CBPS (version 0.10)

CBMSM: Covariate Balancing Propensity Score (CBPS) for Marginal Structural Models

Description

CBMSM estimates propensity scores such that both covariate balance and prediction of treatment assignment are maximized. With longitudinal data, the method returns marginal structural model weights that can be entered directly into a linear model. The method also handles multiple binary treatments administered concurrently.

Usage

CBMSM(formula, id, time, data, type="MSM", twostep = TRUE, 
			msm.variance = "approx", time.vary = FALSE, ...)
	  CBMSM.fit(treat, X, id, time, MultiBin.fit, twostep,
				msm.variance, time.vary, ...)

Arguments

formula

A list of formulas of the form treat ~ X. The function assumes that there is one formula for each time, and they are ordered from the first time to the last time.

id

A vector which identifies the unit associated with each row of treat and X.

time

A vector which identifies the time period associated with each row of treat and X.

data

An optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from

twostep

Set to TRUE to use a two-step estimator, which will run substantially faster than continuous-updating. Default is FALSE, which uses the continuous-updating estimator described by Imai and Ratkovic (2014).

msm.variance

Default is FALSE, which uses the low-rank approximation of the variance described in Imai and Ratkovic (2014). Set to TRUE to use the full variance matrix.

time.vary

Default is FALSE, which uses the same coefficients across time period. Set to TRUE to fit one set per time period.

treat

A vector of treatment assignments. For N observations over T time periods, the length of treat should be N*T.

X

A covariate matrix. For N observations over T time periods, X should have N*T rows.

type

"MSM" for a marginal structural model, with multiple time periods or "MultiBin" for multiple binary treatments at the same time period.

MultiBin.fit

A parameter for whether the multiple binary treatments occur concurrently (FALSE) or over consecutive time periods (TRUE) as in a marginal structural model. Setting type = "MultiBin" when calling CBMSM will set Mult

...

Other parameters to be passed through to optim()

Value

• weights
  The optimal weights.
• fitted.values
  The fitted propensity score for each observation.
• y
  The treatment vector used.
• x
  The covariate matrix.
• id
  The vector id used in CBMSM.fit.
• time
  The vector time used in CBMSM.fit.
• model
  The model frame.
• call
  The matched call.
• formula
  The formula supplied.
• data
  The data argument.
• treat.hist
  A matrix of the treatment history, with each observation in rows and time in columns.
• treat.cum
  A vector of the cumulative treatment history, by individual.

Details

Fits covariate balancing propensity scores for marginal structural models.

References

Imai, Kosuke and Marc Ratkovic. 2014. ``Covariate Balancing Propensity Score.'' Journal of the Royal Statistical Society, Series B (Statistical Methodology). http://imai.princeton.edu/research/CBPS.html Imai, Kosuke and Marc Ratkovic. ``Robust Estimation of Inverse Probability Weights for Marginal Structural Models.'' Journal of the American Statistical Association, Forthcoming. http://imai.princeton.edu/research/MSM.html

See Also

plot.CBMSM

Examples

##Load Blackwell data

data(Blackwell)

form1<-"d.gone.neg ~ d.gone.neg.l1 + d.gone.neg.l2 + d.neg.frac.l3 + camp.length + camp.length + 
		deminc + base.poll + year.2002 + year.2004 + year.2006 + base.und + office"


##Fitting the models in Imai and Ratkovic  (2014)
##Warning: may take a few mintues; setting time.vary to FALSE
##Results in a quicker fit but with poorer balance

fit1<-CBMSM(formula = form1, time=Blackwell$time,id=Blackwell$demName,data=Blackwell, type="MSM",  
	  iterations = NULL, twostep = TRUE, msm.variance = "full", time.vary = TRUE)

fit2<-CBMSM(formula = form1, time=Blackwell$time,id=Blackwell$demName,data=Blackwell, type="MSM",  
	  iterations = NULL, twostep = TRUE, msm.variance = "approx", time.vary = TRUE)


##Assessing balance

bal1<-balance.CBMSM(fit1)
bal2<-balance.CBMSM(fit2)

##Effect estimation: Replicating Effect Estimates in 
##Table 3 of Imai and Ratkovic (2014)

lm1<-lm(demprcnt[time==1]~fit1$treat.hist,data=Blackwell,weights=fit1$glm.weights)
lm2<-lm(demprcnt[time==1]~fit1$treat.hist,data=Blackwell,weights=fit1$weights)
lm3<-lm(demprcnt[time==1]~fit1$treat.hist,data=Blackwell,weights=fit2$weights)

lm4<-lm(demprcnt[time==1]~fit1$treat.cum,data=Blackwell,weights=fit1$glm.weights)
lm5<-lm(demprcnt[time==1]~fit1$treat.cum,data=Blackwell,weights=fit1$weights)
lm6<-lm(demprcnt[time==1]~fit1$treat.cum,data=Blackwell,weights=fit2$weights)



### Example: Multiple Binary Treatments Administered at the Same Time
n<-200
k<-4
set.seed(1040)
X1<-cbind(1,matrix(rnorm(n*k),ncol=k))

betas.1<-betas.2<-betas.3<-c(2,4,4,-4,3)/5
probs.1<-probs.2<-probs.3<-(1+exp(-X1 %*% betas.1))^-1

treat.1<-rbinom(n=length(probs.1),size=1,probs.1)
treat.2<-rbinom(n=length(probs.2),size=1,probs.2)
treat.3<-rbinom(n=length(probs.3),size=1,probs.3)
treat<-c(treat.1,treat.2,treat.3)
X<-rbind(X1,X1,X1)
time<-c(rep(1,nrow(X1)),rep(2,nrow(X1)),rep(3,nrow(X1)))
id<-c(rep(1:nrow(X1),3))
y<-cbind(treat.1,treat.2,treat.3) %*% c(2,2,2)+X1 %*% c(-2,8,7,6,2) + rnorm(n,sd=5)

multibin1<-CBMSM(treat~X,id=id,time=time,type="MultiBin",twostep=TRUE)
summary(lm(y~-1+treat.1+treat.2+treat.3+X1, weights=multibin1$w))