GPSCDF: Generalized Propensity Score Cumulative Distribution Function...
In GPSCDF: Generalized Propensity Score Cumulative Distribution Function

Description Usage Arguments Details Value Author(s) References Examples

GPSCDF takes in a generalized propensity score (GPS) object with length >2 and returns the GPS-CDF balancing score.

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GPSCDF(pscores = NULL, data = NULL, trt = NULL, stratify = FALSE,
  nstrat = 5, optimal = FALSE, greedy = FALSE, ordinal = FALSE,
  multinomial = FALSE, caliper = NULL)

`pscores`	The object containing the treatment ordered generalized propensity scores for each subject.
`data`	An optional data frame to attach the calculated balancing score. The data frame will also be used in stratification and matching.
`trt`	An optional object containing the treatment variable.
`stratify`	Option to produce strata based on the power parameter (`ppar`). Default is `FALSE`.
`nstrat`	An optional parameter for the number of strata to be created when `stratify` is set to `TRUE`. Default is `5` strata.
`optimal`	Option to perform optimal matching of subjects based on the power parameter (`ppar`). Default is `FALSE`.
`greedy`	Option to perform greedy matching of subjects based on the power parameter (`ppar`). Default is `FALSE`.
`ordinal`	Specifies ordinal treatment groups for matching. Subjects are matched based on the ratio of the squared difference of power parameters for two subjects, `ppar_i` and `ppar_j`, in the numerator and the squared difference in observed treatment received, `trt_i` and `trt_j`, in the denominator: `(ppar_i-ppar_j)^2/(trt_i-trt_j)^2`. Default is `FALSE`.
`multinomial`	Specifies multinomial treatment groups for matching. Subjects are matched based on the absolute difference of power parameters for two subjects, `ppar_i` and `ppar_j`, who received different treatments: `\|ppar_i - ppar_j\|`. Default is `FALSE`.
`caliper`	An optional parameter for the caliper value used when performing greedy matching. Used when `greedy` is set to `TRUE`. Default is `.25*sd(ppar)`.

The GPSCDF method is used to conduct propensity score matching and stratification for both ordinal and multinomial treatments. The method directly maps any GPS vector (with length >2) to a single scalar value that can be used to produce either average treatment effect (ATE) or average treatment effect among the treated (ATT) estimates. For the K multinomial treatments setting, the balance achieved from each K! ordering of the GPS should be assessed to find the optimal ordering of the GPS vector (see Examples for more details).

`ppar`	The power parameter scalar balancing score to be used in outcome analyses through stratification or matching.
`data`	The user defined dataset with power parameter (ppar), strata, and/or optimal matching variables attached.
`nstrat`	The number of strata used for stratification.
`strata`	The strata produced based on the calculated power parameter (`ppar`).
`optmatch`	The optimal matches produced based on the calculated power parameter (`ppar`).
`optdistance`	The average absolute total distance of power parameters (`ppars`) for optimally matched pairs.
`caliper`	The caliper value used for greedy matching.
`grddata`	The user defined dataset with greedy matching variable attached.
`grdmatch`	The greedy matches produced based on the calculated power parameter (`ppar`).
`grdydistance`	The average absolute total distance of power parameters (`ppars`) for greedy matched pairs.

Derek W. Brown, Thomas J. Greene, Stacia M. DeSantis

Greene, TJ. (2017). Utilizing Propensity Score Methods for Ordinal Treatments and Prehospital Trauma Studies. Texas Medical Center Dissertations (via ProQuest).

### Example: Create data example
N<- 100

set.seed(18201) # make sure data is repeatable
Sigma <- matrix(.2,4,4)
diag(Sigma) <- 1
data<-matrix(0, nrow=N, ncol=6,dimnames=list(c(1:N),
      c("Y","trt",paste("X",c(1:4),sep=""))))
data[,3:6]<-matrix(MASS::mvrnorm(N, mu=rep(0, 4), Sigma,
      empirical = FALSE) , nrow=N, ncol = 4)

dat<-as.data.frame(data)


#Create Treatment Variable
tlogits<-matrix(0,nrow=N,ncol=2)
tprobs<-matrix(0,nrow=N,ncol=3)

alphas<-c(0.25, 0.3)
strongbetas<-c(0.7, 0.4)
modbetas<-c(0.2, 0.3)

for(j in 1:2){
  tlogits[,j]<- alphas[j] + strongbetas[j]*dat$X1 + strongbetas[j]*dat$X2+
                modbetas[j]*dat$X3 + modbetas[j]*dat$X4
}

for(j in 1:2){
  tprobs[,j]<- exp(tlogits[,j])/(1 + exp(tlogits[,1]) + exp(tlogits[,2]))
  tprobs[,3]<- 1/(1 + exp(tlogits[,1]) + exp(tlogits[,2]))
}

set.seed(91187)
for(j in 1:N){
  data[j,2]<-sample(c(1:3),size=1,prob=tprobs[j,])
}


#Create Outcome Variable
ylogits<-matrix(0,nrow=N,ncol=1,dimnames=list(c(1:N),c("Logit(P(Y=1))")))
yprobs<-matrix(0,nrow=N,ncol=2,dimnames=list(c(1:N),c("P(Y=0)","P(Y=1)")))

for(j in 1:N){
  ylogits[j,1]<- -1.1 + 0.7*data[j,2] + 0.6*dat$X1[j] + 0.6*dat$X2[j] +
                 0.4*dat$X3[j] + 0.4*dat$X4[j]

  yprobs[j,2]<- 1/(1+exp(-ylogits[j,1]))

  yprobs[j,1]<- 1-yprobs[j,2]
}

set.seed(91187)
for(j in 1:N){
  data[j,1]<-sample(c(0,1),size=1,prob=yprobs[j,])
}

dat<-as.data.frame(data)


### Example: Using GPSCDF

#Create the generalized propensity score (GPS) vector using any parametric or
#nonparametric model

glm<- nnet::multinom(as.factor(trt)~ X1+ X2+ X3+ X4, data=dat)
probab<- round(predict(glm, newdata=dat, type="probs"),digits=8)
gps<-cbind(probab[,1],probab[,2],1-probab[,1]-probab[,2])


#Create scalar balancing power parameter
fit<-GPSCDF(pscores=gps)

## Not run: 
  fit$ppar

## End(Not run)


#Attach scalar balancing power parameter to user defined data set
fit2<-GPSCDF(pscores=gps, data=dat)

## Not run: 
  fit2$ppar
  fit2$data

## End(Not run)


### Example: Ordinal Treatment

#Stratification
fit3<-GPSCDF(pscores=gps, data=dat, stratify=TRUE, nstrat=5)

## Not run: 
  fit3$ppar
  fit3$data
  fit3$nstrat
  fit3$strata

  library(survival)
  model1<-survival::clogit(Y~as.factor(trt)+X1+X2+X3+X4+strata(strata),
                           data=fit3$data)
  summary(model1)

## End(Not run)


#Optimal Matching
fit4<- GPSCDF(pscores=gps, data=dat, trt=dat$trt, optimal=TRUE, ordinal=TRUE)

## Not run: 
  fit4$ppar
  fit4$data
  fit4$optmatch
  fit4$optdistance

  library(survival)
  model2<-survival::clogit(Y~as.factor(trt)+X1+X2+X3+X4+strata(optmatch),
                           data=fit4$data)
  summary(model2)

## End(Not run)


#Greedy Matching
fit5<- GPSCDF(pscores=gps, data=dat, trt=dat$trt, greedy=TRUE, ordinal=TRUE)

## Not run: 
  fit5$ppar
  fit5$data
  fit5$caliper
  fit5$grddata
  fit5$grdmatch
  fit5$grdydistance

  library(survival)
  model3<-survival::clogit(Y~as.factor(trt)+X1+X2+X3+X4+strata(grdmatch),
                           data=fit5$grddata)
  summary(model3)

## End(Not run)


### Example: Multinomial Treatment

#Create all K! orderings of the GPS vector
gps1<-cbind(gps[,1],gps[,2],gps[,3])
gps2<-cbind(gps[,1],gps[,3],gps[,2])
gps3<-cbind(gps[,2],gps[,1],gps[,3])
gps4<-cbind(gps[,2],gps[,3],gps[,1])
gps5<-cbind(gps[,3],gps[,1],gps[,2])
gps6<-cbind(gps[,3],gps[,2],gps[,1])

gpsarry<-array(c(gps1, gps2, gps3, gps4, gps5, gps6), dim=c(N,3,6))


#Create scalar balancing power parameters for each ordering of the GPS vector
fit6<- matrix(0,nrow=N,ncol=6,dimnames=list(c(1:N),c("ppar1","ppar2","ppar3",
              "ppar4","ppar5","ppar6")))

## Not run: 
for(i in 1:6){
  fit6[,i]<-GPSCDF(pscores=gpsarry[,,i])$ppar
}

  fit6

#Perform analyses (similar to ordinal examples) using each K! ordering of the
#GPS vector. Select ordering which achieves optimal covariate balance
#(i.e. minimal standardized mean difference).

## End(Not run)