Creating the model
Model variables
The following code defines the variables for cost, utility and effect that will be used in the model. There are 14 variables in total; 4 costs, 4 utilities and 6 probabilities.
# Time horizon
th <- as.difftime(24L, units = "hours")
# model variables for cost
c_sumatriptan <- 16.10
c_caffeine <- 1.32
c_ed <- 63.16
c_admission <- 1093.0
# model variables for utility
u_relief_norecurrence <- 1.0
u_relief_recurrence <- 0.9
u_norelief_endures <- -0.30
u_norelief_er <- 0.1
# model variables for effect
p_sumatriptan_recurrence <- 0.594
p_caffeine_recurrence <- 0.703
p_sumatriptan_relief <- 0.558
p_caffeine_relief <- 0.379
p_er <- 0.08
p_admitted <- 0.002Constructing the tree
The following code constructs the decision tree. In the formulation
used by rdecision, a decision tree is a form of
arborescence, a directed graph of nodes and edges, with a
single root and a unique path from the root to each leaf node. Decision
trees comprise three types of node: decision, chance and leaf nodes and
two types of edge: actions (whose sources are decision nodes) and
reactions (whose sources are chance nodes), see
Figure 1.
# Sumatriptan branch
ta <- LeafNode$new("A", utility = u_relief_norecurrence, interval = th)
tb <- LeafNode$new("B", utility = u_relief_recurrence, interval = th)
c3 <- ChanceNode$new()
e1 <- Reaction$new(
c3, ta, p = p_sumatriptan_recurrence, label = "No recurrence"
)
e2 <- Reaction$new(
c3, tb, p = 1.0 - p_sumatriptan_recurrence, cost = c_sumatriptan,
label = "Relieved 2nd dose"
)
td <- LeafNode$new("D", utility = u_norelief_er, interval = th)
te <- LeafNode$new("E", utility = u_norelief_endures, interval = th)
c7 <- ChanceNode$new()
e3 <- Reaction$new(c7, td, p = 1.0 - p_admitted, label = "Relief")
e4 <- Reaction$new(
c7, te, p = p_admitted, cost = c_admission, label = "Hospitalization"
)
tc <- LeafNode$new("C", utility = u_norelief_endures, interval = th)
c4 <- ChanceNode$new()
e5 <- Reaction$new(c4, tc, p = 1.0 - p_er, label = "Endures attack")
e6 <- Reaction$new(c4, c7, p = p_er, cost = c_ed, label = "ER")
c1 <- ChanceNode$new()
e7 <- Reaction$new(c1, c3, p = p_sumatriptan_relief, label = "Relief")
e8 <- Reaction$new(c1, c4, p = 1.0 - p_sumatriptan_relief, label = "No relief")
# Caffeine/Ergotamine branch
tf <- LeafNode$new("F", utility = u_relief_norecurrence, interval = th)
tg <- LeafNode$new("G", utility = u_relief_recurrence, interval = th)
c5 <- ChanceNode$new()
e9 <- Reaction$new(c5, tf, p = p_caffeine_recurrence, label = "No recurrence")
e10 <- Reaction$new(
c5, tg, p = 1.0 - p_caffeine_recurrence, cost = c_caffeine,
label = "Relieved 2nd dose"
)
ti <- LeafNode$new("I", utility = u_norelief_er, interval = th)
tj <- LeafNode$new("J", utility = u_norelief_endures, interval = th)
c8 <- ChanceNode$new()
e11 <- Reaction$new(c8, ti, p = 1.0 - p_admitted, label = "Relief")
e12 <- Reaction$new(
c8, tj, p = p_admitted, cost = c_admission, label = "Hospitalization"
)
th <- LeafNode$new("H", utility = u_norelief_endures, interval = th)
c6 <- ChanceNode$new()
e13 <- Reaction$new(c6, th, p = 1.0 - p_er, label = "Endures attack")
e14 <- Reaction$new(c6, c8, p = p_er, cost = c_ed, label = "ER")
c2 <- ChanceNode$new()
e15 <- Reaction$new(c2, c5, p = p_caffeine_relief, label = "Relief")
e16 <- Reaction$new(c2, c6, p = 1.0 - p_caffeine_relief, label = "No relief")
# decision node
d1 <- DecisionNode$new("d1")
e17 <- Action$new(d1, c1, cost = c_sumatriptan, label = "Sumatriptan")
e18 <- Action$new(d1, c2, cost = c_caffeine, label = "Caffeine-Ergotamine")
# create lists of nodes and edges
V <- list(
d1, c1, c2, c3, c4, c5, c6, c7, c8,
ta, tb, tc, td, te, tf, tg, th, ti, tj
)
E <- list(
e1, e2, e3, e4, e5, e6, e7, e8, e9, e10, e11, e12, e13, e14, e15, e16,
e17, e18
)
# tree
DT <- DecisionTree$new(V, E)
Figure 1. Decision tree for the Sumatriptan model