ATE_internal {CausalMetaR} | R Documentation |
Estimating the Average Treatment Effect (ATE) in an internal target population using multi-source data
Description
Doubly-robust and efficient estimator for the ATE in each internal target population using multi-source data.
Usage
ATE_internal(
X,
Y,
S,
A,
cross_fitting = FALSE,
replications = 10L,
source_model = "MN.glmnet",
source_model_args = list(),
treatment_model_type = "separate",
treatment_model_args = list(),
outcome_model_args = list(),
show_progress = TRUE
)
Arguments
X |
Data frame (or matrix) containing the covariate data in the multi-source data. It should have |
Y |
Vector of length |
S |
Vector of length |
A |
Vector of length |
cross_fitting |
Logical specifying whether sample splitting and cross fitting should be used. |
replications |
Integer specifying the number of sample splitting and cross fitting replications to perform, if |
source_model |
Character string specifying the (penalized) multinomial logistic regression for estimating the source model. It has two options: " |
source_model_args |
List specifying the arguments for the source model (in glmnet or nnet). |
treatment_model_type |
Character string specifying how the treatment model is estimated. Options include " |
treatment_model_args |
List specifying the arguments for the treatment model (in SuperLearner). |
outcome_model_args |
List specifying the arguments for the outcome model (in SuperLearner). |
show_progress |
Logical specifying whether to print a progress bar for the cross-fit replicates completed, if |
Details
Data structure:
The multi-source dataset consists the outcome Y
, source S
, treatment A
, and covariates X
(n \times p
) in the internal populations. The data sources can be trials, observational studies, or a combination of both.
Estimation of nuissance parameters:
The following models are fit:
Propensity score model:
\eta_a(X)=P(A=a|X)
. We perform the decompositionP(A=a|X)=\sum_{s} P(A=a|X, S=s)P(S=s|X)
and estimateP(A=1|X, S=s)
(i.e., the treatment model) andq_s(X)=P(S=s|X)
(i.e., the source model).Outcome model:
\mu_a(X)=E(Y|X, A=a)
The models are estimated by SuperLearner with the exception of the source model which is estimated by glmnet or nnet.
ATE estimation:
The ATE estimator is
\dfrac{\widehat \kappa}{n}\sum\limits_{i=1}^{n} \Bigg[ I(S_i = s) \widehat \mu_a(X_i)
+I(A_i = a) \dfrac{\widehat q_{s}(X_i)}{\widehat \eta_a(X_i)} \Big\{ Y_i - \widehat \mu_a(X_i) \Big\} \Bigg],
where \widehat \kappa=\{n^{-1} \sum_{i=1}^n I(S_i=s)\}^{-1}
. The estimator is doubly robust and non-parametrically efficient.
To achieve non-parametric efficiency and asymptotic normality, it requires that ||\widehat \mu_a(X) -\mu_a(X)||\big\{||\widehat \eta_a(X) -\eta_a(X)||+||\widehat q_s(X) -q_s(X)||\big\}=o_p(n^{-1/2})
.
In addition, sample splitting and cross-fitting can be performed to avoid the Donsker class assumption.
When a data source is a randomized trial, it is still recommended to estimate the propensity score for optimal efficiency.
Value
An object of class "ATE_internal". This object is a list with the following elements:
df_dif |
A data frame containing the treatment effect (mean difference) estimates for the internal populations. |
df_A0 |
A data frame containing the potential outcome mean estimates under A = 0 for the internal populations. |
df_A1 |
A data frame containing the potential outcome mean estimates under A = 1 for the internal populations. |
fit_outcome |
Fitted outcome model. |
fit_source |
Fitted source model. |
fit_treatment |
Fitted treatment model(s). |
References
Robertson, S.E., Steingrimsson, J.A., Joyce, N.R., Stuart, E.A. and Dahabreh, I.J. (2021). Center-specific causal inference with multicenter trials: Reinterpreting trial evidence in the context of each participating center. arXiv preprint arXiv:2104.05905.
Wang, G., McGrath, S., Lian, Y. and Dahabreh, I. (2024) CausalMetaR: An R package for performing causally interpretable meta-analyses, arXiv preprint arXiv:2402.04341.
Examples
ai <- ATE_internal(
X = dat_multisource[, 1:10],
Y = dat_multisource$Y,
S = dat_multisource$S,
A = dat_multisource$A,
source_model = "MN.glmnet",
source_model_args = list(),
treatment_model_type = "separate",
treatment_model_args = list(
family = binomial(),
SL.library = c("SL.glmnet", "SL.nnet", "SL.glm"),
cvControl = list(V = 5L)
),
outcome_model_args = list(
family = gaussian(),
SL.library = c("SL.glmnet", "SL.nnet", "SL.glm"),
cvControl = list(V = 5L)
)
)