diff --git a/R/brier_score.R b/R/brier_score.R
index c3b319e34..045d5c147 100644
--- a/R/brier_score.R
+++ b/R/brier_score.R
@@ -1,4 +1,5 @@
 
+#' Test
 
 #' Re-used documentation for Brier Score components
 #'
diff --git a/design/examples/mCRCpub/00- Load.R b/design/examples/mCRCpub/00- Load.R
new file mode 100644
index 000000000..a20142f4e
--- /dev/null
+++ b/design/examples/mCRCpub/00- Load.R	
@@ -0,0 +1,35 @@
+#' ####################################################
+#'
+#'   2stgTGIOS
+#'   Loading the required R libraries
+#'
+#'   Q1-2022
+#'   Francois Mercier
+#'
+#' ####################################################
+
+
+#' if (!require("remotes")) {
+#'   install.packages("remotes")
+#' }
+#' remotes::install_github("genentech/jmpost")
+#' install.packages("ghibli")
+
+#' General purpose
+#' =================
+library(tidyverse)
+library(tidyselect)
+library(ghibli)
+
+#' Data import/export
+#' =================
+library(haven)
+
+#' Survival
+#' =================
+library(survival)
+library(survminer)
+
+#' Joint models
+#' =================
+library(jmpost)
diff --git a/design/examples/mCRCpub/01- ImportHORIZON.R b/design/examples/mCRCpub/01- ImportHORIZON.R
new file mode 100644
index 000000000..0fe7af7f4
--- /dev/null
+++ b/design/examples/mCRCpub/01- ImportHORIZON.R	
@@ -0,0 +1,101 @@
+#' ####################################################
+#'
+#'   Data preparation
+#'   HORIZONIII study (from PDS)
+#'
+#'   Q3-2024
+#'   Francois Mercier
+#'
+#' ####################################################
+
+
+#' sessionInfo()
+
+#' ----------------------------------
+#' Structure analysis data set:
+#' ----------------------------------
+#' For time to event sub-model (event.df):
+#' ***************************
+#' SUBJID (chr)
+#' STUDY (chr)
+#' ATRT (chr)
+#'
+#' EVENTYR (num) - Time to event (in years)
+#' EVENTFL (0/1) - Flag =1 if the ind died, 0 if censored
+#'
+#' For longi (TGI) sub-model (biom.df):
+#' ***************************
+#' SUBJID (chr)
+#' STUDY (chr)
+#' ATRT (chr)
+#'
+#' BIOMVAL (num) - Biomarker (here, SLD in mm) value
+#' BIOMYR (num) - Biomarker measurement time (in years)
+#' ----------------------------------
+
+
+#' ===============================================
+#' Import and Select
+#' ===============================================================
+
+#' Event data frame
+#' -----------------
+subj<-haven::read_sas("./design/examples/mCRCpub/data/HORIZONIII/rdpsubj.sas7bdat")
+rcist<-haven::read_sas("./design/examples/mCRCpub/data/HORIZONIII/rdprcist.sas7bdat")
+
+#' Only keep patients in PerProtocol set (PP_SET==1)
+#' and exposed to BEV for at least 3 weeks (i.e. at least 1st TA visit)
+subj0<-subj |>
+  filter(PP_SET==1, !is.na(BEV_SDY), !is.na(BEV_EDY), BEV_EDY>3*7) |>
+  mutate(SUBJID=as.character(RANDCODE)) |>
+  select(SUBJID, LDH1_5)
+#' length(unique(subj0$SUBJID))
+#' 645
+
+event.df0<-rcist |>
+  mutate(SUBJID=as.character(RANDCODE)) |>
+  filter(SUBJID %in% subj0$SUBJID) |>
+  group_by(SUBJID) %>% slice(1) %>% ungroup() |>
+  mutate(EVENTYR=OSTIM/365.25, EVENTFL=ifelse(DEATFLAG==1, 0, 1),
+         ATRT="FOLFOX alone", STUDY="2") |>
+  select(SUBJID, STUDY, ATRT, EVENTYR, EVENTFL)
+
+UID.event0<-unique(event.df0$SUBJID)
+#' length(UID.event0)
+#' 645
+
+#' Biomarker (SLD) data frame
+#' -----------------
+#' - remove rows where SLD is NA
+#' - remove rows where patients have PBLCNT=NA i.e. remove patient with at least one post-baseline TA
+biom.df0<-rcist |>
+  filter(!is.na(PBLCNT), !is.na(STLDI)) |>
+  mutate(SUBJID=as.character(RANDCODE), STUDY="2", ATRT="FOLFOX alone",
+         BIOMVAL=ifelse(STLDI==0, 2.5, STLDI*10),
+         BIOMYR=ORDYTRT/365.25) |>
+  select(SUBJID, STUDY, ATRT, BIOMVAL, BIOMYR)
+
+UID.biom0<-unique(biom.df0$SUBJID)
+#' length(UID.biom0)
+#' 660
+
+#' Retain matching patients
+#' -----------------
+
+retainID<-intersect(UID.event0, UID.biom0)
+#' 640
+
+event.df<-event.df0 |> filter(SUBJID %in% retainID)
+#' length(unique(event.df$SUBJID))
+#' 640
+#' saveRDS(event.df, file="./design/examples/mCRCpub/data/HORIZONIII/HorizOSads.rds")
+
+
+biom.df<-biom.df0 |> filter(SUBJID %in% retainID)
+#' length(unique(biom.df$SUBJID))
+#' 640
+#' saveRDS(biom.df, file="./design/examples/mCRCpub/data/HORIZONIII/HorizTGIads.rds")
+
+
+
+
diff --git a/design/examples/mCRCpub/01- ImportPRIME.R b/design/examples/mCRCpub/01- ImportPRIME.R
new file mode 100644
index 000000000..74bcb3529
--- /dev/null
+++ b/design/examples/mCRCpub/01- ImportPRIME.R	
@@ -0,0 +1,96 @@
+#' ####################################################
+#'
+#'   Data preparation
+#'   PRIME study (from PDS)
+#'
+#'   Q3-2024
+#'   Francois Mercier
+#'
+#' ####################################################
+
+
+#' sessionInfo()
+
+#' ----------------------------------
+#' Structure analysis data set:
+#' ----------------------------------
+#' For time to event sub-model (event.df):
+#' ***************************
+#' SUBJID (chr)
+#' STUDY (chr)
+#' ATRT (chr)
+#'
+#' EVENTYR (num) - Time to event (in years)
+#' EVENTFL (0/1) - Flag =1 if the ind died, 0 if censored
+#'
+#' For longi (TGI) sub-model (biom.df):
+#' ***************************
+#' SUBJID (chr)
+#' STUDY (chr)
+#' ATRT (chr)
+#'
+#' BIOMVAL (num) - Biomarker (here, SLD in mm) value
+#' BIOMYR (num) - Biomarker measurement time (in years)
+#' ----------------------------------
+
+
+#' ===============================================
+#' Import and Select
+#' ===============================================================
+
+#' Event data frame
+#' -----------------
+kras<-haven::read_sas("./design/examples/mCRCpub/data/PRIME/biomark_pds2019.sas7bdat")
+kras0<-kras |> select("SUBJID", "BMMTR1")
+
+adsl<-haven::read_sas("./design/examples/mCRCpub/data/PRIME/adsl_pds2019.sas7bdat")
+event.df0<-adsl |>
+    left_join(kras0, by="SUBJID") |>
+    filter(BMMTR1=="Wild-type") |>
+    mutate(STUDY="1", EVENTYR=DTHDY/365.25, EVENTFL=DTH) |>
+  select("SUBJID", "STUDY", "ATRT", "EVENTYR", "EVENTFL")
+
+UID.event0<-unique(event.df0$SUBJID)
+#' length(UID.event0)
+#' 514
+
+
+#' Biomarker (SLD) data frame
+#' -----------------
+adtr<-haven::read_sas("./design/examples/mCRCpub/data/PRIME/adls_pds2019.sas7bdat")
+biom.df0<-adtr |>
+  filter(LSCAT=="Target lesion", !is.na(LSSLD)) |>
+  mutate(STUDY="1", BIOMYR=VISITDY/365.25, BIOMVAL=LSSLD) |>
+  group_by(SUBJID, VISITDY) |> slice(1) |> ungroup() |>
+  select("SUBJID", "BIOMYR", "BIOMVAL")
+
+UID.biom0<-unique(biom.df0$SUBJID)
+#' length(UID.biom0)
+#' 488
+
+
+#' Retain matching patients
+#' -----------------
+retainID<-intersect(UID.event0, UID.biom0)
+#' 263
+
+event.df<-event.df0 |> filter(SUBJID %in% retainID)
+#' length(unique(event.df$SUBJID))
+#' 263
+#' saveRDS(event.df, file="./design/examples/mCRCpub/data/PRIME/PRIMEOSads.rds")
+
+desn0<-event.df0 |>
+    filter(SUBJID %in% retainID) |>
+    select(SUBJID, STUDY, ATRT)
+
+biom.df<-biom.df0 |>
+    filter(SUBJID %in% retainID) |>
+    left_join(desn0, by="SUBJID")
+#' length(unique(biom.df$SUBJID))
+#' 263
+#' saveRDS(biom.df, file="./design/examples/mCRCpub/data/PRIME/PRIMETGIads.rds")
+
+
+
+
+
diff --git a/design/examples/mCRCpub/02- DescHORIZON.R b/design/examples/mCRCpub/02- DescHORIZON.R
new file mode 100644
index 000000000..b47624210
--- /dev/null
+++ b/design/examples/mCRCpub/02- DescHORIZON.R	
@@ -0,0 +1,65 @@
+#' ####################################################
+#'
+#'   Descriptive plots
+#'   HORIZONIII study (from PDS)
+#'
+#'   Q3-2024
+#'   Francois Mercier
+#'
+#' ####################################################
+
+
+#' sessionInfo()
+
+#' ===============================================
+#' Visualize SLD
+#' ===============================================
+
+#' biom.df<-readRDS("./design/examples/mCRCpub/data/HORIZONIII/HorizTGIads.rds")
+#' summary(biom.df)
+
+ybreaks<-c(3, 30, 100, 300)
+g0<-ggplot(biom.df, aes(x=BIOMYR, y=BIOMVAL))+
+  geom_line(aes(group=SUBJID), colour="grey", alpha=0.2)+
+  geom_point(colour="orange4", alpha=0.6, size=0.9)+
+  scale_x_continuous("Year", breaks=0.5*(0:5))+
+  scale_y_continuous("SLD (mm)", breaks=ybreaks)+
+  theme_minimal()+
+  theme(panel.grid.minor=element_blank())
+g0
+
+set.seed(130)
+retainIDsub<-sample(retainID, size=60)
+
+g0sub<-biom.df |> filter(SUBJID %in% retainIDsub) |>
+  ggplot(aes(x=BIOMYR, y=BIOMVAL))+
+  geom_line(aes(group=SUBJID), colour="grey", alpha=0.2)+
+  geom_point(colour="orange4", alpha=0.6, size=0.9)+
+  facet_wrap(~as.factor(SUBJID))+
+  scale_x_continuous("Year", breaks=0.5*(0:5))+
+  scale_y_continuous("SLD (mm)", breaks=ybreaks)+
+  theme_minimal()+
+  theme(panel.grid.minor=element_blank())
+g0sub
+
+
+#' ===============================================
+#' Visualize OS
+#' ===============================================
+
+#' event.df<-readRDS("./design/examples/mCRCpub/data/HORIZONIII/HorizOSads.rds")
+#' summary(event.df)
+
+cox<-coxph(Surv(EVENTYR, EVENTFL)~1, data=event.df)
+summary(cox)
+
+os.kmest<-survfit(Surv(EVENTYR, EVENTFL)~1, data=event.df)
+mycols<-c(rev(ghibli::ghibli_palettes$YesterdayMedium)[c(2,4)])
+g1<-survminer::ggsurvplot(os.kmest, data=event.df,
+   risk.table=T, break.x.by=0.5, legend.title="",
+   xlab="Time (year)", ylab="Overall survival",
+   risk.table.fontsize=4, legend=c(0.8, 0.8), palette = mycols)
+g1
+
+
+
diff --git a/design/examples/mCRCpub/02- DescPRIME.R b/design/examples/mCRCpub/02- DescPRIME.R
new file mode 100644
index 000000000..5a371524a
--- /dev/null
+++ b/design/examples/mCRCpub/02- DescPRIME.R	
@@ -0,0 +1,56 @@
+#' ####################################################
+#'
+#'   Descriptive plots
+#'   PRIME study (from PDS)
+#'
+#'   Q3-2024
+#'   Francois Mercier
+#'
+#' ####################################################
+
+
+#' sessionInfo()
+
+#' ===============================================
+#' Visualize SLD
+#' ===============================================
+
+#' biom.df<-readRDS("./design/examples/mCRCpub/data/PRIME/PRIMETGIads.rds")
+#' summary(biom.df)
+
+#' Display SLD spaghetti
+ybreaks<-c(3, 30, 100, 300)
+mycols<-c(rev(ghibli::ghibli_palettes$YesterdayMedium)[c(2,4)])
+g0<-ggplot(data=biom.df, aes(x=BIOMYR, y=BIOMVAL))+
+    geom_point(colour="grey33", alpha=0.3, size=0.9)+
+    geom_line(aes(group=SUBJID, colour=as.factor(ATRT)), alpha=0.6)+
+    facet_wrap(~ATRT)+
+    scale_x_continuous("Year", breaks=0.5*(0:5))+
+    scale_y_continuous("SLD (mm)", breaks=ybreaks)+
+    scale_colour_manual(values=mycols, guide="none")+
+    theme_minimal()+
+    theme(panel.grid.minor=element_blank())
+g0
+
+#' ===============================================
+#' Visualize OS
+#' ===============================================
+
+#' event.df<-readRDS("./design/examples/mCRCpub/data/PRIME/PRIMEOSads.rds")
+#' summary(event.df)
+
+cox<-coxph(Surv(EVENTYR, EVENTFL)~ATRT, data=event.df)
+summary(cox)
+
+os.kmest<-survfit(Surv(EVENTYR, EVENTFL)~ATRT, data=event.df)
+
+#' Display OS KM
+g1<-survminer::ggsurvplot(os.kmest,
+  data=event.df, risk.table=T, break.x.by=.5, legend.title="",
+  xlab="Year", ylab="Overall survival", palette = mycols,
+  risk.table.fontsize=4, legend=c(0.8, 0.8))
+g1
+
+
+
+
diff --git a/design/examples/mCRCpub/03- jmHORIZON.R b/design/examples/mCRCpub/03- jmHORIZON.R
new file mode 100644
index 000000000..28e789576
--- /dev/null
+++ b/design/examples/mCRCpub/03- jmHORIZON.R	
@@ -0,0 +1,139 @@
+#' ####################################################
+#'
+#'   Joint models
+#'   HORIZONIII study (from PDS)
+#'
+#'   Q3-2024
+#'   Francois Mercier
+#'
+#' ####################################################
+
+
+#' sessionInfo()
+
+
+#' biom.df<-readRDS("./design/examples/mCRCpub/data/PRIME/HorizTGIads.rds")
+#' summary(biom.df)
+
+#' event.df<-readRDS("./design/examples/mCRCpub/data/PRIME/HorizOSads.rds")
+#' summary(event.df)
+
+
+#' ===============================================
+#' Model SLD
+#' ===============================================
+
+######
+#' !!!!!!!!!!!
+######
+event.subset.for.test<-event.df |> filter(SUBJID %in% retainIDsub)
+biom.subset.for.test<-biom.df |> filter(SUBJID %in% retainIDsub)
+######
+#' !!!!!!!!!!!
+######
+
+tgi.dat<-DataJoint(
+  subject = DataSubject(data=event.subset.for.test, subject="SUBJID", arm="ATRT", study="STUDY"),
+  longi   = DataLongitudinal(data=biom.subset.for.test, threshold=3, formula= BIOMVAL~BIOMYR)
+  )
+
+tgi.in<-JointModel(longitudinal=LongitudinalSteinFojo(
+  mu_bsld=prior_lognormal(log(70), .2),
+  mu_ks=prior_lognormal(log(0.01), .3),
+  mu_kg=prior_lognormal(log(0.01), .3),
+  omega_bsld=prior_lognormal(log(0.5), 0.3),
+  omega_ks=prior_lognormal(log(0.7), 0.3),
+  omega_kg=prior_lognormal(log(0.7), 0.3),
+  sigma=prior_lognormal(log(0.2), 0.1)))
+
+tgi.samples<-sampleStanModel(tgi.in, data=tgi.dat, iter_warmup=2000,
+  iter_sampling=1000, chains=3, parallel=3, refresh=500)
+tgi.out<-as.CmdStanMCMC(tgi.samples)
+print(tgi.out, max_rows=500, digits=5)
+
+#' Display profiles OBS vs IPRED for 10 random individuals
+selected_subjects<-sample(event.subset.for.test$SUBJID, 10)
+longquant_obs<-LongitudinalQuantities(tgi.samples, grid=GridObserved(subjects=selected_subjects))
+g2<-autoplot(longquant_obs)+
+    theme_minimal()+
+    theme(panel.grid.minor=element_blank())
+g2
+summary(longquant_obs)
+
+#' mu_BSLD: hist(rlnorm(1000, log(70), .2))
+#' mu_ks: hist(rlnorm(1000, log(0.01), .3))
+#' om_BSLD: hist(rlnorm(1000, log(0.5), 0.3))
+#' om_ks: hist(rlnorm(1000, log(0.7), 0.3))
+#' om_sigma: hist(rlnorm(1000, log(0.2), 0.1))
+
+
+#' ===============================================
+#' Model OS
+#' ===============================================
+
+surv.dat<-DataJoint(
+  subject  = DataSubject(data=event.df, subject="SUBJID", arm="ATRT", study="STUDY"),
+  survival = DataSurvival(data=event.df, formula=Surv(EVENTYR, EVENTFL)~1)
+)
+
+surv.in<-JointModel(survival=SurvivalWeibullPH())
+
+surv.samples<-sampleStanModel(surv.in, data=surv.dat, iter_warmup=2000,
+    iter_sampling=1000, chains=3, parallel=3, refresh=500)
+surv.out<-as.CmdStanMCMC(surv.samples)
+print(surv.out, max_rows=500, digits=5)
+
+#' Display PRED vs OBS surv curves
+expected.surv<-SurvivalQuantities(surv.samples, type="surv",
+  grid=GridGrouped(times=seq(from=0, to=3, by=0.1),
+                   groups=split(event.df$SUBJID, event.df$ATRT)))
+
+mycols<-c(rev(ghibli::ghibli_palettes$YesterdayMedium)[c(2,4)])
+g3<-autoplot(expected.surv, add_km=T, add_wrap=F)+
+    scale_fill_manual(values=mycols)+
+    scale_colour_manual(values=mycols)+
+    theme_minimal()+
+    theme(panel.grid.minor=element_blank())
+g3
+
+
+#' ===============================================
+#' Model JM
+#' ===============================================
+
+jm.dat<-DataJoint(
+  subject  = DataSubject(data=event.df, subject="SUBJID", arm="ATRT", study="STUDY"),
+  longitudinal = DataLongitudinal(data=biom.df, threshold=2, formula= BIOMVAL~BIOMYR),
+  survival = DataSurvival(data=event.df, formula=Surv(EVENTYR, EVENTFL)~1)
+)
+
+jm.in<-JointModel(
+  longitudinal=LongitudinalSteinFojo(
+    mu_bsld=prior_lognormal(log(70), .2),
+    mu_ks=prior_lognormal(log(0.01), .3),
+    mu_kg=prior_lognormal(log(0.01), .3),
+    omega_bsld=prior_lognormal(log(0.5), 0.3),
+    omega_ks=prior_lognormal(log(0.7), 0.3),
+    omega_kg=prior_lognormal(log(0.7), 0.3),
+    sigma=prior_lognormal(log(0.2), 0.1)),
+  survival=SurvivalWeibullPH(),
+  link=Link(linkTTG(prior_normal(0.01, 3)))
+)
+
+jm.samples<-sampleStanModel(jm.in, data=jm.dat,
+    iter_sampling=1000, iter_warmup=2000, chains=3, parallel_chains=3)
+
+jm.out<-as.CmdStanMCMC(jm.samples)
+print(jm.out, max_rows=500, digits=5)
+
+#' Display PRED vs OBS surv curves
+expected.surv<-SurvivalQuantities(jm.samples, type="surv",
+    grid=GridGrouped(times=seq(from=0, to=3, by=0.1),
+    groups=split(event.df$SUBJID, event.df$ATRT)))
+
+g4<-autoplot(expected.surv, add_km=T, add_wrap=F)+
+    scale_fill_manual(values=mycols)+
+    scale_colour_manual(values=mycols)+
+    theme_minimal()+
+    theme(panel.grid.minor=element_blank())
+g4
diff --git a/design/examples/mCRCpub/03- jmPRIME.R b/design/examples/mCRCpub/03- jmPRIME.R
new file mode 100644
index 000000000..60e512a64
--- /dev/null
+++ b/design/examples/mCRCpub/03- jmPRIME.R	
@@ -0,0 +1,128 @@
+#' ####################################################
+#'
+#'   Joint models
+#'   PRIME study (from PDS)
+#'
+#'   Q3-2024
+#'   Francois Mercier
+#'
+#' ####################################################
+
+
+#' sessionInfo()
+
+
+#' biom.df<-readRDS("./design/examples/mCRCpub/data/PRIME/PRIMETGIads.rds")
+#' summary(biom.df)
+
+#' event.df<-readRDS("./design/examples/mCRCpub/data/PRIME/PRIMEOSads.rds")
+#' summary(event.df)
+
+
+#' ===============================================
+#' Model SLD
+#' ===============================================
+
+tgi.dat<-DataJoint(
+  subject = DataSubject(data=event.df, subject="SUBJID", arm="ATRT", study="STUDY"),
+  longi   = DataLongitudinal(data=biom.df, threshold=3, formula= BIOMVAL~BIOMYR)
+  )
+
+tgi.in<-JointModel(longitudinal=LongitudinalSteinFojo(
+    mu_bsld = prior_lognormal(log(70), .1),
+    mu_ks = prior_lognormal(log(1.8), .1),
+    mu_kg = prior_lognormal(log(0.15), .1),
+    omega_bsld = prior_lognormal(log(0.1), .1),
+    omega_ks = prior_lognormal(log(0.1), .5),
+    omega_kg = prior_lognormal(log(0.1), .5),
+    sigma = prior_lognormal(log(0.18), .5),
+))
+
+tgi.samples<-sampleStanModel(tgi.in, data=tgi.dat,
+                             iter_sampling = 1000,
+                             iter_warmup = 2000,
+                             chains = 3, parallel_chains = 3)
+tgi.out<-as.CmdStanMCMC(tgi.samples)
+print(tgi.out, max_rows=500, digits=5)
+
+#' Display profiles OBS vs IPRED for 10 random individuals
+selected_subjects<-head(event.df$SUBJID, 10)
+longquant_obs<-LongitudinalQuantities(tgi.samples, grid=GridObserved(subjects=selected_subjects))
+autoplot(longquant_obs)
+
+
+#' ===============================================
+#' Model OS
+#' ===============================================
+
+surv.dat<-DataJoint(
+  subject  = DataSubject(data=event.df, subject="SUBJID", arm="ATRT", study="STUDY"),
+  survival = DataSurvival(data=event.df, formula=Surv(EVENTYR, EVENTFL)~ATRT)
+)
+
+surv.in<-JointModel(survival=SurvivalWeibullPH())
+
+surv.samples<-sampleStanModel(surv.in, data=surv.dat,
+                              iter_sampling = 1000,
+                              iter_warmup = 2000,
+                              chains = 3, parallel_chains = 3)
+surv.out<-as.CmdStanMCMC(surv.samples)
+print(surv.out, max_rows=500, digits=5)
+
+#' Display PRED vs OBS surv curves
+expected.surv<-SurvivalQuantities(surv.samples, type="surv",
+  grid=GridGrouped(times=seq(from=0, to=4, by=0.1),
+  groups=split(event.df$SUBJID, event.df$ATRT)))
+
+mycols<-c(rev(ghibli::ghibli_palettes$YesterdayMedium)[c(2,4)])
+g3<-autoplot(expected.surv, add_km=T, add_wrap=F)+
+    scale_fill_manual(values=mycols)+
+    scale_colour_manual(values=mycols)+
+    theme_minimal()+
+    theme(panel.grid.minor=element_blank())
+g3
+
+
+#' ===============================================
+#' Model JM
+#' ===============================================
+
+jm.dat<-DataJoint(
+  subject  = DataSubject(data=event.df, subject="SUBJID", arm="ATRT", study="STUDY"),
+  longitudinal = DataLongitudinal(data=biom.df, threshold=3, formula= BIOMVAL~BIOMYR),
+  survival = DataSurvival(data=event.df, formula=Surv(EVENTYR, EVENTFL)~ATRT)
+)
+
+jm.in<-JointModel(
+  longitudinal=LongitudinalSteinFojo(
+    mu_bsld = prior_lognormal(log(70), .1),
+    mu_ks = prior_lognormal(log(1.8), .1),
+    mu_kg = prior_lognormal(log(0.15), .1),
+    omega_bsld = prior_lognormal(log(0.1), .1),
+    omega_ks = prior_lognormal(log(0.1), .5),
+    omega_kg = prior_lognormal(log(0.1), .5),
+    sigma = prior_lognormal(log(0.18), .5),
+  ),
+  survival = SurvivalWeibullPH(),
+  link = Link(linkTTG(prior_normal(0.01, 3)))
+)
+
+jm.samples<-sampleStanModel(jm.in,
+  data = jm.dat,
+  iter_sampling = 1000,
+  iter_warmup = 2000,
+  chains = 3, parallel_chains = 3)
+
+jm.out<-as.CmdStanMCMC(jm.samples)
+print(jm.out, max_rows=500, digits=5)
+
+#' Display PRED vs OBS surv curves
+expected.surv<-SurvivalQuantities(jm.samples, type="surv",
+       grid=GridGrouped(times=seq(from=0, to=4, by=0.1),
+       groups=split(event.df$SUBJID, event.df$ATRT)))
+autoplot(expected.surv, add_km=T, add_wrap=F)+
+    scale_fill_manual(values=mycols)+
+    scale_colour_manual(values=mycols)+
+    theme_minimal()+
+    theme(panel.grid.minor=element_blank())
+
diff --git a/design/examples/mCRCpub/data/HORIZONIII/HorizOSads.rds b/design/examples/mCRCpub/data/HORIZONIII/HorizOSads.rds
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diff --git a/design/examples/mCRCpub/data/PRIME/biomark_pds2019.sas7bdat b/design/examples/mCRCpub/data/PRIME/biomark_pds2019.sas7bdat
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diff --git a/design/examples/mCRCpub/trash/expon-ph-benchmark.R b/design/examples/mCRCpub/trash/expon-ph-benchmark.R
new file mode 100644
index 000000000..b35a92159
--- /dev/null
+++ b/design/examples/mCRCpub/trash/expon-ph-benchmark.R
@@ -0,0 +1,156 @@
+#' #############################################################################
+#'
+#' Fit Weibull PH model to ‘pb’ data from the {flexsurv} package,
+#' using various tools/packages:
+#' I. flexsurv
+#' II. survstan
+#' III. jmpost
+#'
+#' Initiated on: 2024-03-28
+#' Author: F. Mercier
+#'
+#' #############################################################################
+
+
+
+#' ===========================================================
+#'
+#' INSTALL AND LOAD NECESSARY LIBRARIES
+#'
+#' ===========================================================
+
+#' General
+#' ==========================
+library(Rcpp)
+library(cli)
+library(here)
+library(tidyverse)
+
+#' Survival
+#' ==========================
+#' install.packages("devtools")
+#' install.packages("cmdstanr", repos = c("https://mc-stan.org/r-packages/", getOption("repos")))
+#' devtools::install("~/jmpost")
+library(cmdstanr)
+library(flexsurv)
+library(survstan)
+library(jmpost)
+
+
+#' ===========================================================
+#'
+#' DATA PREP
+#'
+#' ===========================================================
+
+#' From the flexsurv package
+head(bc, 2)
+
+#' recyrs represents the time (in years) of death or cancer recurrence when
+#' censrec is 1, or (right-)censoring when censrec is 0.
+#' The covariate group is a factor representing a prognostic score, with 3 levels:
+#' "Good" (the reference), "Medium" and "Poor".
+#' In flexsur, the baseline Weibull model is implemented as:
+#' S(t) = exp(-(t/mu)^alpha), with alpha=shape param, mu=scale param.
+#' group is a linear effect on log(mu)
+
+
+#' ===========================================================
+#'
+#' Weibull PH model fits
+#'
+#' ===========================================================
+
+#' Flexsurv
+#' ==========================
+# flexsurv.exp<-flexsurvreg(Surv(recyrs, censrec)~group, data=bc, dist="exp")
+# flexsurv.exp
+# plot(flexsurv.exp)
+# flexsurv.exp$AIC
+# flexsurv.exp$res
+
+flexsurv.weiph<-flexsurvreg(Surv(recyrs, censrec)~group, data=bc, dist="weibullph")
+flexsurv.weiph
+
+#' Survstan
+#' ==========================
+# survstan.exp<-survstan::phreg(Surv(recyrs, censrec)~group, data=bc, dist="exponential")
+# sumsurvstan<-summary(survstan.exp)
+# sumsurvstan$AIC
+# sumsurvstan$coefficients
+# sumsurvstan$tbl
+
+survstan.weiph<-survstan::phreg(Surv(recyrs, censrec)~group, data=bc, dist="weibull")
+summary(survstan.weiph)
+
+
+#' jmpost
+#' ==========================
+# jmpost.survonly.exp<-JointModel(survival=SurvivalExponential(lambda=prior_lognormal(log(0.06), 1)))
+
+# bc1<-bc %>% mutate(ID=as.character(1:n()), study=1)
+
+# jdat<-DataJoint(
+#   subject=DataSubject(data=bc1, subject="ID", arm="group", study="study"),
+#   survival=DataSurvival(data=bc1, formula=Surv(recyrs, censrec)~group)
+#   )
+
+# mp<-sampleStanModel(jmpost.survonly.exp, data=jdat, iter_warmup=4000,
+#                     iter_sampling=1000, chains=4, refresh=0)
+
+# vars<-c("sm_exp_lambda", "beta_os_cov")
+# mp@results$summary(vars)
+
+jmpost.weiph<-JointModel(survival=SurvivalWeibullPH())
+
+bc1<-bc %>% mutate(ID=as.character(1:n()), study=1)
+
+jdat<-DataJoint(
+    subject=DataSubject(data=bc1, subject="ID", arm="group", study="study"),
+    survival=DataSurvival(data=bc1, formula=Surv(recyrs, censrec)~group)
+)
+
+mp<-sampleStanModel(jmpost.weiph, data=jdat, iter_warmup=4000,
+                    iter_sampling=1000, chains=4, refresh=0)
+mp@results
+
+# vars<-c("sm_exp_lambda", "beta_os_cov")
+# mp@results$summary(vars)
+
+
+
+#' ===========================================================
+#'
+#' Pooling results together
+#'
+#' ===========================================================
+
+flexsurv.prep<-as_tibble(signif(flexsurv.exp$res, 3)) |>
+  rename(Estimate=est, SE=se, P025=`L95%`, P975=`U95%`) |>
+  relocate(SE, .after=Estimate) |>
+  mutate(meth="flexsurv", rowN=1:3, libel=c("lambda", "beta_group_Medium", "beta_group_Poor"), .before=1)
+
+survstan.prep1<-as_tibble(signif(sumsurvstan$tbl, 3)) |>
+  rename(Estimate=estimate, P025=`2.5%`, P975=`97.5%`, SE=se)
+survstan.prep2<-as_tibble(signif(sumsurvstan$coefficients[,1:2], 3)) |>
+  rename(SE=StdErr) |>
+  mutate(P025=999, P975=999, .after=1)
+survstan.prep<-rbind(survstan.prep1, survstan.prep2) |>
+  mutate(meth="survstan", rowN=1:3, libel=c("lambda", "beta_group_Medium", "beta_group_Poor"), .before=1)
+
+jmpost.prep<-as_tibble(mp@results$summary(vars)) |>
+  rename(Estimate=mean, SE=sd, P025=q5, P975=q95) |>
+  select(Estimate, SE, P025, P975) |>
+  mutate(meth="jmpost", rowN=1:3, libel=c("lambda", "beta_group_Medium", "beta_group_Poor"), .before=1)
+
+
+altogether<-rbind(flexsurv.prep, survstan.prep, jmpost.prep)
+
+
+
+
+
+
+
+
+
diff --git a/design/examples/mCRCpub/trash/expon-ph-outputs.R b/design/examples/mCRCpub/trash/expon-ph-outputs.R
new file mode 100644
index 000000000..4119df177
--- /dev/null
+++ b/design/examples/mCRCpub/trash/expon-ph-outputs.R
@@ -0,0 +1,296 @@
+#' #############################################################################
+#'
+#' For a time to event model of ‘pb’ data from the {flexsurv} package,
+#' assuming an exponential baseline hazard, the goal here is to
+#' illustrate the way to assess:
+#' (i) Convergence
+#' (ii) GoF
+#'
+#' Solutions proposed by {survstan} will be used as benchmark
+#'
+#' Initiated on: 2024-02-14
+#' Author: F. Mercier
+#'
+#' #############################################################################
+
+
+#' ===========================================================
+#'
+#' INSTALL AND LOAD NECESSARY LIBRARIES
+#'
+#' ===========================================================
+
+library(survstan)
+library(here)
+install.packages("cmdstanr",
+                 repos = c("https://stan-dev.r-universe.dev/", getOption("repos")))
+if (!require("remotes")) {
+    install.packages("remotes")
+}
+remotes::install_github("genentech/jmpost")
+
+library(tidyverse)
+library(flexsurv)
+library(cmdstanr)
+library(posterior)
+library(bayesplot)
+library(tidybayes)
+library(ggdist)
+library(bayestestR)
+library(loo)
+library(jmpost)
+
+library(cmdstanr)
+check_cmdstan_toolchain()
+cmdstan_path()
+file <- file.path(cmdstan_path(), "examples", "bernoulli", "bernoulli.stan")
+mod <- cmdstan_model(file)
+mod$print()
+mod$exe_file()
+data_list <- list(N = 10, y = c(0,1,0,0,0,0,0,0,0,1))
+
+fit <- mod$sample(
+    data = data_list,
+    seed = 123,
+    chains = 4,
+    parallel_chains = 4,
+    refresh = 500 # print update every 500 iters
+)
+fit$summary()
+
+
+#' ===========================================================
+#'
+#' Data (from the flexsurv package)
+#'
+#' ===========================================================
+
+head(bc, 2)
+glimpse(bc)
+rbind(head(bc), tail(bc))
+
+#' Kaplan-Meier plot and Risk table
+p001 <- ggsurvfit::survfit2(Surv(recyrs, censrec) ~ group, data = bc) |>
+    ggsurvfit(linewidth = 1) +
+    add_confidence_interval() +
+    add_risktable() +
+    add_quantile(y_value = 0.5, color = "gray50", linewidth = 0.75) +
+    scale_ggsurvfit()
+p001
+
+#' Checking independent censoring
+p002 <- ggsurvfit::survfit2(Surv(recyrs, 1-censrec) ~ group, data = bc) |>
+    ggsurvfit(linewidth = 1) +
+    add_confidence_interval() +
+    scale_ggsurvfit()
+p002
+
+#' Kernel density estimate for the hazard
+futime=bc$recyrs; fustat=bc$censrec
+fit1 <- muhaz::muhaz(futime, fustat, bw.method="g")
+plot(fit1)
+summary(fit1)
+
+
+#' ===========================================================
+#'
+#' jmpost exponential PH implementation
+#'
+#' ===========================================================
+
+
+jmpost.survonly.exp<-JointModel(survival=SurvivalExponential(lambda=prior_lognormal(log(0.06), 1)))
+
+bc1<-bc %>% mutate(ID=as.character(1:n()), study=1)
+
+jdat<-DataJoint(
+  subject=DataSubject(data=bc1, subject="ID", arm="group", study="study"),
+  survival=DataSurvival(data=bc1, formula=Surv(recyrs, censrec)~group)
+)
+
+mp<-sampleStanModel(jmpost.survonly.exp, data=jdat, iter_warmup=4000,
+                    iter_sampling=1000, chains=4, refresh=0)
+
+mp@results
+##
+vars<-c("sm_exp_lambda", "beta_os_cov")
+# mp@results$summary(vars)
+
+
+#' ===========================================================
+#'
+#' I. POSTERIOR DISTRIBUTION SUMMARY
+#'
+#' ===========================================================
+
+
+#' Convert the samples in a df
+#' ------------------------------------------------------------\
+my_fitall_df <- posterior::as_draws_df(mp@results)
+my_pars<-c("sm_exp_lambda", "beta_os_cov[1]", "beta_os_cov[2]")
+my_fitpop_df<-posterior::subset_draws(my_fitall_df, variable=my_pars)
+
+#' Summarize the posterior samples
+#' ------------------------------------------------------------\
+#' Using {posterior}
+posterior::summarise_draws(my_fitpop_df)
+
+
+#' Quantiles or Highest density interval
+#' ------------------------------------------------------------\
+#' For each parameter, it is possible to extract various quantities:
+#' mean_hdci(), median_hdci(), etc ... from [median|mean|mode]_[qi|hdi]
+#' see: ggdist:: ?mean_qi
+my_fitpop_df %>%
+  tidybayes::spread_rvars(sm_exp_lambda) %>%
+    ggdist::mean_hdci()
+my_fitpop_df %>%
+  tidybayes::spread_rvars(sm_exp_lambda) %>%
+    ggdist::mean_qi()
+
+#' Median (and associated uncertainty expressed as lower and upper bounds for
+#' pmf containing 50%, 89%, 90% of the distribution density
+#' = e.g. 89% credibility interval for the median)
+#' for sm_exp_lambda across all chains
+my_fitpop_df %>%
+  tidybayes::spread_rvars(sm_exp_lambda) %>%
+  tidybayes::median_qi(.width = c(.50, .89, .95))
+
+#' Q1, median, Q3 of sm_exp_lambda across all chains
+lambda_samples<-my_fitpop_df %>%
+  tidybayes::spread_draws(sm_exp_lambda)
+lambda_samples$sm_exp_lambda %>% quantile(., probs=c(0.025, 0.5, 0.975))
+
+
+#' Posterior density
+#' using tidybayes see https://mjskay.github.io/tidybayes/articles/tidy-rstanarm.html
+#' ------------------------------------------------------------\
+
+my_fitpop_df %>%
+  tidybayes::spread_draws(sm_exp_lambda) %>%
+  tidybayes::median_qi(., .width = c(.95, .66)) %>%
+  ggplot(aes(y = NA, x = sm_exp_lambda, xmin = .lower, xmax = .upper)) +
+  scale_x_continuous("Lambda_0")+
+  scale_y_discrete("")+
+  tidybayes::geom_pointinterval()+
+  labs(title="sm_exp_lambda posterior distributions",
+       caption="OS analysis / mercief3 / 2024-02-20")+
+  theme_minimal()
+
+#' (Post-warmup) Posterior distributions
+#' ------------------------------------------------------------\
+bayesplot::mcmc_areas(my_fitpop_df, pars = my_pars, prob = 0.8)+
+  theme_minimal()
+bayesplot::mcmc_dens_overlay(my_fitpop_df, pars=my_pars)+
+  theme_minimal()
+
+
+
+#' ===========================================================
+#'
+#' II. CONVERGENCE
+#'
+#' ===========================================================
+
+
+#' Checking that Rhat<1.05
+#' ------------------------------------------------------------\
+#' see https://cran.r-project.org/web/packages/bayesplot/vignettes/visual-mcmc-diagnostics.html
+
+#' Using {bayesplot}
+rhats <- bayesplot::rhat(mp@results)
+print(rhats)
+color_scheme_set("brightblue") # see help("color_scheme_set")
+bayesplot::mcmc_rhat(rhats)+ yaxis_text(hjust = 1)
+
+
+#' Checking ESS
+#' ------------------------------------------------------------\
+#' Using {bayesplot}
+#' see https://cran.r-project.org/web/packages/bayesplot/vignettes/visual-mcmc-diagnostics.html
+neff_ratios <- bayesplot::neff_ratio(mp@results)
+print(neff_ratios)
+color_scheme_set("brightblue") # see help("color_scheme_set")
+bayesplot::mcmc_neff(neff_ratios, size = 2)+ yaxis_text(hjust = 1)
+
+
+#' Checking autocorrelation
+#' ------------------------------------------------------------\
+#' Using {bayesplot}
+#' see https://cran.r-project.org/web/packages/bayesplot/vignettes/visual-mcmc-diagnostics.html
+bayesplot::mcmc_acf_bar(my_fit_df, pars="sm_weibull_ph_lambda", lags=10)+
+  theme_minimal()
+
+
+#' Caterpillar plot for each param
+#' ------------------------------------------------------------\
+bayesplot::mcmc_trace(my_fit_df,  pars = my_pars)+
+  theme_minimal()
+
+
+
+#' ===========================================================
+#'
+#' III. GOODNESS OF FIT
+#'
+#' ===========================================================
+
+# Log Likelihood
+#' ===========================================================
+log_lik <- mp@results$draws("log_lik", format = "draws_matrix") |>
+  apply(1, sum) |>
+  mean()
+log_lik
+
+# AIC
+k <- 2
+-2 * log_lik + k * 4
+
+# BIC
+(4 * log(nrow(bc1))) + (-2 * log_lik)
+
+# Leave one out CV
+mp@results$loo()
+
+
+
+
+
+#' ===========================================================
+#'
+#' IV. PREDICTIONS
+#'
+#' Overlaying KM and posterior survival curves
+#' See example:
+#' https://stablemarkets.netlify.app/post/post2/specifying-accelerated-failure-time-models-in-stan/
+#'
+#'
+#' ===========================================================
+
+# Calculate the survival distribution for each subject at each desired timepoint
+# To get different quantities change the `pweibullPH` to the desired distribution
+# function e.g. hweibullPH / HweibullPH
+
+zparms<-my_fitpop_df |>
+    pivot_longer(cols = 1:3, names_to = "parms", values_to = "value") |>
+    group_by(parms) |>
+        tidybayes::median_qi() |>
+    ungroup()
+
+jdat<-DataJoint(
+    subject=DataSubject(data=bc1, subject="ID", arm="group", study="study"),
+    survival=DataSurvival(data=bc1, formula=Surv(recyrs, censrec)~group)
+)
+
+set.seed(13579)
+covs <- data.frame(ID = bc1$ID, trt=bc1$group)
+s1 <- simsurv(dist="exponential",
+              x=covs, betas=c(trt=0),
+              lambdas = zsurv$lambda[1], maxt = max(bc1$recyrs))
+
+survfit2(Surv(eventtime, status) ~ 1, data = s1) |>
+    ggsurvfit(linewidth = 1) +
+    add_confidence_interval() +
+    add_risktable() +
+    add_quantile(y_value = 0.6, color = "gray50", linewidth = 0.75) +
+    scale_ggsurvfit()
diff --git a/design/examples/mCRCpub/trash/trash.R b/design/examples/mCRCpub/trash/trash.R
new file mode 100644
index 000000000..575f2daf4
--- /dev/null
+++ b/design/examples/mCRCpub/trash/trash.R
@@ -0,0 +1,46 @@
+<!--
+
+    ## Comparing {flexsurv}, {survstan} and {jmpost}
+
+    ### Data preparation
+
+    ### Flexsurv implementation
+
+    The details of the exponential model implementation in {flexsurv} are
+provided in the reference article
+([DOI](https://www.jstatsoft.org/article/view/v070i08)). The exponential
+distribution has a single parameter and only supports a hazard that is
+constant over time. The hazard is equal to the rate parameter.
+
+```{r, eval=FALSE, echo=TRUE}
+flexsurv.exp<-flexsurv::flexsurvreg(Surv(recyrs, censrec)~group, data=bc, dist="exp")
+flexsurv.exp
+```
+
+The same model in {survstan} would be implemented as follow:
+
+    ```{r, eval=FALSE, echo=TRUE}
+survstan.exp<-survstan::phreg(Surv(recyrs, censrec)~group, data=bc, dist="exponential")
+summary(survstan.exp)
+
+```
+
+
+As shown in the below table, these various model calls provide
+consistent outputs. More details on the {jmpost} outputs are provided in
+the separate vignette ABC123.
+
+```{r, file="expon-ph-benchmark.R", echo=FALSE}
+library(knitr)
+library(kableExtra)
+
+# Create table
+altogether %>%
+    kable(escape = F) %>%
+    kable_styling()
+```
+
+Both `jmpost` and `survstan` implement these analysis in Stan, a
+probabilistic programming language supporting Bayesian approach.
+
+-->
diff --git a/man/Brier-Score-Shared.Rd b/man/Brier-Score-Shared.Rd
index a9c7e6869..ea9eb9539 100644
--- a/man/Brier-Score-Shared.Rd
+++ b/man/Brier-Score-Shared.Rd
@@ -2,7 +2,8 @@
 % Please edit documentation in R/brier_score.R
 \name{Brier-Score-Shared}
 \alias{Brier-Score-Shared}
-\title{Re-used documentation for Brier Score components}
+\title{Test
+Re-used documentation for Brier Score components}
 \arguments{
 \item{t}{(\code{numeric})\cr timepoints to calculate the desired quantity at.}
 
@@ -22,6 +23,7 @@ package.}
 \item{...}{not used.}
 }
 \description{
+Test
 Re-used documentation for Brier Score components
 }
 \keyword{internal}
diff --git a/vignettes/.gitignore b/vignettes/.gitignore
index 097b24163..3432c3fd8 100644
--- a/vignettes/.gitignore
+++ b/vignettes/.gitignore
@@ -1,2 +1,2 @@
 *.html
-*.R
+
diff --git a/vignettes/statistical-specification.Rmd b/vignettes/statistical-specification.Rmd
index ac75248c1..000f46422 100644
--- a/vignettes/statistical-specification.Rmd
+++ b/vignettes/statistical-specification.Rmd
@@ -9,8 +9,8 @@ output:
 link-citations: true
 vignette: >
   %\VignetteIndexEntry{Statistical Specifications}
-  %\VignetteEngine{knitr::rmarkdown}
   %\VignetteEncoding{UTF-8}
+  %\VignetteEngine{knitr::rmarkdown}
 editor_options:
   chunk_output_type: console
 ---
diff --git a/vignettes/survivalonly-1-statsspecs.Rmd b/vignettes/survivalonly-1-statsspecs.Rmd
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+---
+title: "01. Survival models"
+subtitle: "Part 1. Statistical specifications"
+package: jmpost
+output: rmarkdown::html_vignette
+vignette: >
+  %\VignetteIndexEntry{Model Fitting}
+  %\VignetteEncoding{UTF-8}
+  %\VignetteEngine{knitr::rmarkdown}
+editor_options:
+  chunk_output_type: console
+  markdown: 
+    wrap: 72
+---
+
+```{r, include=FALSE}
+knitr::opts_chunk$set(echo = TRUE, collapse = TRUE)
+```
+
+## Scope of this document
+
+This document describes how to analyze survival data using parametric
+survival models implemented in the `jmpost` R package. It is organized
+in 4 sections:
+
+-   Introduction
+
+-   Modeling framework
+
+-   Implementation
+
+## 1. Introduction
+
+Survival analysis, also referred to as time-to-event or failure time
+analysis, investigates the duration until one or more events of interest
+occur and the factors influencing these durations. Comprehensive
+introductions to survival analysis are provided by Kalbfleisch and
+Prentice (2002), Collett (2003), and Hosmer et al. (2008).
+
+Three predominant approaches to modeling survival data are commonly
+employed:
+
+1.  Hazard Rate Models: These models describe the instantaneous rate of
+    the event (the hazard) as a function of time, treated as a
+    continuous variable. This category includes the widely used class of
+    proportional hazards (PH) regression models.
+
+2.  Event Time Models: These models directly analyze the event time
+    itself, also treating time as a continuous variable. The accelerated
+    failure time (AFT) models fall under this category.
+
+3.  Discrete Time Models: These models analyze the occurrence of events
+    when time is considered as a discrete variable, with the additive
+    hazard regression (AHR) model being a specific example.
+
+In the current version of the `jmpost` package, we focus on the first
+approach, specifically on PH models within a Bayesian framework.
+
+Proportional hazards (PH) models are pivotal in survival analysis and
+rely on the key assumption that the hazard ratio (HR) comparing any two
+levels of a covariate remains constant over time. The Cox PH model is
+the most popular among these models for two primary reasons: (a) it does
+not require assumptions about the probability distribution of survival
+times, and (b) it generally fits data well across various parametric
+models.
+
+In contrast, fully parametric PH models require a distributional
+assumption (Kalbfleisch and Prentice 2002; Lawless 2002). When the
+appropriate distribution is selected, parametric models can provide more
+efficient estimates, reflected in smaller standard errors compared to
+the Cox model (Collett 2003). Moreover, using the Cox PH model in joint
+modeling of time-to-event and longitudinal data (Wulfsohn and Tsiatis
+1997) often leads to underestimation of standard errors of parameter
+estimates (Hsieh et al. 2006; Rizopoulos 2012). Consequently, most joint
+modeling methods are based on parametric response distributions (Hwang
+and Pennell 2014).
+
+Furthermore, the application of Cox proportional hazards (PH) models in
+joint modeling of time-to-event and longitudinal data often results in
+the underestimation of the standard errors of parameter estimates
+(Wulfsohn and Tsiatis 1997; Hsieh et al. 2006; Rizopoulos 2012). As a
+result, many methods for joint modeling are predicated on parametric
+response distributions (Hwang and Pennell 2014).
+
+Bayesian inference offers several advantages:
+
+-   The ability to make probability statements about parameters.
+
+-   Natural handling of hierarchical structures.
+
+-   Robust statistical properties, particularly with small sample sizes.
+
+-   The capacity to easily quantify uncertainty in predicted quantities.
+
+These properties are highly advantageous for joint models and are
+equally beneficial when applied to survival models independently.
+
+`jmpost` is developed in Stan, a high-level language (itself implemented
+in C++) designed for Bayesian modeling and inference. Stan primarily
+utilizes a variant of the No-U-Turn sampler (NUTS) (Hoffman & Gelman,
+2014) to generate posterior samples based on a user-specified model and
+data.
+
+While Stan is an exceptionally flexible and powerful tool for
+statistical modeling, it can be challenging to learn and is not
+inherently user-friendly. To address this barrier, we introduce `jmpost`
+as an additional layer atop Stan, simplifying the encoding of
+proportional hazards (PH) models. This includes both stand-alone PH
+models and those integrated within joint models.
+
+## 2. Modeling framework
+
+### 2.1. Distribution of time-to-event data
+
+Let $T$ denote a continuous non-negative random variable representing
+survival time. This variable can be specified by its density function
+$f(t)$ and cumulative distribution function $F(t)$. The hazard function,
+defined as
+
+$$
+h(t) = \lim_{\Delta \to 0} \frac{P(t < T \leq t + \Delta \mid T > t)}{\Delta}
+$$
+
+plays a central role in modeling the time to event. The hazard function
+represents the risk of an event occurring immediately after time $t$,
+given that no event has occurred up to time $t$. From this definition,
+we can derive that $h(t) = \frac{f(t)}{S(t)}$, where $S(t) = 1 - F(t)$
+is the survival function, representing the probability of no event
+occurring until time $t$.
+
+From the hazard function, we can define the cumulative hazard function
+as
+
+$$
+H(t) = \int_0^t h(\tau) \, d\tau
+$$
+
+which is related to the survival function by $S(t) = \exp(-H(t))$. The
+relationships between $h(t)$, $H(t)$, $f(t)$, and $S(t)$ constitute the
+fundamental formulas that represent key concepts in survival modeling.
+
+In practice, the exact event time may not be observed due to right
+censoring, such as when the event occurs after the conclusion of a
+clinical trial. Formally, let $T_i^*$ be the true event time and $C_i$
+be the censoring time (e.g., the end of the study). We observe
+$T_i = \min(T_i^*, C_i)$. To distinguish censored observations, we use
+an event indicator $d_i$, which is 0 for right censoring ($T_i^* > C_i$)
+and 1 if the event is observed ($T_i = T_i^*$). Thus, the observed
+outcome is defined by the pair $\{T_i, d_i\}$, where $T_i > 0$.
+
+### 2.2. Parametric model
+
+Parametric time-to-event models are constructed by specifying the
+outcome distribution. For instance, suppose $T$ follows an exponential
+distribution:
+
+$$ T \sim \text{exp}(\lambda) \quad \text{with} \; \lambda > 0, $$
+
+with
+
+$$ f(t) = \lambda \cdot \exp(-\lambda t) \quad \text{and} \quad F(t) = 1 - \exp(-\lambda t). $$
+
+This leads to
+
+$$ S(t) = 1 - F(t) = \exp(-\lambda t). $$
+
+Using $h(t) = \frac{f(t)}{S(t)}$, we get $h(t) = \lambda$. The hazard
+function for the exponential distribution is constant.
+
+However, the exponential distribution is often too restrictive. In
+principle, any positive continuous distribution (or transformation to
+obtain such) can be used for the outcome. One of the most commonly used
+distributions is the Weibull distribution, a two-parameter model
+flexible enough to characterize both monotonic increasing and decreasing
+hazard rates over time. Different parameterizations exist for this
+distribution. Within `jmpost`, the survival and hazard functions are
+implemented using the following parameterization:
+
+$$ S(t) = \exp(-(\lambda t)^\gamma) $$
+
+$$ h(t) = \lambda \gamma \cdot t^{\gamma-1} $$
+
+where $\gamma > 0$ is the shape parameter and $\lambda > 0$ is the scale
+parameter. The density function can be derived from
+$f(t) = h(t) \cdot S(t)$.
+
+Additionally, a log-logistic distribution can also be considered. Its
+hazard and survival functions are:
+
+$$ S(t) = \frac{1}{1 + (t/b)^a} $$
+
+$$ h(t) = \frac{(a/b) \cdot (t/b)^{a-1}}{1 + (t/b)^a} $$
+
+where $a$ is the shape parameter and $b$ is the scale parameter.
+
+To summarize, the parameters involved in each type of parametric
+survival model are recapitulated in [Table 1](#table1).
+
+<a name="table1"> Table 1. Parameters associated with each survival
+model </a>
+
+| Model        | Parameter | Variable name          | Interpretation             | Default prior |
+|---------------|---------------|---------------|---------------|---------------|
+| Exponential  | $\lambda$ | `sm_exp_lambda`        | Time invariant hazard rate | xxx           |
+| Weibull      | $\gamma$  | `sm_weibull_ph_gamma`  | Shape                      | xxx           |
+|              | $\lambda$ | `sm_weibull_ph_lambda` | Scale                      | xxx           |
+| Log-logistic | $a$       | `sm_loglogis_a`        | Shape                      | xxx           |
+|              | $b$       | `sm_loglogis_b`        | Scale                      | xxx           |
+
+### 2.3. Covariate model
+
+In many cases, additional characteristics of the individuals, such as
+age, sex, tumor stage, etc., are known. These characteristics are
+referred to as covariates. Let $X_i$ denote the $p \times 1$ vector of
+values from the covariate matrix $X$ for individual $i$, and let $\beta$
+be a $p \times 1$ vector of regression coefficients. It is plausible to
+assume that $X$ influences the shape, scale, or both parameters of the
+model. However, a common approach is to assume that $X$ affects only the
+scale parameter. The typical formulation for this relationship is:
+
+$$
+\log(\mu_i) = X_i^T \beta
+$$
+
+To ensure identifiability, we assume that the design vector $X_i$ does
+not include a constant term; that is, no intercept is included in the
+above equation.
+
+Various regression models can be fitted, such as proportional hazard
+(PH) models, accelerated failure time (AFT) models, proportional odds
+(PO) models, etc. Currently, `jmpost` implements only PH regression
+models. PH models are defined as:
+
+$$
+h_i(t) = h_0(t) \cdot \exp(X_i^T \beta)
+$$
+
+where $h_0(t)$ is the baseline hazard function.
+
+The hazard ratio (HR) quantifies the relative increase in the hazard
+associated with a unit increase in the relevant covariate, $X_i$, while
+holding all other covariates in the model constant.
+
+### 2.4. Log-likelihood
+
+We can specify the relevant parameter(s) as $\theta$. In the case of the
+exponential distribution, $\theta = \lambda$. For other distributions,
+$\theta = (\mu, \alpha)$, where $\mu$ represents the location or scale
+parameter, and $\alpha$ describes the shape or variance of the
+distribution. The objective of the statistical analysis is the
+estimation of $\theta$, which can then be used to obtain estimates for
+all relevant quantities (e.g., the survival function).
+
+Based on the observed outcomes $\{T_i, d_i\}$ for $i = 1, \ldots, n$,
+the likelihood function can be written as:
+
+$$
+L(\theta) = \prod_{i=1}^{n} f(T_i)^{d_i} \cdot S(T_i)^{1 - d_i} \cdot g(d_i)
+$$
+
+where $g(d_i)$ is the density function of $d_i$. We assume that $C_i$
+and consequently $d_i$ are independent of $T_i$. This type of censoring
+is known as non-informative censoring. Hence, we will ignore the
+$g(d_i)$ part afterwards.
+
+The maximum likelihood estimator maximizes the above log-likelihood
+function. Given that $f(t) = h(t) \cdot S(t)$, the log-likelihood can
+therefore be expressed as:
+
+$$
+\log L(\theta) = \sum_{i=1}^{n} \left[ d_i \cdot \log h(T_i) + \log S(T_i) \right]
+$$
+
+Since $H(t) = -\log S(t)$, the log-likelihood can also be expressed as:
+
+$$
+\log L(\theta) = \sum_{i=1}^{n} \left[ d_i \cdot \log h(T_i) - H(T_i) \right]
+$$
+
+### 2.5. Bayesian inference
+
+In a full Bayesian setting, the parameters are modeled directly using a
+prior probability distribution, which is updated by the observed data
+into a posterior distribution. The posterior distribution is the focus
+of the inferential process. Therefore, when using a Bayesian framework,
+the model must be completed by specifying suitable prior distributions
+for the $\theta$ parameters.
+
+Within `jmpost`, all parameters have default priors assigned to them,
+but users can explicitly specify the priors if they wish. The default
+choice of prior distribution for the regression coefficients is
+$N(\mu_\beta = 0, \sigma_\beta = 2)$, defined on the log scale. This
+amounts to specifying a "minimally informative" prior on the regression
+coefficients that determine the location parameter---in other words, we
+are not including strong prior information in this aspect of our model.
+The observed data (and the censoring structure) will primarily drive the
+update to the posterior distribution.
+
+There are several choices of prior distributions for the model
+parameters related to the baseline hazard (see [Table 1](#table1)). In
+theory, any distribution defined in the $(0, +\infty)$ domain would be
+viable as a prior distribution; however, the most common choices
+include:
+
+-   A half-normal, half-t, half-Cauchy, or exponential prior
+    distribution for the Weibull shape parameter.
+-   A half-normal, half-t, half-Cauchy, or exponential prior
+    distribution for the log-logistic scale parameter.
+
+### 2.6. Estimation
+
+The `jmpost` package is built on top of the `cmdstanr` R package (Stan
+Development Team, 2019), the most advanced R interface for Stan. Stan, a
+C++ library, provides a powerful platform for statistical modeling
+(Carpenter et al., 2017) and uses the No-U-Turn Sampler (NUTS), a
+specific implementation of Hamiltonian Monte Carlo (HMC) (Hoffman and
+Gelman, 2014). Models in `jmpost` are written in the Stan programming
+language, translated into C++ code, and compiled at runtime.
+
+Estimation in `jmpost` relies on full Bayesian inference. HMC, a form of
+Markov chain Monte Carlo (MCMC), uses gradient information of the log
+posterior to efficiently sample from the posterior space.
+
+Leveraging `cmdstanr`, `jmpost` allows users to control various aspects
+of the estimation process, including the number of MCMC chains, the
+number of warm-up and sampling iterations, and the number of computing
+cores used.
+
+## 3. Implementation
+
+The design of `jmpost` is modular, with distinct sets of functions
+tailored to specific objectives. These functions can be broadly
+categorized into three main groups: **Data Preparation**, **Model
+Fitting and Assessment**, and **Sensitivity Analysis and Predictions**,
+as illustrated schematically in Figure 1.
+
+![Figure 1.](path/to/figure1.png)
+
+## 4. References
+
+### References
+
+-   Baio, G. (2020). survHE: Survival analysis for health economic
+    evaluation and cost-effectiveness modeling. *Journal of Statistical
+    Software*, doi:
+    [10.18637/jss.v095.i14](https://doi.org/10.18637/jss.v095.i14).
+-   Carpenter, B., Gelman, A., Hoffman, M. D., et al. (2017). Stan: A
+    probabilistic programming language. *Journal of Statistical
+    Software*, doi:
+    [10.18637/jss.v076.i01](https://doi.org/10.18637/jss.v076.i01).
+-   Collett, D. (2003). *Modelling Survival Data in Medical Research*.
+    Chapman and Hall/CRC, Florida.
+-   Hoffman, M. D., & Gelman, A. (2014). The No-U-turn sampler:
+    Adaptively setting path lengths in Hamiltonian Monte Carlo. *Journal
+    of Machine Learning Research*, 15, 1593-1623.
+-   Hosmer, D. W., Lemeshow, S., & May, S. (2008). *Applied Survival
+    Analysis: Regression Modeling of Time-to-Event Data*. John Wiley &
+    Sons, New Jersey.
+-   Hsieh, F., Tseng, Y.-K., & Wang, J.-L. (2006). Joint modeling of
+    survival and longitudinal data: Likelihood approach revisited.
+    *Biometrics*, 62, 1037-1043.
+-   Hwang, W., & Pennell, M. L. (2014). Semiparametric Bayesian joint
+    modeling of a binary and continuous outcome with applications in
+    toxicological risk assessment. *Statistics in Medicine*, 33,
+    1162-1175.
+-   Jackson, C. (2016). flexsurv: A platform for parametric survival
+    modeling in R. *Journal of Statistical Software*, doi:
+    [10.18637/jss.v070.i08](https://doi.org/10.18637/jss.v070.i08).
+-   Kalbfleisch, J. D., & Prentice, R. L. (2002). *The Statistical
+    Analysis of Failure Time Data*. John Wiley & Sons, New Jersey.
+-   Lawless, J. F. (2002). *Statistical Models and Methods for Lifetime
+    Data*. John Wiley & Sons, New Jersey.
+-   Rizopoulos, D. (2012). *Joint Models for Longitudinal and
+    Time-to-Event Data With Applications in R*. Chapman and Hall/CRC,
+    Florida.
+-   Wulfsohn, M. S., & Tsiatis, A. A. (1997). A joint model for survival
+    and longitudinal data measured with error. *Biometrics*, 53,
+    330-339.