| Title: | Bounding Treatment Effects by Limited Information Pooling |
|---|---|
| Description: | Estimation and inference methods for bounding average treatment effects (on the treated) that are valid under an unconfoundedness assumption. The bounds are designed to be robust in challenging situations, for example, when the conditioning variables take on a large number of different values in the observed sample, or when the overlap condition is violated. This robustness is achieved by only using limited "pooling" of information across observations. For more details, see the paper by Lee and Weidner (2021), "Bounding Treatment Effects by Pooling Limited Information across Observations," <arXiv:2111.05243>. |
| Authors: | Sokbae Lee [aut, cre], Martin Weidner [aut] |
| Maintainer: | Sokbae Lee <[email protected]> |
| License: | GPL-3 |
| Version: | 0.1.0 |
| Built: | 2025-03-12 05:02:37 UTC |
| Source: | https://github.com/atbounds/atbounds-r |
Bounds the average treatment effect (ATE) under the unconfoundedness assumption without the overlap condition.
atebounds( Y, D, X, rps, Q = 3L, studentize = TRUE, alpha = 0.05, x_discrete = FALSE, n_hc = NULL )atebounds( Y, D, X, rps, Q = 3L, studentize = TRUE, alpha = 0.05, x_discrete = FALSE, n_hc = NULL )
Y |
n-dimensional vector of binary outcomes |
D |
n-dimensional vector of binary treatments |
X |
n by p matrix of covariates |
rps |
n-dimensional vector of the reference propensity score |
Q |
bandwidth parameter that determines the maximum number of observations for pooling information (default: Q = 3) |
studentize |
TRUE if the columns of X are studentized and FALSE if not (default: TRUE) |
alpha |
(1-alpha) nominal coverage probability for the confidence interval of ATE (default: 0.05) |
x_discrete |
TRUE if the distribution of X is discrete and FALSE otherwise (default: FALSE) |
n_hc |
number of hierarchical clusters to discretize non-discrete covariates; relevant only if x_discrete is FALSE. The default choice is n_hc = ceiling(length(Y)/10), so that there are 10 observations in each cluster on average. |
An S3 object of type "ATbounds". The object has the following elements.
call |
a call in which all of the specified arguments are specified by their full names |
type |
ATE |
cov_prob |
Confidence level: 1-alpha |
y1_lb |
estimate of the lower bound on the average of Y(1), i.e. E[Y(1)] |
y1_ub |
estimate of the upper bound on the average of Y(1), i.e. E[Y(1)] |
y0_lb |
estimate of the lower bound on the average of Y(0), i.e. E[Y(0)] |
y0_ub |
estimate of the upper bound on the average of Y(0), i.e. E[Y(0)] |
est_lb |
estimate of the lower bound on ATE, i.e. E[Y(1) - Y(0)] |
est_ub |
estimate of the upper bound on ATE, i.e. E[Y(1) - Y(0)] |
est_rps |
the point estimate of ATE using the reference propensity score |
se_lb |
standard error for the estimate of the lower bound on ATE |
se_ub |
standard error for the estimate of the upper bound on ATE |
ci_lb |
the lower end point of the confidence interval for ATE |
ci_ub |
the upper end point of the confidence interval for ATE |
Sokbae Lee and Martin Weidner. Bounding Treatment Effects by Pooling Limited Information across Observations.
Y <- RHC[,"survival"] D <- RHC[,"RHC"] X <- RHC[,c("age","edu")] rps <- rep(mean(D),length(D)) results_ate <- atebounds(Y, D, X, rps, Q = 3)Y <- RHC[,"survival"] D <- RHC[,"RHC"] X <- RHC[,c("age","edu")] rps <- rep(mean(D),length(D)) results_ate <- atebounds(Y, D, X, rps, Q = 3)
Bounds the average treatment effect on the treated (ATT) under the unconfoundedness assumption without the overlap condition.
attbounds( Y, D, X, rps, Q = 3L, studentize = TRUE, alpha = 0.05, x_discrete = FALSE, n_hc = NULL )attbounds( Y, D, X, rps, Q = 3L, studentize = TRUE, alpha = 0.05, x_discrete = FALSE, n_hc = NULL )
Y |
n-dimensional vector of binary outcomes |
D |
n-dimensional vector of binary treatments |
X |
n by p matrix of covariates |
rps |
n-dimensional vector of the reference propensity score |
Q |
bandwidth parameter that determines the maximum number of observations for pooling information (default: Q = 3) |
studentize |
TRUE if X is studentized elementwise and FALSE if not (default: TRUE) |
alpha |
(1-alpha) nominal coverage probability for the confidence interval of ATE (default: 0.05) |
x_discrete |
TRUE if the distribution of X is discrete and FALSE otherwise (default: FALSE) |
n_hc |
number of hierarchical clusters to discretize non-discrete covariates; relevant only if x_discrete is FALSE. The default choice is n_hc = ceiling(length(Y)/10), so that there are 10 observations in each cluster on average. |
An S3 object of type "ATbounds". The object has the following elements.
call |
a call in which all of the specified arguments are specified by their full names |
type |
ATT |
cov_prob |
Confidence level: 1-alpha |
est_lb |
estimate of the lower bound on ATT, i.e. E[Y(1) - Y(0) | D = 1] |
est_ub |
estimate of the upper bound on ATT, i.e. E[Y(1) - Y(0) | D = 1] |
est_rps |
the point estimate of ATT using the reference propensity score |
se_lb |
standard error for the estimate of the lower bound on ATT |
se_ub |
standard error for the estimate of the upper bound on ATT |
ci_lb |
the lower end point of the confidence interval for ATT |
ci_ub |
the upper end point of the confidence interval for ATT |
Sokbae Lee and Martin Weidner. Bounding Treatment Effects by Pooling Limited Information across Observations.
Y <- RHC[,"survival"] D <- RHC[,"RHC"] X <- RHC[,c("age","edu")] rps <- rep(mean(D),length(D)) results_att <- attbounds(Y, D, X, rps, Q = 3)Y <- RHC[,"survival"] D <- RHC[,"RHC"] X <- RHC[,c("age","edu")] rps <- rep(mean(D),length(D)) results_att <- attbounds(Y, D, X, rps, Q = 3)
The electronic fetal monitoring (EFM) and cesarean section (CS) dataset from Neutra, Greenland, and Friedman (1980) consists of observations on 14,484 women who delivered at Beth Israel Hospital, Boston from January 1970 to December 1975. The purpose of the study is to evaluate the impact of EFM on cesarean section (CS) rates. It is found by Neutra, Greenland, and Friedman (1980) that relevant confounding factors are: nulliparity (nullipar), arrest of labor progression (arrest), malpresentation (breech), and year of study (year). The dataset provided in the R package is from the supplementary materials of Richardson, Robins, and Wang (2017), who used this dataset to illustrate their proposed methods for modeling and estimating relative risk and risk difference.
EFMEFM
A data frame with 14484 rows and 6 variables:
Outcome: 1 if delivery was via cesarean section; 0 otherwise
Treatment: 1 if electronic fetal monitoring (EFM) was used; 0 otherwise
Covariate: 1 = arrest of labor progression; 0 otherwise
Covariate: 1 = malpresentation (breech); 0 otherwise
Covariate: 1 = nulliparity; 0 otherwise
Year of study: 0,...,5 (actual values are 1970,...,1975)
The dataset from Neutra, Greenland, and Friedman (1980) is available as part of supplementary materials of Richardson, Robins, and Wang (2017) on Journal of the American Statistical Association website at doi:10.1080/01621459.2016.1192546.
Neutra, R.R., Greenland, S. and Friedman, E.A., 1980. Effect of fetal monitoring on cesarean section rates. Obstetrics and gynecology, 55(2), pp.175-180.
Richardson, T.S., Robins, J.M. and Wang, L., 2017. On modeling and estimation for the relative risk and risk difference. Journal of the American Statistical Association, 112(519), pp.1121-1130.
The right heart catheterization (RHC) dataset is publicly available on the Vanderbilt Biostatistics website. RHC is a diagnostic procedure for directly measuring cardiac function in critically ill patients. The dependent variable is 1 if a patient survived after 30 days of admission, 0 if a patient died within 30 days. The treatment variable is 1 if RHC was applied within 24 hours of admission, and 0 otherwise. The sample size was n = 5735, and 2184 patients were treated with RHC. Connors et al. (1996) used a propensity score matching approach to study the efficacy of RHC, using data from the observational study called SUPPORT (Murphy and Cluff, 1990). Many authors used this dataset subsequently. The 72 covariates are constructed, following Hirano and Imbens (2001).
RHCRHC
A data frame with 5735 rows and 74 variables:
Outcome: 1 if a patient survived after 30 days of admission, and 0 if a patient died within 30 days
Treatment: 1 if RHC was applied within 24 hours of admission, and 0 otherwise.
Age in years
Years of education
Cardiovascular symptoms
Congestive Heart Failure
Dementia, stroke or cerebral infarct, Parkinson’s disease
Psychiatric history, active psychosis or severe depression
Chronic pulmonary disease, severe pulmonary disease
Chronic renal disease, chronic hemodialysis or peritoneal dialysis
Cirrhosis, hepatic failure
Upper GI bleeding
Solid tumor, metastatic disease, chronic leukemia/myeloma, acute leukemia, lymphoma
Immunosuppression, organ transplant, HIV, Diabetes Mellitus, Connective Tissue Disease
transfer (> 24 hours) from another hospital
Definite myocardial infarction
DASI - Duke Activity Status Index
Estimate of prob. of surviving 2 months
APACHE score
Glasgow coma score
Weight
Temperature
Mean Blood Pressure
Respiratory Rate
Heart Rate
PaO2/FI02 ratio
PaCO2
PH
WBC
Hematocrit
Sodium
Potassium
Creatinine
Bilirubin
Albumin
1 if the primary disease category is CHF, and 0 otherwise (Omitted category = ARF).
1 if the primary disease category is Cirrhosis, and 0 otherwise (Omitted category = ARF).
1 if the primary disease category is Colon Cancer, and 0 otherwise (Omitted category = ARF).
1 if the primary disease category is Coma, and 0 otherwise (Omitted category = ARF).
1 if the primary disease category is COPD, and 0 otherwise (Omitted category = ARF).
1 if the primary disease category is Lung Cancer, and 0 otherwise (Omitted category = ARF).
1 if the primary disease category is MOSF w/Malignancy, and 0 otherwise (Omitted category = ARF).
1 if the primary disease category is MOSF w/Sepsis, and 0 otherwise (Omitted category = ARF).
1 if cancer is metastatic, and 0 otherwise (Omitted category = no cancer).
1 if cancer is localized, and 0 otherwise (Omitted category = no cancer).
1 if medical insurance category is Medicaid, and 0 otherwise (Omitted category = Private).
1 if medical insurance category is Medicare, and 0 otherwise (Omitted category = Private).
1 if medical insurance category is Medicare & Medicaid, and 0 otherwise (Omitted category = Private).
1 if medical insurance category is No Insurance, and 0 otherwise (Omitted category = Private).
1 if medical insurance category is Private & Medicare, and 0 otherwise (Omitted category = Private).
1 if Black, and 0 otherwise (Omitted category = White).
1 if Other, and 0 otherwise (Omitted category = White).
1 if Income >$50k, and 0 otherwise (Omitted category = under $11k).
1 if Income $11–$25k, and 0 otherwise (Omitted category = under $11k).
1 if Income $25–$50k, and 0 otherwise (Omitted category = under $11k).
Respiratory diagnosis
Cardiovascular diagnosis
Neurological diagnosis
Gastrointestinal diagnosis
Renal diagnosis
Metabolic diagnosis
Hematological diagnosis
Sepsis diagnosis
Trauma diagnosis
Orthopedic diagnosis
Do Not Resuscitate status on day 1
Female
1 if the secondary disease category is Cirrhosis, and 0 otherwise (Omitted category = NA).
1 if secondary disease category is Colon Cancer, and 0 otherwise (Omitted category = NA).
1 if the secondary disease category is Coma, and 0 otherwise (Omitted category = NA).
1 if the secondary disease category is Lung Cancer, and 0 otherwise (Omitted category = NA).
1 if the secondary disease category is MOSF w/Malignancy, and 0 otherwise (Omitted category = NA).
1 if the secondary disease category is MOSF w/Sepsis, and 0 otherwise (Omitted category = NA).
weight = 0 (missing)
The dataset is publicly available on the Vanderbilt Biostatistics website at https://hbiostat.org/data/.
Connors, A.F., Speroff, T., Dawson, N.V., Thomas, C., Harrell, F.E., Wagner, D., Desbiens, N., Goldman, L., Wu, A.W., Califf, R.M. and Fulkerson, W.J., 1996. The effectiveness of right heart catheterization in the initial care of critically III patients. JAMA, 276(11), pp.889-897. doi:10.1001/jama.1996.03540110043030
Hirano, K., Imbens, G.W. Estimation of Causal Effects using Propensity Score Weighting: An Application to Data on Right Heart Catheterization, 2001. Health Services & Outcomes Research Methodology 2, pp.259–278. doi:10.1023/A:1020371312283
D. J. Murphy, L. E. Cluff, SUPPORT: Study to understand prognoses and preferences for outcomes and risks of treatments—study design, 1990. Journal of Clinical Epidemiology, 43, pp. 1S–123S https://www.jclinepi.com/issue/S0895-4356(00)X0189-8 .
Simulates observations from the data-generating process considered in Lee and Weidner (2021)
simulation_dgp(n, ps_spec = "overlap", x_discrete = FALSE)simulation_dgp(n, ps_spec = "overlap", x_discrete = FALSE)
n |
sample size |
ps_spec |
specification of the propensity score: "overlap" or "non-overlap" (default: "overlap") |
x_discrete |
TRUE if the distribution of the covariate is uniform on -3.0, -2.9, ..., 3.0 and FALSE if the distribution of the covariate is uniform on [–3,3] (default: FALSE) |
An S3 object of type "ATbounds". The object has the following elements.
outcome |
n observations of binary outcomes |
treat |
n observations of binary treatments |
covariate |
n observations of a scalar covariate |
ate_oracle |
the sample analog of E[Y(1) - Y(0)] |
att_oracle |
the sample analog of E[DY(1) - Y(0)|D=1] |
Sokbae Lee and Martin Weidner. Bounding Treatment Effects by Pooling Limited Information across Observations.
data <- simulation_dgp(100, ps_spec = "overlap") y <- data$outcome d <- data$treat x <- data$covariate ate <- data$ate_oracle att <- data$att_oracledata <- simulation_dgp(100, ps_spec = "overlap") y <- data$outcome d <- data$treat x <- data$covariate ate <- data$ate_oracle att <- data$att_oracle
Produce a summary for an ATbounds object.
## S3 method for class 'ATbounds' summary(object, ...)## S3 method for class 'ATbounds' summary(object, ...)
object |
ATbounds object |
... |
Additional arguments for summary generic |
A summary is produced with bounds estimates and confidence intervals. In addition, it has the following elements.
Lower_Bound |
lower bound estimate and lower end point of the confidence interval |
Upper_Bound |
upper bound estimate and upper end point of the confidence interval |
Sokbae Lee and Martin Weidner. Bounding Treatment Effects by Pooling Limited Information across Observations.
Y <- RHC[,"survival"] D <- RHC[,"RHC"] X <- RHC[,c("age","edu")] rps <- rep(mean(D),length(D)) results_ate <- atebounds(Y, D, X, rps, Q = 3) summary(results_ate)Y <- RHC[,"survival"] D <- RHC[,"RHC"] X <- RHC[,c("age","edu")] rps <- rep(mean(D),length(D)) results_ate <- atebounds(Y, D, X, rps, Q = 3) summary(results_ate)