R/OR.r

In SemiParBIVProbit: Semiparametric Copula Regression Models

OR <- function(x, nm.end, E = TRUE, treat = TRUE, type = "bivariate", ind = NULL, 
   n.sim = 100, prob.lev = 0.05, length.out = NULL, hd.plot = FALSE, or.plot = FALSE, 
   main = "Histogram and Kernel Density of Simulated Odds Ratios", 
   xlab = "Simulated Odds Ratios", ...){

if(x$Cont == "YES") stop("This function is not suitable for bivariate models with continuous/discrete margins.")
if(x$Cont == "NO" && x$VC$ccss == "yes" ) stop("This function is not suitable for selection models.")


CIs <- est.AT <- NULL

etap.noi <- X.int <- X.noi <- eti1 <- eti0 <- etno <- indS <- bs <- ind.excl <- p.int1 <- p.int0 <- d.int1 <- d.int0 <- p.etn <- d.etn <- ass.p <- ass.pst <- C.11 <- C.10 <- sig2 <- peti1s <- peti0s <- sigma2.st <- sigma2s <- eti1s <- eti0s <- d0 <- d1 <- p.etns <- etnos <- etds <- ass.ps <- delta.AT <- 1
diffEf <- fy1.y2 <- est.ATso <- y2 <- CIF <- Pr <- Effects <- NULL
diffEf <- diffEf0 <- 0


m2  <- x$VC$m2 
m3  <- x$VC$m3 
bin.link <- x$VC$bl  
end <- 0
epsilon <- 0.0000001 # 0.9999999 sqrt(.Machine$double.eps)
max.p   <- 0.9999999
est.ATb <- NA
indD <- list()


if(x$v1[1] %in% x$v2[-1]) {end <- 1; eq <- 2} 
if(x$v2[1] %in% x$v1[-1]) {end <- 2; eq <- 1}

if( !( type %in% c("naive","univariate","bivariate") ) ) stop("Error in parameter type value. It should be one of: naive, univariate or bivariate.")
if( !(x$margins[2] %in% bin.link) && eq == 2 ) stop("It does not make sense to calculate OR when the outcome is continuous.")
if(missing(nm.end)) stop("You must provide the name of the endogenous variable.")

if(x$Model=="BSS" || x$Model=="BPO" || x$Model=="BPO0" || end==0) stop("Calculation of this ratio is valid for recursive models only.")
if(is.character(nm.end)==FALSE) stop("nm.end is not a character!")
if( !is.null(ind) && E == FALSE) stop("ind is not designed to be used when some observations are excluded from the OR's calculation.")
if( type == "naive" && E == FALSE) stop("It does not make sense to calculate the naive estimate from the treated only.")

if( !is.null(ind) ){ 

    if(is.logical(ind) == FALSE) stop("ind must be a logical variable.")
    if(length(table(ind))!=2 ) stop("ind must be a logical binary variable.")
    if( length(ind) != x$n ) stop("ind must have the same length as the number of observations used in fitting.")   

}



if( is.null(ind) ) ind <- 1:x$n


if(E == FALSE ) {

 if(!(x$margins[2] %in% bin.link)) ind <- 1:x$n  
 
 if(eq==1) X.int <- as.matrix(x$X1[ind,])
 if(eq==2) X.int <- as.matrix(x$X2[ind,]) 

    if(treat == TRUE)  ind <- as.logical(X.int[, nm.end]) 
    if(treat == FALSE) ind <- as.logical(X.int[, nm.end])!=TRUE
                                              
}



#################################################################################

if(type == "naive" && !(x$margins[2] %in% bin.link)) stop("Please fit a bivariate model with intercept and endogenous variable only and then use OR with the univariate type option.")

#################################################################################

if(type == "naive" && x$margins[2] %in% bin.link){ # it looks fine from comparing the naive and univariate options

if(eq==2){
y1 <- x$y1[ind] 
y2 <- x$y2[ind]
}

if(eq==1){
y1 <- x$y2[ind] 
y2 <- x$y1[ind]
}

tab2 <- table(y1, y2)                                  

n00 <- tab2[1,1]
n01 <- tab2[1,2]
n10 <- tab2[2,1]
n11 <- tab2[2,2]

est.AT <- (n00*n11)/(n01*n10)

sv <- qnorm(prob.lev/2,lower.tail = FALSE) * sqrt(sum(1/tab2))

CIs <- exp( c(log(est.AT) - sv, log(est.AT) + sv) )

est.ATb <- est.ATso <- NULL

}





########################################################

if(type != "naive" && x$margins[2] %in% bin.link){

########################################################
# Set-up
########################################################


if(type == "bivariate"){

	indD[[1]] <- 1:x$X1.d2 
	indD[[2]] <- x$X1.d2+(1:x$X2.d2)
	
}


if(eq==1){ X.int <- as.matrix(x$X1[ind,])

    if(type == "bivariate") ind.int <- indD[[1]]
   
                    
}

if(eq==2){ X.int <- as.matrix(x$X2[ind,])

    if(type == "bivariate") ind.int <- indD[[2]]

}


if(type == "bivariate") coef.int <- as.numeric(coef(x)[ind.int])
	   

               
d0 <- d1 <- X.int
d0[,nm.end] <- 0
d1[,nm.end] <- 1


if(type == "bivariate"){

	eti1 <- d1%*%coef.int 
	eti0 <- d0%*%coef.int 
	
}


if(type == "univariate"){

if(eq==1) ngam <- x$gam1
if(eq==2) ngam <- x$gam2

        eti1 <- d1%*%coef(ngam) 
        eti0 <- d0%*%coef(ngam) 

}

#############################################################################
# OR
#############################################################################

p.int1 <- probm(eti1, x$margins[eq])$pr 
p.int0 <- probm(eti0, x$margins[eq])$pr 

est.AT <- ( mean(p.int1, na.rm = TRUE) * (1 - mean(p.int0, na.rm = TRUE)) ) / ( (1 - mean(p.int1, na.rm = TRUE))*mean(p.int0, na.rm = TRUE)  ) 

#############################################################################
# CIs OR
#############################################################################

 if(type == "univariate") {bs <- rMVN(n.sim, mean = coef(ngam), sigma=ngam$Vp)
                           eti1s <- d1%*%t(bs)
                           eti0s <- d0%*%t(bs) 
                           }
 if(type == "bivariate")  {bs <- rMVN(n.sim, mean = coef(x), sigma=x$Vb)
                           eti1s <- d1%*%t(bs[,ind.int])
                           eti0s <- d0%*%t(bs[,ind.int]) 
                           }  

 peti1s <- probm(eti1s, x$margins[eq])$pr 
 peti0s <- probm(eti0s, x$margins[eq])$pr 

 est.ATb <- ( colMeans(peti1s, na.rm = TRUE)*(1-colMeans(peti0s, na.rm = TRUE)) ) / ( (1-colMeans(peti1s, na.rm = TRUE))*colMeans(peti0s, na.rm = TRUE) )    

######################################################## 

CIs <- as.numeric(quantile(est.ATb, c(prob.lev/2,1-prob.lev/2), na.rm = TRUE))

if(hd.plot == TRUE){
  
  hist(est.ATb, freq = FALSE, main=main, 
       xlab=xlab, 
       ylim=c(0,max(density(est.ATb)$y,hist(est.ATb, plot = FALSE)$density)), ...)
  lines(density(est.ATb))

 }


}




















if(type != "naive" && !(x$margins[2] %in% bin.link)) {


if(is.null(length.out)) length.out <- length( seq( min(ceiling(x$y2)) , max(floor(x$y2)) ) ) 
 y2  <- round( seq( min(ceiling(x$y2)) , max(floor(x$y2)), length.out = length.out  ), 2 ) 
ly2  <- length(y2)
data <- x$dataset[ind,]
 
 

 if(type == "bivariate")  { 
                            ind.int <- 1:x$X1.d2 
                            bs <- rMVN(n.sim, mean = coef(x), sigma = x$Vb)
                            coefe  <- x$coef[ind.int]
                            coefes <- t(bs[, ind.int]) 
                          }
                          
 if(type == "univariate") { bs <- rMVN(n.sim, mean = coef(x$gam1), sigma = x$gam1$Vp) 
                            coefe  <- x$gam1$coefficient 
                            coefes <- t(bs) 
                          }
 

sratio <- function(x11, x00, x01, x10) (x11*x00)/(x01*x10)  
fy1.y2 <- fy10.y2 <- fy1.y2S <- fy10.y2S <- list()
diffE  <- NA 

diffES <- list()
diffEfSquant <- as.data.frame(matrix(NA, ly2 - 1, 2))


for(i in 1:ly2) {

data[, 2]   <- y2[i]
lpm    <- as.matrix( predict.gam(x$gam1, newdata = data, type = "lpmatrix") )
eta1   <- lpm%*%coefe
etins  <- lpm%*%coefes

fy1.y2[[i]]   <- mean(probm(eta1, x$margins[eq])$pr )
fy10.y2[[i]]  <- 1 - fy1.y2[[i]]
fy1.y2S[[i]]  <- colMeans( probm(etins, x$margins[eq])$pr  )
fy10.y2S[[i]] <- 1 - fy1.y2S[[i]]


}


for(i in 1:(ly2-1)) {

  diffE[i]          <- sratio(fy1.y2[[i+1]], fy10.y2[[i]], fy10.y2[[i+1]], fy1.y2[[i]] )
  diffES[[i]]       <- sratio(fy1.y2S[[i+1]], fy10.y2S[[i]], fy10.y2S[[i+1]], fy1.y2S[[i]] )     
  diffEfSquant[i, ] <- quantile(diffES[[i]], probs = c(prob.lev/2,1-prob.lev/2), na.rm = TRUE) 
                            } 




Effects <- data.frame(Ratios = diffE, diffEfSquant)  
names(Effects)[2:3] <- names(quantile(c(1,1), probs = c(prob.lev/2,1-prob.lev/2)))
dimnames(Effects)[[1]] <- y2[2:ly2]


if(or.plot == TRUE){

plot(y2[2:ly2], diffE, log = "y", ylab = "OR", xlab = "Treatment", pch = 16, ylim = c(min(diffEfSquant[,1]),max(diffEfSquant[,2])))
lines(y2[2:ly2], diffE, type = "l")
for (i in 1:(ly2-1)) lines( y = c(diffEfSquant[i,1], diffEfSquant[i,2]), x = c(y2[i+1],y2[i+1]))

}




}


rm(etap.noi, X.int, X.noi, eti1, eti0, etno, indS, bs, ind.excl, p.int1, p.int0, d.int1, d.int0,
   p.etn, d.etn, ass.p, ass.pst, C.11, C.10, sig2, peti1s, peti0s, sigma2.st, sigma2s, eti1s, eti0s, d0, d1,
   p.etns, etnos, etds, ass.ps)   


res <- c(CIs[1], est.AT, CIs[2])


out <- list(res=res, prob.lev=prob.lev, sim.OR=est.ATb, mar2=x$margins[2], type = type,
            Ratios = Effects, treat = y2, eq = eq, bl = x$VC$bl)
 
 
 
class(out) <- "OR"

out


}