Description Usage Arguments Details Value Note Author(s) References Examples
sace
estimates survivor average causal effects (SACE) with outcomes truncated by death.
1 2 
Z 
a logical vector. Exposure indicator. Convetionally, 
S 
a logical vector. Survival indicator. 
Y 
a numeric vector. (Univariate) outcomes. May have 
X 
an optional numeric matrix or vector. Baseline covariates. 
A 
an optional numeric matrix or vector. Substitution variable(s) which satisfies the assumptions of "exclusion restriction" and "substitution relevance". See references. If 
subset 
an optional vector specifying a subset of obervations to be used. 
optim.method 
The method to be used for maximum likelihood optimization. See optim. 
max.step 
integer. Maximum iterating steps of maximum likelihood optimization. 
singular.ok 
logical. Refers to the OLS estimation of the coefficients 
need.variance 
logical. Is variance of parameters and estimators needed? See details. 
hessian 
logical. If 
This function sace
, gives estimation of average causal effects (ACE) with outcomes truncated by death. The identification of SACE relies on the existence of a substitution variable and requires the assumptions of monotonicity, ignorability, exclusion restriction, and relevance. While the naive estimates given by the coefficient of Z
from lm(Y ~ Z + X + A, subset = S == 1)
are restricted among survivors and therefore may be subject to selection bias, this method gives consistent estimates of the SACE (survivor average causal effect), defined as the average causal effect among the subgroup consisting of subjects who would survive under either exposure, i.e. among the alwayssurvivor group (G=LL). See references for details of the assumptions and the model parameterizations.
Parameters beta
and gamma
are estimated by MLE, using optim.
If need.variance == TRUE
, the asymptotic variance estimators of both parameters and estimators will be given. This requires the numDeriv package.
a list with following elements:
CALL 
function call. 
data 
data used (within the specified subset). 
optim.method 
method used for optimization. 
need.variance 
is variance of parameters and estimators needed? 
n 
sample size. 
mu_0_LL 
average potential outcomes among control group, E[ Y(0)  G=LL ]. 
mu_1_LL 
average potential outcomes among treatment group, E[ Y(1)  G=LL ]. 
sace 
survivor average causal effect, equals 
beta 
Pr{S(1)=1 X,A}=expit(β_0+X' β_1+ A β_2), estimated by MLE. 
gamma 
Pr{S(0)=1 X,A}/Pr{S(1)=1 X,A}=expit(γ_0+X' γ_1+ A γ_2), estimated by MLE. 
beta_gamma.convergence 
indicator of convergence of MLE optimization of beta and gamma. 0 means convergence. See optim. 
alpha_1 
E[Y(0) Z=0, G=LL, X, A ]=α_{10}+X' α_{11}+ A α_{12}, coefficients of 
alpha_2 
E[Y(1) Z=1, G=LL, X, A ]=α_{20}+X' α_{21}+ G α_{22}, coefficients of 
The following items will be given only if need.variance == TRUE
:
beta.var 
estimated asymptotic covariance matrix of beta. 
gamma.var 
estimated asymptotic covariance matrix of gamma. 
relevance.Pvalue 
P value of the asymptotic chisquared test on the relevance assumption for the substitution variable. A large P value suggests that the relevance assumption may not hold, namely, the substitution variable(s) may have little impact on the latent survival type. 
alpha_1.var 
estimated asymptotic covariance matrix of alpha_1. 
alpha_2.var 
estimated asymptotic covariance matrix of alpha_2. 
mu_0_LL.var 
estimated asymptotic variance of mu_0_LL. 
mu_1_LL.var 
estimated asymptotic variance of mu_1_LL. 
sace.var 
estimated asymptotic variance of the SACE. 
The length of vectors Z
, Y
, S
, as well as the row number of matrix X
and A
must equal the sample size n
.
Linbo Wang <linbo.wang@utoronto.ca>
Zhixuan Shao <shaozhixuansh@pku.edu.cn>
Linbo Wang, XiaoHua Zhou, Thomas S. Richardson; Identification and estimation of causal effects with outcomes truncated by death, Biometrika, Volume 104, Issue 3, 1 September 2017, Pages 597612, https://doi.org/10.1093/biomet/asx034
1 2 3 4  attach(simulated_data)
X < cbind(X.X1, X.V2, X.V3)
sace.result < sace(Z, S, Y, X, A)
sace

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