diff --git a/R/predprobDist.R b/R/predprobDist.R
index 270807a6..3576bcfb 100644
--- a/R/predprobDist.R
+++ b/R/predprobDist.R
@@ -5,71 +5,109 @@ NULL
 #' Compute the predictive probability that the trial will be
 #' successful, with a prior distribution on the SOC
 #'
+#' @description `r lifecycle::badge("experimental")`
+#'
 #' Compute the predictive probability of trial success given current data.
 #' Success means that at the end of the trial the posterior probability
-#' Pr(P_E > P_S + delta_0 | data) >= thetaT. Then the
+#' `Pr(P_E > P_S + delta_0 | data) >= thetaT`. Then the
 #' predictive probability for success is:
-#' pp = sum over i: Pr(Y=i|x,n)*I{Pr(P_E > P_S + delta|x,Y=i)>=thetaT},
-#' where Y is the number of future responses in the treatment group and x is
-#' the current number of responses in the treatment group (out of n).
-#' Prior is P_E ~ beta(a, b), default uniform which is a beta(1,1).
+#' `pp = sum over i: Pr(Y = i | x , n)*I{Pr(P_E > P_S + delta | x,Y=i) >= thetaT}`,
+#' where `Y` is the number of future responses in the treatment group and `x` is
+#' the current number of responses in the treatment group out of `n`.
+#' Prior is `P_E ~ beta(a, b)` and uniform which is a beta(1,1).
 #' However, also a beta mixture prior can be specified. Analogously
-#' for P_S either a classic beta prior or a beta mixture prior can be
+#' for `P_S` either a classic beta prior or a beta mixture prior can be
 #' specified.
 #'
 #' Also data on the SOC might be available. Then the predictive probability is
 #' more generally defined as
-#' pp = sum over i, j: Pr(Y=i|x,n)*Pr(Z=j|xS, nS)*I{Pr(P_E > P_S +
-#' delta|x,xS,Y=i,Z=j)>=thetaT}
-#' where Z is the future number of responses in the SOC group, and xS is the
+#' `pp = sum over i, j: Pr(Y = i | x, n)*Pr(Z = j | xS, nS )*I{Pr(P_E > P_S + delta | x,xS, Y=i, Z=j ) >= thetaT}`
+#' where `Z` is the future number of responses in the SOC group, and `xS` is the
 #' current number of responses in the SOC group.
 #'
+#' In the case where `NmaxControl = 0`, a table with the following contents will be included in the return output :
+#' - `i`: `Y = i`, number of future successes in `Nmax-n` subjects.
+#' - `density`: `Pr(Y = i|x)` using beta-(mixture)-binomial distribution.
+#' - `posterior`: `Pr(P_E > P_S + delta | x, Y = i)` using beta posterior.
+#' - `success`: indicator `I(b>thetaT)`.
+#'
 #' A table with the following contents will be
-#' included in the \code{tables} attribute of the return value
+#' included in the  return value
 #' (in the case that NmaxControl is zero):
 #' i: Y=i (number of future successes in Nmax-n subjects)
 #' py: Pr(Y=i|x) using beta-(mixture)-binomial distribution
 #' b: Pr(P_E > P_S + delta | x, Y=i)
 #' bgttheta: indicator I(b>thetaT)
 #'
-#' If NmaxControl is not zero, i.e., when data on the control treatment
+#' If `NmaxControl` is not zero, i.e., when data on the control treatment
 #' is available in this trial, then a list with will be included with the
 #' following elements:
 #' pyz: matrix with the probabilities Pr(Y=i, Z=j | x, xS)
 #' b: matrix with Pr(P_E > P_S + delta | x, xS, Y=i, Z=j)
 #' bgttheta: matrix of indicators I(b>thetaT)
 #'
-#' @param x number of successes (in the treatment group)
-#' @param n number of patients (in the treatment group)
-#' @param xS number of successes in the SOC group (default: 0)
-#' @param nS number of patients in the SOC group (default: 0)
-##' @param Nmax maximum number of patients at the end of the trial (in the
-##' treatment group)
-##' @param NmaxControl maximum number of patients at the end of the trial in the
-##' SOC group (default: 0)
-##' @param delta margin by which the response rate in the treatment group should
-##' be better than in the SOC group (default: 0)
-##' @param relativeDelta see \code{\link{postprobDist}}
-##' @param parE the beta parameters matrix, with K rows and 2 columns,
-##' corresponding to the beta parameters of the K components. default is a
-##' uniform prior.
-##' @param weights the mixture weights of the beta mixture prior. Default are
-##' uniform weights across mixture components.
-##' @param parS beta prior parameters in the SOC group (default: uniform)
-##' @param weightsS weights for the SOC group (default: uniform)
-##' @param thetaT threshold on the probability to be used
-##' @return The predictive probability, a numeric value. In addition, a
-##' list called \code{tables} is returned as attribute of the returned number.
-##'
-##' @references Lee, J. J., & Liu, D. D. (2008). A predictive probability
-##' design for phase II cancer clinical trials. Clinical Trials, 5(2),
-##' 93-106. doi:10.1177/1740774508089279
-##'
-##' @example examples/predprobDist.R
-##' @export
+#' @note
+#'
+#' # Delta from postprobDist :
+#'
+#' The desired improvement is denoted as `delta`. There are two options in using `delta`.
+#' The absolute case when `relativeDelta = FALSE` and relative as when `relativeDelta = TRUE`.
+#'
+#' 1. The absolute case is when we define an absolute delta, greater than `P_S`,
+#' the response rate of the `SOC` group such that
+#' the posterior is `Pr(P_E > P_S + delta | data)`.
+#'
+#' 2. In the relative case, we suppose that the treatment group's
+#' response rate is assumed to be greater than `P_S + (1-P_S) * delta` such that
+#' the posterior is `Pr(P_E > P_S + (1 - P_S) * delta | data)`.
+#'
+#' @typed x : number
+#' number of successes in the treatment group at interim
+#' @typed n : number
+#' number of patients in the treatment group at interim
+#' @typed xS : number
+#' number of successes in the SOC group at interim
+#' @typed nS : number
+#' number of patients in the SOC group
+#' @typed Nmax : number
+#' maximum number of patients in the treatment group at the end of the trial
+#' @typed NmaxControl : number
+#' maximum number of patients at the end of the trial in the
+#' SOC group
+#' @typed delta :
+#' margin by which the response rate in the treatment group should
+#' be better than in the SOC group
+#' @typed relativeDelta :
+#' see `[postprobDist()]`
+#' @typed parE :
+#' the beta parameters matrix, with K rows and 2 columns,
+#' corresponding to the beta parameters of the K components. default is a
+#' uniform prior.
+#' @typed weights :
+#' the mixture weights of the beta mixture prior. Default are
+#' uniform weights across mixture components.
+#' @typed parS :
+#' beta prior parameters in the SOC group
+#' @typed weightsS :
+#' weights for the SOC group
+#' @typed thetaT :
+#' threshold on the probability to be used
+#' @return A `list` is returned with names `result` for predictive probability and
+#'  `table` of numeric values with counts of responses in the remaining patients,
+#'  probabilities of these counts, corresponding probabilities to be above threshold,
+#'  and trial success indicators.
+#'
+#' @references Lee, J. J., & Liu, D. D. (2008). A predictive probability
+#' design for phase II cancer clinical trials. Clinical Trials, 5(2),
+#' 93-106. doi:10.1177/1740774508089279
+#'
+#' @example examples/predprobDist.R
+#' @export
 predprobDist <- function(x, n,
-                         xS = 0, nS = 0,
-                         Nmax, NmaxControl = 0,
+                         xS = 0,
+                         nS = 0,
+                         Nmax,
+                         NmaxControl = 0,
                          delta = 0,
                          relativeDelta = FALSE,
                          parE = c(a = 1, b = 1),
@@ -77,59 +115,49 @@ predprobDist <- function(x, n,
                          parS = c(a = 1, b = 1),
                          weightsS,
                          thetaT) {
-  ## ensure reasonable numbers
+  # ensure reasonable numbers
   stopifnot(
     n <= Nmax,
     nS <= NmaxControl,
     x <= n,
     xS <= nS
   )
-
-  ## remaining active patients to be seen:
+  # remaining active patients to be seen:
   mE <- Nmax - n
-
-  ## if par is a vector => situation where there is only one component
+  # if par is a vector => situation where there is only one component
   if (is.vector(parE)) {
-    ## check that it has exactly two entries
+    # check that it has exactly two entries
     stopifnot(identical(length(parE), 2L))
-
-    ## and transpose to matrix with one row
+    # and transpose to matrix with one row
     parE <- t(parE)
   }
-
-  ## if prior weights of the beta mixture are not supplied
+  # if prior weights of the beta mixture are not supplied
   if (missing(weights)) {
     weights <- rep(1, nrow(parE))
-    ## (don't need to be normalized, this is done in h_getBetamixPost)
+    # (don't need to be normalized, this is done in h_getBetamixPost)
   }
-
-  ## if parS is a vector => situation where there is only one component
+  # if parS is a vector => situation where there is only one component
   if (is.vector(parS)) {
-    ## check that it has exactly two entries
+    # check that it has exactly two entries
     stopifnot(identical(length(parS), 2L))
-
-    ## and transpose to matrix with one row
+    # and transpose to matrix with one row
     parS <- t(parS)
   }
-
-  ## if prior weights of the beta mixture are not supplied
+  # if prior weights of the beta mixture are not supplied
   if (missing(weightsS)) {
     weightsS <- rep(1, nrow(parS))
   }
-
-  ## now compute updated parameters for beta mixture distribution on the
-  ## treatment proportion
+  # now compute updated parameters for beta mixture distribution on the
+  # treatment proportion
   activeBetamixPost <- h_getBetamixPost(x = x, n = n, par = parE, weights = weights)
-
-  ## now with the beta binomial mixture:
+  # now with the beta binomial mixture:
   py <- with(
     activeBetamixPost,
     dbetabinomMix(x = 0:mE, m = mE, par = par, weights = weights)
   )
-
   if (NmaxControl == 0) {
-    ## here is the only difference to predprob.R:
-    ## how to compute the posterior probabilities
+    # here is the only difference to predprob.R:
+    # how to compute the posterior probabilities
     b <- postprobDist(
       x = x + c(0:mE),
       n = Nmax,
@@ -140,40 +168,29 @@ predprobDist <- function(x, n,
       parS = parS,
       weightsS = weightsS
     )
-
-    ret <- structure(sum(py * (b > thetaT)),
-      tables =
-        round(
-          cbind(
-            i = c(0:mE),
-            py,
-            b,
-            bgttheta = (b > thetaT)
-          ),
-          4
-        )
+    ret <- list(
+      result = sum(py * (b > thetaT)),
+      table = data.frame(
+        counts = c(0:mE),
+        # cumul_counts = xS + (0:NmaxControl),
+        density = py,
+        posterior = b,
+        success = (b > thetaT)
+      )
     )
   } else {
-    ## in this case also data on the SOC is available!
-
-    ## determine remaining sample size and probabilities of response
-    ## counts in future SOC patients:
+    # in this case also data on the SOC is available!
+    # determine remaining sample size and probabilities of response
+    # counts in future SOC patients:
     mS <- NmaxControl - nS
-
-    controlBetamixPost <- h_getBetamixPost(
-      x = xS, n = nS, par = parS,
-      weights = weightsS
-    )
-
+    controlBetamixPost <- h_getBetamixPost(x = xS, n = nS, par = parS, weights = weightsS)
     pz <- with(
       controlBetamixPost,
       dbetabinomMix(x = 0:mS, m = mS, par = par, weights = weights)
     )
-
-    ## determine resulting posterior probabilities:
+    # determine resulting posterior probabilities:
     outcomesY <- x + c(0:mE)
-    outcomesZ <- xS + c(0:mS)
-
+    outcomesZ <- xS + c(0:mS) # 15 more chances to get success counts
     pyz <- b <- matrix(
       nrow = 1 + mE,
       ncol = 1 + mS,
@@ -183,11 +200,10 @@ predprobDist <- function(x, n,
           0:mS
         )
     )
-
-    for (i in seq_along(outcomesY)) {
+    for (i in seq_along(outcomesY)) { # outside?
       for (j in seq_along(outcomesZ)) {
-        ## calculate the posterior probability for this combination
-        ## of counts
+        # calculate the posterior probability for this combination
+        # of counts
         b[i, j] <-
           postprobDist(
             x = outcomesY[i],
@@ -201,25 +217,22 @@ predprobDist <- function(x, n,
             parS = parS,
             weightsS = weightsS
           )
-
-        ## what are the joint probabilities of active and control counts?
-        ## => because they are independent, just multiply them
-        pyz[i, j] <- py[i] * pz[j]
+        # what are the joint probabilities of active and control counts?
+        # => because they are independent, just multiply them
+        pyz[i, j] <- py[i] * pz[j] # this is the matrix that Daniel was talking about
       }
     }
-
-    ## should we print something?
+    # should we print something? predprob part
     ret <- structure(sum(pyz * (b > thetaT)),
       tables =
         list(
           pyz = pyz,
           b = b,
-          bgttheta = (b > thetaT)
+          success = (b > thetaT)
         )
     )
   }
-
-  return(ret)
+  ret
 }
 
-## todo: predprobDistFail
+# todo: predprobDistFail
diff --git a/design/design-doc_predprobDist.Rmd b/design/design-doc_predprobDist.Rmd
new file mode 100644
index 00000000..9bb21c54
--- /dev/null
+++ b/design/design-doc_predprobDist.Rmd
@@ -0,0 +1,241 @@
+---
+title: "Design Document"
+output: html_document
+date: "2023-12-04"
+---
+
+## Example inputs / Sanity check
+
+```{r setup, include=FALSE}
+x <- 16
+n <- 23
+xS <- 5
+nS <- 10
+Nmax <- 40
+NmaxControl <- 20
+delta <- 0
+thetaT <- 0.6
+parE <- c(1, 1)
+parS <- c(1, 1)
+weights <- c(2, 1)
+weightsS <- c(2, 1)
+relativeDelta <- FALSE
+
+# helper test
+mE <- Nmax - n
+parE <- t(parE)
+weights <- rep(1, nrow(parE))
+parS <- t(parS)
+weightsS <- rep(1, nrow(parS))
+
+activeBetamixPost <- h_getBetamixPost(x = x, n = n, par = parE, weights = weights)
+# now with the beta binomial mixture:
+density_y <- with(activeBetamixPost, dbetabinomMix(x = 0:mE, m = mE, par = par, weights = weights))
+```
+
+# Sanity Check
+```{r}
+predprobDist(
+  x = 16, n = 23, Nmax = 40, delta = 0, thetaT = 0.9,
+  parE = c(0.6, 0.4), parS = c(7, 11)
+)
+```
+
+# Helper function if NmaxControl == 0, or when there is no control
+```{r}
+h_predprobdist_single_arm <- function(x,
+                                         n,
+                                         delta,
+                                         relativeDelta,
+                                         parE,
+                                         weights,
+                                         parS,
+                                         weightsS,
+                                         thetaT,
+                                         density,
+                                         mE) {
+  posterior_x <- postprobDist(
+    x = x + c(0:mE),
+    n = Nmax,
+    delta = delta,
+    relativeDelta = relativeDelta,
+    parE = parE,
+    weights = weights,
+    parS = parS,
+    weightsS = weightsS
+  )
+  list(
+    result = sum(density * (posterior_x > thetaT)),
+    table = data.frame(
+      counts = c(0:mE),
+      cumul_counts = x + (0:mE),
+      density = density_y,
+      posterior = posterior_x,
+      success = (posterior_x > thetaT)
+    )
+  )
+}
+```
+
+# Testing helper function if NmaxControl == 0, or when there is no control
+```{r}
+# testing
+h_get_predproblist_nocontrol(
+  x = x,
+  n = Nmax,
+  delta = delta,
+  relativeDelta = relativeDelta,
+  parE = parE,
+  weights = weights,
+  parS = parS,
+  weightsS = weightsS,
+  thetaT = thetaT,
+  density = density_y,
+  mE = 17
+)
+```
+
+# Helper function 1 if NmaxControl != 0
+```{r}
+h_getlistpredprob <- function(NmaxControl, nS, xS, par, weightsS, mS, x, mE, density_y) {
+  mS <- NmaxControl - nS
+  controlBetamixPost <- h_getBetamixPost(
+    x = xS,
+    n = nS,
+    par = parS,
+    weights = weightsS
+  )
+  density_z <- with(
+    controlBetamixPost,
+    dbetabinomMix(x = 0:mS, m = mS, par = par, weights = weights)
+  )
+  ## determine resulting posterior probabilities:
+  outcomesY <- x + c(0:mE)
+  outcomesZ <- xS + c(0:mS)
+  density_yz <- posterior_yz <- matrix(
+    nrow = 1 + mE,
+    ncol = 1 + mS,
+    dimnames =
+      list(
+        0:mE,
+        0:mS
+      )
+  )
+  for (i in seq_along(outcomesY)) {
+    for (j in seq_along(outcomesZ)) {
+      posterior_yz[i, j] <-
+        postprobDist(
+          x = outcomesY[i],
+          n = Nmax,
+          xS = outcomesZ[j],
+          nS = NmaxControl,
+          delta = delta,
+          relativeDelta = relativeDelta,
+          parE = parE,
+          weights = weights,
+          parS = parS,
+          weightsS = weightsS
+        )
+      density_yz[i, j] <- density_y[i] * density_z[j]
+    }
+  }
+  ret <- list(
+    result = sum(density_yz * (posterior_yz > thetaT)),
+    table = data.frame(
+      counts = c(0:mE),
+      cumul_counts = x + (0:mE),
+      density = density_yz,
+      posterior = posterior_yz,
+      success = (posterior_yz > thetaT)
+    )
+  )
+  ret
+}
+```
+
+# Testing helper function if NmaxControl != 0
+```{r}
+h_getlistpredprob(
+  NmaxControl = 20,
+  nS = 10,
+  xS = 5,
+  weightsS = 1,
+  par = c(1, 1),
+  x = 10,
+  mE = 17,
+  density_y = density_y
+)
+```
+
+# Main function
+```{r cars}
+predprobDist <- function(x, n,
+                         xS = 0, nS = 0,
+                         Nmax,
+                         NmaxControl = 0,
+                         delta = 0,
+                         relativeDelta = FALSE,
+                         parE = c(a = 1, b = 1),
+                         weights,
+                         parS = c(a = 1, b = 1),
+                         weightsS,
+                         thetaT) {
+  stopifnot(
+    n <= Nmax,
+    nS <= NmaxControl,
+    x <= n,
+    xS <= nS
+  )
+  mE <- Nmax - n
+  if (is.vector(parE)) {
+    stopifnot(identical(length(parE), 2L))
+    parE <- t(parE)
+  }
+  if (missing(weights)) {
+    weights <- rep(1, nrow(parE))
+  }
+  if (is.vector(parS)) {
+    stopifnot(identical(length(parS), 2L))
+    parS <- t(parS)
+  }
+  if (missing(weightsS)) {
+    weightsS <- rep(1, nrow(parS))
+  }
+  activeBetamixPost <- h_getBetamixPost(x = x, n = n, par = parE, weights = weights)
+  density_y <- with(
+    activeBetamixPost,
+    dbetabinomMix(x = 0:mE, m = mE, par = par, weights = weights)
+  )
+  if (NmaxControl == 0) {
+    ret <- h_get_predproblist_nocontrol(
+      x = x,
+      n = Nmax,
+      delta = delta,
+      relativeDelta = relativeDelta,
+      parE = parE,
+      weights = weights,
+      parS = parS,
+      weightsS = weightsS,
+      thetaT = thetaT,
+      density = density_y,
+      mE = mE
+    )
+  } else {
+    ret <- h_getlistpredprob(
+      NmaxControl = nS,
+      nS = nS, xS = xS, par = parS, weightsS = weightsS,
+      mS = mS, x = x, mE = mE, density_y = density_y
+    )
+  }
+  ret
+}
+```
+
+# An example
+```{r pressure, echo=FALSE}
+predprobDist(
+  x = 16, n = 23, Nmax = 40, delta = 0.1, thetaT = 0.9,
+  parE = rbind(c(1, 1), c(50, 10)),
+  weights = c(2, 1), parS = c(6, 11)
+)
+```
diff --git a/examples/predprobDist.R b/examples/predprobDist.R
index 44b35769..90ce5ca9 100644
--- a/examples/predprobDist.R
+++ b/examples/predprobDist.R
@@ -1,53 +1,53 @@
-## The original Lee and Liu (Table 1) example:
-## Nmax=40, x=16, n=23, beta(0.6,0.4) prior distribution,
-## thetaT=0.9. The control response rate is 60%:
+# The original Lee and Liu (Table 1) example:
+# Nmax=40, x=16, n=23, beta(0.6,0.4) prior distribution,
+# thetaT=0.9. The control response rate is 60%:
 predprob(
   x = 16, n = 23, Nmax = 40, p = 0.6, thetaT = 0.9,
   parE = c(0.6, 0.4)
 )
-## So the predictive probability is 56.6%. 12 responses
-## in the remaining 17 patients are required for success.
+# So the predictive probability is 56.6%. 12 responses
+# in the remaining 17 patients are required for success.
 
-## Now to the modified example, where the control response
-## rate p has a beta(7, 11) distribution.
-## For example if the 60% threshold stems from a trial
-## with 10 patients, of which 6 were observed with response.
+# Now to the modified example, where the control response
+# rate p has a beta(7, 11) distribution.
+# For example if the 60% threshold (control) stems from a trial
+# with 10 patients, of which 6 were observed with response.
 predprobDist(
   x = 16, n = 23, Nmax = 40, delta = 0, thetaT = 0.9,
   parE = c(0.6, 0.4), parS = c(7, 11)
 )
-## Now only 11 responses are needed in the remaining 17 patients
-## in order to have a successful trial.
-## Also, the predictive probability for a Go decision
-## is now 70.8% instead of merely 56.6%.
+# Now only7 responses are needed in the remaining 17 patients
+# in order to have a successful trial.
+# Also, the predictive probability for a Go decision
+# is now 97.78% instead of merely 56.6%.
 
-## If the response threshold of 60% stems from an SOC estimate (e.g. 50% = 5/10)
-## and a margin of e.g. 10%, then the margin can be specified with
-## the delta argument:
+# If the response threshold of 60% stems from an SOC estimate (e.g. 50% = 5/10)
+# and a margin of e.g. 10%, then the margin can be specified with
+# the delta argument:
 predprobDist(
   x = 16, n = 23, Nmax = 40, delta = 0.1, thetaT = 0.9,
   parE = c(1, 1), parS = c(6, 11)
 )
-## This again changes the result: Only 10 future responses are required,
-## the predictive probability of success is now 80%.
+# This again changes the result: Only 10 future responses are required,
+# the predictive probability of success is now 80%.
 
-## Next we will use a beta mixture prior, with a weight of 1/3 for an
-## informative beta(50, 10) prior, on the experimental response rate:
+# Next we will use a beta mixture prior, with a weight of 1/3 for an
+# informative beta(50, 10) prior, on the experimental response rate:
 predprobDist(
   x = 16, n = 23, Nmax = 40, delta = 0.1, thetaT = 0.9,
   parE = rbind(c(1, 1), c(50, 10)),
   weights = c(2, 1), parS = c(6, 11)
 )
-## Now still 10 future responses are required for success, but the predictive
-## success probability is higher (87.2%).
+# Now still 10 future responses are required for success, but the predictive
+# success probability is higher (87.2%).
 
-## We can also have additional controls in our trial. For example
-## assume that in the interim analysis we had 10 control patients observed
-## with 5 responses out of 20 in total at the end.
-## We also had historical control data (say 60 patients of
-## which 20 responded), but in order to be robust against changes in the response
+# We can also have additional controls in our trial. For example
+# assume that in the interim analysis we had 10 control patients observed
+# with 5 responses out of 20 in total at the end.
+# We also had historical control data (say 60 patients of
+# which 20 responded), but in order to be robust against changes in the response
 # rate over time, we will again use a beta mixture, putting only 1/3 of weight
-## on the historical controls:
+# on the historical controls:
 predprobDist(
   x = 16, n = 23, xS = 5, nS = 10,
   Nmax = 40, NmaxControl = 20,
@@ -57,8 +57,8 @@ predprobDist(
   parS = rbind(c(1, 1), c(20, 40)),
   weightsS = c(2, 1)
 )
-## Now we only have 59.9% predictive probability of success. The bgttheta matrix
-## lists the cases where we would have success, for all possible combinations
-## of future responses in the control and experimental arms. We see that the
-## success threshold for experimental responses depends on the number of
-## control responses.
+# Now we only have 59.9% predictive probability of success. The bgttheta matrix
+# lists the cases where we would have success, for all possible combinations
+# of future responses in the control and experimental arms. We see that the
+# success threshold for experimental responses depends on the number of
+# control responses.
diff --git a/inst/WORDLIST b/inst/WORDLIST
index 1db7dca6..b5d955a2 100644
--- a/inst/WORDLIST
+++ b/inst/WORDLIST
@@ -125,6 +125,7 @@ PointMass
 pointmass
 postL
 postprob
+postprobDist
 postU
 ppL
 PProbust
diff --git a/man/predprobDist.Rd b/man/predprobDist.Rd
index 9dffe3f2..6389a81e 100644
--- a/man/predprobDist.Rd
+++ b/man/predprobDist.Rd
@@ -22,129 +22,152 @@ predprobDist(
 )
 }
 \arguments{
-\item{x}{number of successes (in the treatment group)}
+\item{x}{(\code{number}):\cr number of successes in the treatment group at interm}
 
-\item{n}{number of patients (in the treatment group)}
+\item{n}{(\code{number}):\cr number of patients in the treatment group at interim}
 
-\item{xS}{number of successes in the SOC group (default: 0)}
+\item{xS}{(\code{number}):\cr number of successes in the SOC group at interim}
 
-\item{nS}{number of patients in the SOC group (default: 0)}
+\item{nS}{(\code{number}):\cr number of patients in the SOC group}
 
-\item{Nmax}{maximum number of patients at the end of the trial (in the
-treatment group)}
+\item{Nmax}{(\code{number}):\cr maximum number of patients in the treatment group at the end of the trial}
 
-\item{NmaxControl}{maximum number of patients at the end of the trial in the
-SOC group (default: 0)}
+\item{NmaxControl}{(\code{number}):\cr maximum number of patients at the end of the trial in the
+SOC group}
 
-\item{delta}{margin by which the response rate in the treatment group should
-be better than in the SOC group (default: 0)}
+\item{delta}{(``):\cr margin by which the response rate in the treatment group should
+be better than in the SOC group}
 
-\item{relativeDelta}{see \code{\link{postprobDist}}}
+\item{relativeDelta}{(``):\cr see \verb{[postprobDist()]}}
 
-\item{parE}{the beta parameters matrix, with K rows and 2 columns,
+\item{parE}{(``):\cr the beta parameters matrix, with K rows and 2 columns,
 corresponding to the beta parameters of the K components. default is a
 uniform prior.}
 
-\item{weights}{the mixture weights of the beta mixture prior. Default are
+\item{weights}{(``):\cr the mixture weights of the beta mixture prior. Default are
 uniform weights across mixture components.}
 
-\item{parS}{beta prior parameters in the SOC group (default: uniform)}
+\item{parS}{(``):\cr beta prior parameters in the SOC group}
 
-\item{weightsS}{weights for the SOC group (default: uniform)}
+\item{weightsS}{(``):\cr weights for the SOC group}
 
-\item{thetaT}{threshold on the probability to be used}
+\item{thetaT}{(``):\cr threshold on the probability to be used}
 }
 \value{
-The predictive probability, a numeric value. In addition, a
-list called \code{tables} is returned as attribute of the returned number.
+A \code{list} is returned with names \code{result} for predictive probability and
+\code{table} of numeric values with counts of responses in the remaining patients,
+probabilities of these counts, corresponding probabilities to be above threshold,
+and trial success indicators.
 }
 \description{
+\ifelse{html}{\href{https://lifecycle.r-lib.org/articles/stages.html#experimental}{\figure{lifecycle-experimental.svg}{options: alt='[Experimental]'}}}{\strong{[Experimental]}}
+
 Compute the predictive probability of trial success given current data.
 Success means that at the end of the trial the posterior probability
-Pr(P_E > P_S + delta_0 | data) >= thetaT. Then the
+\code{Pr(P_E > P_S + delta_0 | data) >= thetaT}. Then the
 predictive probability for success is:
-pp = sum over i: Pr(Y=i|x,n)*I{Pr(P_E > P_S + delta|x,Y=i)>=thetaT},
-where Y is the number of future responses in the treatment group and x is
-the current number of responses in the treatment group (out of n).
-Prior is P_E ~ beta(a, b), default uniform which is a beta(1,1).
+\verb{pp = sum over i: Pr(Y = i | x , n)*I\{Pr(P_E > P_S + delta | x,Y=i) >= thetaT\}},
+where \code{Y} is the number of future responses in the treatment group and \code{x} is
+the current number of responses in the treatment group out of \code{n}.
+Prior is \code{P_E ~ beta(a, b)} and uniform which is a beta(1,1).
 However, also a beta mixture prior can be specified. Analogously
-for P_S either a classic beta prior or a beta mixture prior can be
+for \code{P_S} either a classic beta prior or a beta mixture prior can be
 specified.
-}
-\details{
+
 Also data on the SOC might be available. Then the predictive probability is
 more generally defined as
-pp = sum over i, j: Pr(Y=i|x,n)*Pr(Z=j|xS, nS)*I{Pr(P_E > P_S +
-delta|x,xS,Y=i,Z=j)>=thetaT}
-where Z is the future number of responses in the SOC group, and xS is the
+\verb{pp = sum over i, j: Pr(Y = i | x, n)*Pr(Z = j | xS, nS )*I\{Pr(P_E > P_S + delta | x,xS, Y=i, Z=j ) >= thetaT\}}
+where \code{Z} is the future number of responses in the SOC group, and \code{xS} is the
 current number of responses in the SOC group.
 
+In the case where \code{NmaxControl = 0}, a table with the following contents will be included in the return output :
+\itemize{
+\item \code{i}: \code{Y = i}, number of future successes in \code{Nmax-n} subjects.
+\item \code{density}: \code{Pr(Y = i|x)} using beta-(mixture)-binomial distribution.
+\item \code{posterior}: \code{Pr(P_E > P_S + delta | x, Y = i)} using beta posterior.
+\item \code{success}: indicator \code{I(b>thetaT)}.
+}
+
 A table with the following contents will be
-included in the \code{tables} attribute of the return value
+included in the  return value
 (in the case that NmaxControl is zero):
 i: Y=i (number of future successes in Nmax-n subjects)
 py: Pr(Y=i|x) using beta-(mixture)-binomial distribution
 b: Pr(P_E > P_S + delta | x, Y=i)
 bgttheta: indicator I(b>thetaT)
 
-If NmaxControl is not zero, i.e., when data on the control treatment
+If \code{NmaxControl} is not zero, i.e., when data on the control treatment
 is available in this trial, then a list with will be included with the
 following elements:
 pyz: matrix with the probabilities Pr(Y=i, Z=j | x, xS)
 b: matrix with Pr(P_E > P_S + delta | x, xS, Y=i, Z=j)
 bgttheta: matrix of indicators I(b>thetaT)
 }
+\note{
+Delta from postprobDist :
+
+The desired improvement is denoted as \code{delta}. There are two options in using \code{delta}.
+The absolute case when \code{relativeDelta = FALSE} and relative as when \code{relativeDelta = TRUE}.
+\enumerate{
+\item The absolute case is when we define an absolute delta, greater than \code{P_S},
+the response rate of the \code{SOC} group such that
+the posterior is \code{Pr(P_E > P_S + delta | data)}.
+\item In the relative case, we suppose that the treatment group's
+response rate is assumed to be greater than \code{P_S + (1-P_S) * delta} such that
+the posterior is \code{Pr(P_E > P_S + (1 - P_S) * delta | data)}.
+}
+}
 \examples{
-## The original Lee and Liu (Table 1) example:
-## Nmax=40, x=16, n=23, beta(0.6,0.4) prior distribution,
-## thetaT=0.9. The control response rate is 60\%:
+# The original Lee and Liu (Table 1) example:
+# Nmax=40, x=16, n=23, beta(0.6,0.4) prior distribution,
+# thetaT=0.9. The control response rate is 60\%:
 predprob(
   x = 16, n = 23, Nmax = 40, p = 0.6, thetaT = 0.9,
   parE = c(0.6, 0.4)
 )
-## So the predictive probability is 56.6\%. 12 responses
-## in the remaining 17 patients are required for success.
+# So the predictive probability is 56.6\%. 12 responses
+# in the remaining 17 patients are required for success.
 
-## Now to the modified example, where the control response
-## rate p has a beta(7, 11) distribution.
-## For example if the 60\% threshold stems from a trial
-## with 10 patients, of which 6 were observed with response.
+# Now to the modified example, where the control response
+# rate p has a beta(7, 11) distribution.
+# For example if the 60\% threshold (control) stems from a trial
+# with 10 patients, of which 6 were observed with response.
 predprobDist(
   x = 16, n = 23, Nmax = 40, delta = 0, thetaT = 0.9,
   parE = c(0.6, 0.4), parS = c(7, 11)
 )
-## Now only 11 responses are needed in the remaining 17 patients
-## in order to have a successful trial.
-## Also, the predictive probability for a Go decision
-## is now 70.8\% instead of merely 56.6\%.
-
-## If the response threshold of 60\% stems from an SOC estimate (e.g. 50\% = 5/10)
-## and a margin of e.g. 10\%, then the margin can be specified with
-## the delta argument:
+# Now only7 responses are needed in the remaining 17 patients
+# in order to have a successful trial.
+# Also, the predictive probability for a Go decision
+# is now 97.78\% instead of merely 56.6\%.
+
+# If the response threshold of 60\% stems from an SOC estimate (e.g. 50\% = 5/10)
+# and a margin of e.g. 10\%, then the margin can be specified with
+# the delta argument:
 predprobDist(
   x = 16, n = 23, Nmax = 40, delta = 0.1, thetaT = 0.9,
   parE = c(1, 1), parS = c(6, 11)
 )
-## This again changes the result: Only 10 future responses are required,
-## the predictive probability of success is now 80\%.
+# This again changes the result: Only 10 future responses are required,
+# the predictive probability of success is now 80\%.
 
-## Next we will use a beta mixture prior, with a weight of 1/3 for an
-## informative beta(50, 10) prior, on the experimental response rate:
+# Next we will use a beta mixture prior, with a weight of 1/3 for an
+# informative beta(50, 10) prior, on the experimental response rate:
 predprobDist(
   x = 16, n = 23, Nmax = 40, delta = 0.1, thetaT = 0.9,
   parE = rbind(c(1, 1), c(50, 10)),
   weights = c(2, 1), parS = c(6, 11)
 )
-## Now still 10 future responses are required for success, but the predictive
-## success probability is higher (87.2\%).
-
-## We can also have additional controls in our trial. For example
-## assume that in the interim analysis we had 10 control patients observed
-## with 5 responses out of 20 in total at the end.
-## We also had historical control data (say 60 patients of
-## which 20 responded), but in order to be robust against changes in the response
+# Now still 10 future responses are required for success, but the predictive
+# success probability is higher (87.2\%).
+
+# We can also have additional controls in our trial. For example
+# assume that in the interim analysis we had 10 control patients observed
+# with 5 responses out of 20 in total at the end.
+# We also had historical control data (say 60 patients of
+# which 20 responded), but in order to be robust against changes in the response
 # rate over time, we will again use a beta mixture, putting only 1/3 of weight
-## on the historical controls:
+# on the historical controls:
 predprobDist(
   x = 16, n = 23, xS = 5, nS = 10,
   Nmax = 40, NmaxControl = 20,
@@ -154,11 +177,11 @@ predprobDist(
   parS = rbind(c(1, 1), c(20, 40)),
   weightsS = c(2, 1)
 )
-## Now we only have 59.9\% predictive probability of success. The bgttheta matrix
-## lists the cases where we would have success, for all possible combinations
-## of future responses in the control and experimental arms. We see that the
-## success threshold for experimental responses depends on the number of
-## control responses.
+# Now we only have 59.9\% predictive probability of success. The bgttheta matrix
+# lists the cases where we would have success, for all possible combinations
+# of future responses in the control and experimental arms. We see that the
+# success threshold for experimental responses depends on the number of
+# control responses.
 }
 \references{
 Lee, J. J., & Liu, D. D. (2008). A predictive probability
diff --git a/tests/test-predprob.R b/tests/testthat/test-predprob.R
similarity index 100%
rename from tests/test-predprob.R
rename to tests/testthat/test-predprob.R