.

Usage

lead_crime

Format

lead_crime

A data frame with 4,134 rows and 17 columns:

log_lead

The log of lead exposure level measured in micrograms per deciliter.

serious

Whether the juvenile comitted a serious offense.

complain

Whether the juvenile comitted an offense worthy of complaint.

matched_sets

Matched set membership.

...

Source

https://scholarworks.iu.edu/dspace/handle/2022/25638

A function to compute a conservative upper bound on the worst-case expectation under the sharp null

Description

A function to compute a conservative upper bound on the worst-case expectation under the sharp null

Usage

max_expectation(z, gamma, f_pi, with_variance = FALSE)

Arguments

Value

a list containing the worst-case expectation, and/or variance and the solution to the optimization problem.

Examples

# A vector of observed doses
doses <- c(0, 0.1, 0.4, 0.8)
# values of test statistic under 4! permutations
values <- c(1, 0.5, 0.3, 0.8, 1, 0.7)
upper_bound <- max_expectation(z = doses, gamma = 1, f_pi = values)

Find the max ratio of probabilities between two permutations.

Description

Find the max ratio of probabilities between two permutations.

Usage

max_ratio(z, gamma)

Arguments

Value

the maximum ratio between the probability of two different permutations under the Rosenbaum model with doses z and unmeasured confounding level gamma.

Examples

# A vector of observed doses
doses <- c(0, 0.1, 0.4, 0.8)
ratio <- max_ratio(z = doses, gamma = 1)

Find the max ratio of probabilities between two permutations.

Description

Find the max ratio of probabilities between two permutations.

Usage

max_ratio_new(z, gamma)

Arguments

Value

the maximum ratio between the probability of two different permutations under the Rosenbaum model with doses z and unmeasured confounding level gamma.

Examples

# A vector of observed doses
doses <- c(0, 0.1, 0.4, 0.8)
ratio <- max_ratio_new(z = doses, gamma = 1)

Find the max ratio of probabilities between two permutations for each matched set.

Description

Find the max ratio of probabilities between two permutations for each matched set.

Usage

max_ratios_summary(Z, index, gamma)

Arguments

Value

A vector of length equaling the number of unique indices that contains the maximum ratio between any two permutations for each of the matched sets.

Examples

# A vector of observed doses
doses <- c(0, 0.1, 0.4, 0.8, 1)
matched_set <- c(1, 1, 1, 2, 2)
ratios <- max_ratios_summary(Z = doses, index = matched_set, gamma = 1)

Sharp null sensitivity analysis for continuous exposures and binary outcomes using normal approximation.

Description

Sharp null sensitivity analysis for continuous exposures and binary outcomes using normal approximation.

Usage

normal_test_gen(
  Z,
  Q,
  index,
  gamma,
  trans = identity,
  weights = NA,
  obsT = NULL,
  direct = "upper"
)

Arguments

Value

A list containing the following:

Examples

# Load the data
data <- lead_crime
# Make a threshold at log(3.5) transformation function.
above = function(Z) { return(Z > log(3.5)) }
# Conduct randomization test using normal approximation.
solution <- normal_test_gen(data$log_lead, data$complain, data$matched_sets,
gamma = 0, trans = above)

A function to find the maximum and minimum probability of a permutation.

Description

A function to find the maximum and minimum probability of a permutation.

Usage

prob_bounds(z, gamma)

Arguments

Value

a list containing the maximum and minimum probability of a permutation under the Rosenbaum model with doses z and unmeasured confounding level gamma.

Examples

# A vector of observed doses
doses <- c(0, 0.1, 0.4, 0.8)
bounds <- prob_bounds(z = doses, gamma = 1)

Statistic based on inner product between transformations of dose and outcome.

Description

Statistic based on inner product between transformations of dose and outcome.

Usage

sharp_double_statistic(z, r, q1, q2)

Arguments

Value

a vector with values corresponding to the inner product of transformed by q1 permutations of z with transformed by q2 versions of r.

Examples

# dose vector
dose <- c(0, 0.1, 0.4)
# outcome vector
outcome <- c(1, 1.1, 1.5)
# transforms
transform1 <- function(x) x
transform2 <- function (x) x
theta <- sharp_double_statistic(z = dose, r = outcome, q1 = transform1,
q2 = transform2)

Asymptotic sharp null sensitivity analysis for a class of test statistics accommodating continuous exposures and any scalar outcome.

Description

Asymptotic sharp null sensitivity analysis for a class of test statistics accommodating continuous exposures and any scalar outcome.

Usage

sharp_null_double_test(
  Z,
  R,
  index,
  gamma = 0,
  q1 = NA,
  q2 = NA,
  X = NA,
  stratum_weights = rep(NA, nostratum),
  conservative_variance = TRUE,
  double_rank = TRUE
)

Arguments

Value

A list containing the deviate, one-sided p-value, observed value of the test statistic in each matched set, and conservative standard deviation estimate.

Examples

# Load the data
data <- lead_bmd
# conduct sharp null test at gamma = 0.
result <- sharp_null_double_test(Z = data$log_lead,
R = -data$lumbar_spine_bmd, index = data$matched_sets, gamma = 0)

A function for variance estimation

Description

A function for variance estimation

Usage

var_est(y, W, H_Q)

Arguments

Value

a conservative estimate of the standard deviation of the test statistic.

Examples

test_stat <- c(1, 2, 1.5)
weight <- rep(1, 3)
Q <- matrix(1:9, nrow = 3, ncol = 2)
hat <- Q %*% solve(t(Q) %*% Q) %*% t(Q)

Asymptotic sensitivity analysis for weak nulls with continuous exposures.

Description

Asymptotic sensitivity analysis for weak nulls with continuous exposures.

Usage

weak_null_test(
  Z,
  R,
  index,
  gamma = 0,
  theta = 0,
  X = NA,
  estimand_function = extract_OLS,
  gamma_star_vec = NULL,
  kappa_inv_vec = NULL
)

Arguments

Value

A list containing the deviate, one-sided p-value, observed value of the test statistic in each matched set, and conservative standard deviation estimate.

Examples

# Load the data
data <- lead_bmd
# prepare data
threshold <- log(0.74675)
match_info = data |> dplyr::group_by(matched_sets) |>
dplyr::summarise(below = sum(log_lead < threshold) > 0, disc = var(log_lead) > 0,
above = sum(log_lead > threshold) > 0)
below_indices <- match_info$matched_sets[match_info$below]
disc_indices <- match_info$matched_sets[match_info$disc]
above_indices <- match_info$matched_sets[match_info$above]
# outcome analysis using the stochastic intervention statistic, weak null
below_nbp <- data |> dplyr::filter(matched_sets %in% below_indices & matched_sets
%in% disc_indices)
above_below <- below_nbp |> dplyr::filter(matched_sets %in% above_indices)
extract_below_threshold_vs_baseline_function <- function(z, r) {
  extract_below_threshold_vs_baseline(z, r, threshold)
}
# one-sided test that estimand defined by estimand_function is 0 at gamma = 0
result <- weak_null_test(Z = above_below$log_lead,
R = above_below$lumbar_spine_bmd,
index = above_below$matched_sets, gamma = 0, theta = 0,
estimand_function = extract_below_threshold_vs_baseline_function)