ciccr (version 0.3.0)

avg_AR_logit: An Average of the Upper Bound on Causal Attributable Risk

Description

Averages the upper bound on causal attributable risk using prospective and retrospective logistic regression models under the monotone treatment response (MTR) and monotone treatment selection (MTS) assumptions.

Usage

avg_AR_logit(
  y,
  t,
  x,
  sampling = "cc",
  p_upper = 1L,
  length = 21L,
  interaction = TRUE,
  eps = 1e-08
)

Value

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

est

(length)-dimensional vector of the average of the upper bound of causal attributable risk

pseq

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

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

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

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)

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).

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 = avg_AR_logit(y, t, x, sampling = 'cc')