cicc_RR {ciccr}

Causal Inference on Relative Risk

Description

Provides upper bounds on the average of log relative risk under the monotone treatment response (MTR) and monotone treatment selection (MTS) assumptions.

Usage

cicc_RR(y, t, x, sampling = "cc", cov_prob = 0.95)

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')

cov_prob

coverage probability of a uniform confidence band (default = 0.95)

Value

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

est

estimates of the upper bounds on the average of log relative risk at p=0 and p=1

se

pointwise standard errors at p=0 and p=1

ci

the upper end points of the uniform confidence band at p=0 and p=1

pseq

two end points: p=0 and p=1

References

Jun, S.J. and Lee, S. (2023). 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_RR = cicc_RR(y, t, x, sampling = 'cc', cov_prob = 0.95)