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.

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
)

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.
exp_lower: The expectation of the pivot attained by the unmeasured confounders equalling 1 minus the baseline potential outcome.
var_upper: The variance of the pivot attained by the unmeasured confounders equalling the baseline potential outcome.
var_lower: The variance of the pivot attained by the unmeasured confounders equalling 1 minus 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.

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".
trans: The transformation of the doses to use for the test statistic. Default is the identity function.
direction: A string indicating the direction of testing the attributable effect with respect to Delta; "greater", "equal", or "less"
M: The numeric penalty parameter to ensure correct sign relationship.
eps: precision parameter for the objective function if solving feasible = "Yes"
alternative: For constraining the rejection region using the test statistic with baseline potential outcomes, should it be constructed with "lower" alternative, "upper" alternative, or "both."
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 optimal solution.
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.

Examples

Run this code

# 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
  )

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