apply_permutation_to_matrix
                        A function that returns a permuted vector
                        according to a matrix and permutation vector.
binary_thresh_attribute
                        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.
change_Delta            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.
constant_effects_test   Asymptotic sensitivity analysis for weak nulls
                        with continuous exposures assuming constant
                        effects across matched sets.
dev_TV                  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.
dose_attributable_general
                        Inference for general attributable effects in
                        sensitivity analysis with continuous exposures
                        and binary outcomes. Gurobi must be installed
                        to use this function.
dose_sensitivity_mc_gen
                        Sharp null monte-carlo sensitivity analysis for
                        continuous exposures and binary outcomes.
dose_thresh_attributable_one_sided
                        Inference for threshold attributable effects in
                        sensitivity analysis with continuous exposures
                        and binary outcomes. Gurobi must be installed
                        to use this function.
extract_OLS             A function that returns the coefficient from
                        regressing an outcome vector on a dose vector.
extract_above_threshold_vs_baseline
                        Compute average of outcomes above dose
                        threshold minus average of outcomes.
extract_below_threshold_vs_baseline
                        Compute average of outcomes below dose
                        threshold minus average of outcomes.
extract_max_vs_baseline
                        Compute largest dose outcome minus average of
                        other outcomes.
extract_min_vs_baseline
                        Compute smallest dose outcome minus average of
                        other outcomes.
extract_stochastic_intervention
                        Compute weighted sum of outcomes.
extract_threshold_effect
                        Compute difference in average outcomes above
                        and below a dose threshold.
extract_threshold_effect_function
                        Function factory for extract_threshold_effect.
lead_bmd                Matched lead bone mineral density dataset
lead_crime              Matched lead crime dataset
max_expectation         A function to compute a conservative upper
                        bound on the worst-case expectation under the
                        sharp null
max_ratio               Find the max ratio of probabilities between two
                        permutations.
max_ratio_new           Find the max ratio of probabilities between two
                        permutations.
max_ratios_summary      Find the max ratio of probabilities between two
                        permutations for each matched set.
normal_test_gen         Sharp null sensitivity analysis for continuous
                        exposures and binary outcomes using normal
                        approximation.
prob_bounds             A function to find the maximum and minimum
                        probability of a permutation.
sharp_double_statistic
                        Statistic based on inner product between
                        transformations of dose and outcome.
sharp_null_double_test
                        Asymptotic sharp null sensitivity analysis for
                        a class of test statistics accommodating
                        continuous exposures and any scalar outcome.
var_est                 A function for variance estimation
weak_null_test          Asymptotic sensitivity analysis for weak nulls
                        with continuous exposures.
