dose_thresh_attributable_one_sided {doseSens}

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

Z

A length N vector of (nonnegative) observed doses.

Q

A length N vector of observed binary outcomes.

index

A length N vector of indices indicating matched set membership.

gamma

The nonnegative sensitivity parameter; gamma = 0 means no unmeasured confounding.

alpha

Level of the test.

monotone

Whether to impose a monotonicity constraint on the potential outcomes

Delta

A numeric for the attributable effect to be tested for.

sign

The sign of monotonicity - "positive" or "negative".

direction

A string indicating the direction of testing the attributable effect with respect to Delta; "greater", "equal", or "less"

threshold

The threshold for the TAE.

M

The numeric penalty parameter to ensure correct sign relationship.

eps

precision parameter for the objective function if solving feasible = "Yes"

mv_threshold

The number of allowed monotonicity violations.

baseline

The baseline dose level for defining the threshold attributable effect.

relax

Whether to solve the continuous relaxation.

feasible

Whether to look for a feasible solution or to find the optima.

MIPgap

Gurobi parameter specifying the precision of the mixed integer program solution; default is 0.01.

WorkLimit

Gurobi parameter specifying the maximum work units before stopping; default is 1000.

OutputFlag

0 if Gurobi print output is desired, 1 otherwise; default 0.

Value

A list containing the following:

sol

A gurobi object containing the solution to the optimization. If feasible is TRUE, then failing to find a solution indiciates rejection. If feasible is FALSE, then optimal value greater than zero indiciates rejection.

attribut

The attributable effect attained by the least rejectable allocation of potential outcomes and unmeasured confounders.

search

A list of length the number of matched sets containing the matrix of compatible baseline potential outcomes in each matched set.

null_exp

The null expectation of the pivot attained by the least rejectable allocation of potential outcomes and unmeasured confounders.

obsT

The value of the pivot attained by the least rejectable allocation of potential outcomes and unmeasured confounders.

nps

A vector with length the number of matched sets containing the size of each matched set.

start.ind

A vector with length the number of matched sets containing the starting index of the decision variables pertaining to each matched set in the optimization program.

exp_upper

The expectation of the pivot attained by the unmeasured confounders equalling the baseline potential outcome.

var_upper

The variance of the pivot attained by the unmeasured confounders equalling the baseline potential outcome.

dose

A list of length the number of matched sets containing the vector of doses observed in each matched set.

model

The initialized gurobi model.

Examples

# To run the following example, Gurobi must be installed.
# Load the data
data <- treat_out_match
# Solve the mixed-integer program.
solution = dose_thresh_attributable_one_sided(data$treat,
data$complain, data$match_ind,
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)