cicc_AR {ciccr}R Documentation

Causal Inference on Attributable Risk

Description

Provides an upper bound on the average of attributable risk under the monotone treatment response (MTR) and monotone treatment selection (MTS) assumptions.

Usage

cicc_AR(
  y,
  t,
  x,
  sampling = "cc",
  p_upper = 1L,
  cov_prob = 0.95,
  length = 21L,
  interaction = TRUE,
  no_boot = 0L,
  eps = 1e-08
)

Arguments

y

n-dimensional vector of binary outcomes

t

n-dimensional vector of binary treatments

x

n by d matrix of covariates

sampling

'cc' for case-control sampling; 'cp' for case-population sampling; 'rs' for random sampling (default = 'cc')

p_upper

a specified upper bound for the unknown true case probability (default = 1)

cov_prob

coverage probability of a confidence interval (default = 0.95)

length

specified length of a sequence from 0 to p_upper (default = 21)

interaction

TRUE if there are interaction terms in the retrospective logistic model; FALSE if not (default = TRUE)

no_boot

number of bootstrap repetitions to compute the confidence intervals (default = 0)

eps

a small constant that determines the trimming of the estimated probabilities. Specifically, the estimate probability is trimmed to be between eps and 1-eps (default = 1e-8).

Value

An S3 object of type "ciccr". The object has the following elements:

est

(length)-dimensional vector of the upper bounds on the average of attributable risk

ci

(length)-dimensional vector of the upper ends of pointwise one-sided confidence intervals

pseq

(length)-dimensional vector of a grid from 0 to p_upper

cov_prob

the nominal coverage probability

return_code

status of existence of missing values in bootstrap replications

References

Jun, S.J. and Lee, S. (2020). Causal Inference under Outcome-Based Sampling with Monotonicity Assumptions. https://arxiv.org/abs/2004.08318.

Manski, C.F. (1997). Monotone Treatment Response. Econometrica, 65(6), 1311-1334.

Manski, C.F. and Pepper, J.V. (2000). Monotone Instrumental Variables: With an Application to the Returns to Schooling. Econometrica, 68(4), 997-1010.

Examples

# use the ACS_CC dataset included in the package.
  y = ciccr::ACS_CC$topincome
  t = ciccr::ACS_CC$baplus
  x = ciccr::ACS_CC$age
  results_AR = cicc_AR(y, t, x, sampling = 'cc', no_boot = 100)


[Package ciccr version 0.3.0 Index]