cicc_AR {ciccr}

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)