# Note that this work was done in R-3.0.2 and OpenBUGS 3.2.1

rm(list=objects()) # clear workspace

# load relevant libraries
library(R2OpenBUGS)
library(metafor) # for forest plots and classical meta-analysis

## bring in WOMAC pain week 2 data

data<-read.csv("Naproxen_WOMAC_week2_b.csv",na.strings=".")

#              Study         WPCFP   SEWPCFP    Flare
# 1       Internal Study 1 -1.05000 0.1528635     1
# 2       Internal Study 2 -1.00000 0.2403829     0
# 3  Schnitzer et al. 2005 -1.31000 0.1550000     1
# 4       Internal Study 3 -0.85000 0.4305848     1
# 5       Internal Study 4 -0.49000 0.1938418     0
# 6       Internal Study 5 -1.47760 0.3068106     0
# 7       Internal Study 6 -0.95000 0.1531060     1
# 8       Internal Study 7 -1.00000 0.1725125     1
# 9       Internal Study 8 -1.10000 0.3288237     0
# 10      Internal Study 9 -0.83000 0.2249078     1
# 11     Internal Study 10 -0.80138 0.2253445     1
# 12  Baerwald et al. 2010 -1.23000 0.2214520     1
# 13 Schnitzer et al. 2010 -1.27000 0.2156965     1


########################################
# Forest plot as presented in Figure 3 #
########################################


forest(data$WPCFP,data$SEWPCFP,slab=data$Study,
       xlab="Difference in Mean WOMAC pain for Naproxen-placebo at Week 2")
       text(-6, 15, "Study", cex=0.95, adj=0, font=2)
       text(2, 15, "Mean + 95%CI",cex=0.95, adj=0, font=2)



###########################
### Fixed effects model ###
###########################

linebugs1<-function(){
    for (i in 1:num) {
        prec.y[i] <- 1/(se_wp[i] * se_wp[i]) # define precision based on observe within study arm SEs
        y[i] ~ dnorm(d, prec.y[i])  # Define likelihood
        pred[i] ~ dnorm(d, prec.y[i]) # predictive distribution
    }  
    d~dnorm(0,0.0001)  # prior for treatment difference. Low precision, centred around 0  
}

## Write out the model based on the "linebugs" function above

write.model(linebugs1,"linemodel1.txt")

## Prepare data in list format - only keep columns that will be used within the model
num=nrow(data)
linedata1<-list(y=data$WPCFP,se_wp=data$SEWPCFP,num=num)

## Initial values for MCMC. 
## Each random variable in the BUGS model should have an initial value.  Here taking random sample from 
## normal distributin

lineinits1<-function(){
  list(d=rnorm(1,0,2))    
    }
 
## Run the model using OpenBUGS
## debug=T opens the OpenBUGS window and allows you to review, debug, interact with the OpenBUGS run.
## Must close the OpenBUGS window to return to R.
## total iterations 10000 if which 5000 are the burnin.  Posterior distributions formed from the final 
## 5000 iterations. Using 3 chains (MCMC initial values)

WOMAC.FE<-bugs(linedata1,lineinits1,c("d"),"linemodel1.txt",n.iter=10000,n.burnin=5000, n.chains=3,debug=T,codaPkg=F)

##############################
# Random effects model       #
##############################

linebugs2<-function(){
    for (i in 1:num) {
        prec.y[i] <- 1/(se_wp[i] * se_wp[i])  # define precision based on observe within study arm SEs
        y[i] ~ dnorm(mu[i], prec.y[i]) # define likelihood
        mu[i]~ dnorm(d, prec.bsv) # random effects distribution for the treatment difference.
    }    
    d~dnorm(0,0.0001) # prior for treatment difference. Low precision, centred around 0
    tau ~ dunif(0.0001, 20) # uniform prior for between study SD
    tau.sq <- tau * tau
    prec.bsv <- 1/(tau.sq) # define precision in terms of tau
    pred~dnorm(d,prec.bsv)  # predictive distribution
}

## Write out the model based on the "linebugs" function above

write.model(linebugs2,"linemodel2.txt")

## Prepare data in list format - only keep columns that will be used within the model
num=nrow(data)
linedata2<-list(y=data$WPCFP,se_wp=data$SEWPCFP,num=num)

## Initial values for MCMC. 
## Each random variable in the BUGS model should have an initial value
# taking random samples from normal/uniform distribuion as appropriate

lineinits2<-function(){
  list(d=rnorm(1,0,2),tau=runif(1,0.01,20),pred=rnorm(1,0,2))    
    }
 
## Run the model using OpenBUGS
## debug=T opens the OpenBUGS window and allows you to review, debug, interact with the OpenBUGS run.
## Must close the OpenBUGS window to return to R.
## total iterations 10000 if which 5000 are the burnin.  Posterior distributions formed from the final 
## 5000 iterations.  Using 3 chains (MCMC initial values)

WOMAC.RE<-bugs(linedata2,lineinits2,c("d","tau","pred"),"linemodel2.txt",n.iter=10000,n.burnin=5000, n.chains=3,debug=T,codaPkg=F)

################# meta-regression ################
##################################################

# meta-regressin model

linebugs_MR<-function(){
    for (i in 1:num) {
        prec.y[i] <- 1/(se_wp[i] * se_wp[i]) # define precision based on observe within study arm SEs
        y[i] ~ dnorm(mu[i], prec.y[i]) # define likelihood
        mu[i]<- delta[i] + FLCOV*Flare[i] # functional form of mu[i]
        delta[i]~ dnorm(d,prec.bsv) # random effects distribution for the treatment difference with no flare
    }
    
    d~dnorm(0,0.0001) # prior for treatment difference. Low precision, centred around 0
    FLCOV~dnorm(0,0.0001) # prior for 'flare' covariate. Low precision, centred around 0
    tau ~ dunif(0.0001, 20) # uniform prior for between study SD
    tau.sq <- tau * tau
    prec.bsv <- 1/(tau.sq)  # define precision in terms of tau
    pred~dnorm(d,prec.bsv) # predictive distribution
    
}

## Write out the model based on the "linebugs" function above

write.model(linebugs_MR,"linemodel_MR.txt")

## Prepare data in list format - only keep columns that will be used within the model

linedata_MR<-list(y=data$WPCFP,se_wp=data$SEWPCFP,Flare=data$Flare,num=num)

## Initial values for MCMC. 
## Each random variable in the BUGS model should have an initial value
# taking random samples from normal/uniform distribuion as appropriate
    
lineinits_MR<-function(){
  list(d=rnorm(1,0,2),tau=runif(1,0.01,20),pred=rnorm(1,0,2),FLCOV=rnorm(1,0,2))    
    }
 
## Run the model using OpenBUGS
## debug=T opens the OpenBUGS window and allows you to review, debug, interact
## with the OpenBUGS run.
## Must close the OpenBUGS window to return to R.

WOMAC.MR<-bugs(linedata_MR,lineinits_MR,c("d","tau","pred","FLCOV"),"linemodel_MR.txt",n.iter=10000,n.burnin=5000, n.chains=3,debug=T,codaPkg=F)

####################################################
##  compare with classical approach using metafor  #
####################################################

# fixed effects analysis
WP_FE <- rma(yi=WPCFP, sei=SEWPCFP, data=data, method="FE", slab=Study)


funnel(WP_FE, xlab="Naproxen - placebo for mean WOMAC pain")

# rank test: Begg and Mazumdar (1994)
ranktest(WP_FE)  

# regression test - Eggers test
regtest(WP_FE, model = "rma", predictor = "sei", ni = NULL)


# random effects
WP_RE <- rma(yi=WPCFP, sei=SEWPCFP, data=data, method="REML", slab=Study)


# Get 95% confidence intervals for tau, tau^2, I^2 and H^2
confint(WP_RE)

# derive prediction interval

predv<-predict(WP_RE)

#  pred     se    ci.lb   ci.ub   cr.lb   cr.ub
# -1.0232 0.0725 -1.1652 -0.8811 -1.3494 -0.6970

# calculate the standard error incorporating the between study variability
reml_predse <- sqrt(predv$se^2 + WP_RE$tau2) # tau2: estimate of total amount of heterogeneity

# meta-regression
WP_MR<-rma(yi=WPCFP, sei=SEWPCFP, mods=Flare, data=data, method="REML", slab=Study)
funnel(WP_MR)
plot(WP_MR)

# -0.92 (-1.20, -0.63)
# FLARE: -0.14 (-0.47, 0.18)
# tau: 0.1371

#######################################################################
# forest plot with classical and Bayesian estimates on the same plot. #
#######################################################################

# pull out relevant summary statistics

fe_summ<-WOMAC.FE$summary

# print out fe_summ
#            mean         sd   2.5%    25%    50%      75%      97.5%     Rhat n.eff
#d        -1.025216 0.05697417 -1.136 -1.064 -1.026 -0.98670 -0.9132925 1.001054 13000
#deviance  3.271001 1.42959277  2.262  2.368  2.721  3.60625  7.3762498 1.001005 15000

fe_est<-fe_summ[1,1]    # row 1 column 1 [1,1] =-1.025216
fe_se<-fe_summ[1,2]     # row 1 column 1 [1,2] =0.05697417

#Random effects
re_summ<-WOMAC.RE$summary

# print out re_summ
#              mean        sd          2.5%        25%      50%     75%      97.5%     Rhat n.eff
#d        -1.0245208 0.0792181  -1.184000000 -1.0740000 -1.02400 -0.9751 -0.8689000 1.001031 24000
#tau       0.1661245 0.0978066   0.009971948  0.0967875  0.15675  0.2226  0.3881025 1.032181   340
#pred     -1.0253628 0.2083730  -1.459000000 -1.1300000 -1.02300 -0.9219 -0.5862900 1.000960 30000
#deviance -2.3352140 4.3680104 -10.160000000 -5.6880000 -2.49550  1.0160  5.9210750 1.002111  1700

re_est<-re_summ[1,1]    # row 1, column 1 [1,1]=-1.0245208
re_se<-re_summ[1,2]     # row 1, column 2 [1,2]=0.0792181

##  prediction interval:
repred<-re_summ[3,1]       # row 3, column 1 [3,1]=-1.0253628
re_pred_se<-re_summ[3,2]   # row 3, column 2 [3,2]=0.2083730

# forest plot of original data with BUGS estimates 
# use forest function with the addpoly function to add the classical and Bayesian estimates


forest(WP_FE, order=rev(order(data$WPCFP)), 
       at=-3:1, ylim=c(-7,16), refline=0,
       xlab="Mean Difference",
       mlab="Frequentist fixed effects estimate")

text(-4.5, 15, "Study", cex=0.95, adj=0, font=2)
text(1, 15, "Mean + 95%CI",cex=0.95, adj=0, font=2)
# add REML estimate and CI
addpoly(x=coef(summary(WP_RE))$estimate, sei=coef(summary(WP_RE))$se,
        row=-2,col="red", mlab="Frequentist random effects estimate",cex=1)
# add REML estimate and prediction interval
addpoly(x=coef(summary(WP_RE))$estimate, sei=reml_predse,
        row=-3,col="blue",mlab="Frequentist prediction interval",cex=1)
# add BUGS FE estimate and CI
addpoly(x=fe_est, sei=fe_se, row=-5,col="black",mlab="Bayesian fixed effects estimate",cex=1)
# add BUGS RE estimate and CI
addpoly(x=re_est, sei=re_se, row=-6,col="red",mlab="Bayesian random effects estimate",cex=1)
#  add BUGS RE prediction interval
addpoly(x=repred, sei=re_pred_se, row=-7,col="blue",mlab="Bayesian prediction interval",cex=1)


# Note old R.12 and earlier use coef(WP_RE)$estimate
# now need to use coef(summary(WP_RE))$estimate