SemiMarkovModel: A semi-Markov model for cohort simulation
In rdecision: Decision Analytic Modelling in Health Economics
SemiMarkovModel R Documentation
A semi-Markov model for cohort simulation
Description
An R6 class representing a semi-Markov model for
cohort simulation.
Details
A class to represent a continuous time semi-Markov chain, modelled
using cohort simulation. As interpreted in rdecision, semi-Markov
models
may include temporary states and transitions are defined by per-cycle
probabilities. Although used widely in health economic modelling, the
differences between semi-Markov models and Markov processes introduce
some caveats for modellers:
If there are temporary states, the result will depend on cycle length.
Transitions are specified by their conditional probability, which
is a per-cycle probability of starting a cycle in one state and
ending it in another; if the cycle length changes, the probabilities should
change, too.
Probabilities and rates cannot be linked by the Kolmogorov forward
equation, where the per-cycle probabilities are given by the matrix
exponential of the transition rate matrix, because this equation does not
apply if there are temporary states. In creating semi-Markov models, it is
the modeller's task to estimate probabilities from published data on
event rates.
The cycle time cannot be changed during the simulation.
Graph theory
A Markov model is a directed multidigraph permitting loops (a loop
multidigraph), optionally labelled, or a quiver. It is a
multidigraph because there are potentially two edges between each pair of
nodes {A,B} representing the transition probabilities from A to B and
vice versa. It is a directed graph because the transition
probabilities refer to transitions in one direction. Each edge can be
optionally labelled. It permits self-loops (edges whose source and target
are the same node) to represent patients that remain in the same state
between cycles.
Transition rates and probabilities
Why semi-Markov?
Beck and Pauker (1983) and later Sonnenberg and Beck (1993) proposed the
use of Markov processes to model the health economics of medical
interventions. Further, they introduced the additional concept of temporary
states, to which patients who transition remain for exactly one cycle. This
breaks the principle that Markov processes are memoryless
and thus the underlying mathematical formalism, first
developed by Kolmogorov, is not applicable. For example, ensuring that all
patients leave a temporary state requires its transition rate to be infinite.
Hence, such models are usually labelled as semi-Markov processes.
Rates and probabilities
Miller and Homan (1994) and Fleurence & Hollenbeak (2007) provide advice
on estimating probabilities from rates. Jones (2017) and Welton (2005)
describe methods for estimating probabilities in multi-state,
multi-transition models, although those methods may not apply to
semi-Markov models with temporary states. In particular, the
"simple" equation, p = 1-e^{-rt} (Briggs 2006) applies only in a
two-state, one transition model (O'Mahony 2015).
Uncertainty in rates
In semi-Markov models, the conditional probabilities of the transitions
from each state are usually modelled by a Dirichlet distribution. In
rdecision, create a Dirichlet distribution for each state and
optionally create model variables for each conditional probability
(\rho_{ij}) linked to an applicable Dirichlet distribution.
Super classes
rdecision::Graph -> rdecision::Digraph -> SemiMarkovModel
Methods
Public methods
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Inherited methods
rdecision::Graph$degree()rdecision::Graph$edge_along()rdecision::Graph$edge_at()rdecision::Graph$edge_index()rdecision::Graph$edge_label()rdecision::Graph$edges()rdecision::Graph$graph_adjacency_matrix()rdecision::Graph$has_edge()rdecision::Graph$has_vertex()rdecision::Graph$is_simple()rdecision::Graph$neighbours()rdecision::Graph$order()rdecision::Graph$size()rdecision::Graph$vertex_along()rdecision::Graph$vertex_at()rdecision::Graph$vertex_index()rdecision::Graph$vertex_label()rdecision::Graph$vertexes()rdecision::Digraph$arrow_source()rdecision::Digraph$arrow_target()rdecision::Digraph$as_DOT()rdecision::Digraph$as_gml()rdecision::Digraph$digraph_adjacency_matrix()rdecision::Digraph$digraph_incidence_matrix()rdecision::Digraph$direct_predecessors()rdecision::Digraph$direct_successors()rdecision::Digraph$is_acyclic()rdecision::Digraph$is_arborescence()rdecision::Digraph$is_connected()rdecision::Digraph$is_polytree()rdecision::Digraph$is_tree()rdecision::Digraph$is_weakly_connected()rdecision::Digraph$paths()rdecision::Digraph$topological_sort()rdecision::Digraph$walk()
Method new()
Creates a semi-Markov model for cohort simulation.
Usage
SemiMarkovModel$new(
V,
E,
tcycle = as.difftime(365.25, units = "days"),
discount.cost = 0,
discount.utility = 0
)
Arguments
VA list of nodes (MarkovStates).
EA list of edges (Transitions).
tcycleCycle length, expressed as an R difftime object.
discount.costAnnual discount rate for future costs. Note this
is a rate, not a probability (i.e. use 0.035 for 3.5%).
discount.utilityAnnual discount rate for future
utility. Note this is a rate, not a probability (i.e. use 0.035
for 3.5%).
Details
A semi-Markov model must meet the following conditions:
It must have at least one node and at least one edge.
All nodes must be of class MarkovState;
All edges must be of class Transition;
The nodes and edges must form a digraph whose underlying
graph is connected;
Each state must have at least one outgoing transition (for
absorbing states this is a self-loop);
For each state the sum of outgoing conditional transition
probabilities must be one. For convenience, one outgoing transition
probability from each state may be set to NA when the
probabilities are defined. Typically, probabilities for self
loops would be set to NA. Transition probabilities in Pt
associated with transitions that are not defined as edges in the
graph are zero. Probabilities can be changed between cycles.
No two edges may share the same source and target nodes (i.e.
the digraph may not have multiple edges). This is to ensure that there
are no more transitions than cells in the transition matrix.
The node labels must be unique to the graph.
Returns
A SemiMarkovModel object. The population of the first
state is set to 1000 and from each state there is an equal
conditional probability of each allowed transition.
Method set_probabilities()
Sets transition probabilities.
Usage
SemiMarkovModel$set_probabilities(Pt)
Arguments
PtPer-cycle transition probability matrix. The row and
column labels must be the state names and each row must sum to one.
Non-zero probabilities for undefined transitions are not allowed. At
most one NA may appear in each row. If an NA is present in a row,
it is replaced by 1 minus the sum of the defined probabilities.
Returns
Updated SemiMarkovModel object
Method transition_probabilities()
Per-cycle transition probability matrix for the model.
Usage
SemiMarkovModel$transition_probabilities()
Returns
A square matrix of size equal to the number of states. If all
states are labelled, the dimnames take the names of the states.
Method transition_cost()
Return the per-cycle transition costs for the model.
Usage
SemiMarkovModel$transition_cost()
Returns
A square matrix of size equal to the number of states. If all
states are labelled, the dimnames take the names of the states.
Method get_statenames()
Returns a character list of state names.
Usage
SemiMarkovModel$get_statenames()
Returns
List of the names of each state.
Method reset()
Resets the model counters.
Usage
SemiMarkovModel$reset(
populations = NULL,
icycle = 0L,
elapsed = as.difftime(0, units = "days")
)
Arguments
populationsA named vector of populations for
the start of the state. The names should be the state names.
Due to the R implementation of matrix algebra, populations
must be a numeric type and is not restricted to being an integer. If
NULL, the population of all states is set to zero.
icycleCycle number at which to start/restart.
elapsedElapsed time since the index (reference) time used for
discounting as an R difftime object.
Details
Resets the state populations, next cycle number and elapsed time
of the model. By default the model is returned to its ground state (zero
people in the all states; next cycle is labelled
zero; elapsed time (years) is zero). Any or all of these can be set via
this function. icycle is simply an integer counter label for each
cycle, elapsed sets the elapsed time in years from the index time
from which discounting is assumed to apply.
Returns
Updated SemiMarkovModel object.
Method get_populations()
Gets the occupancy of each state.
Usage
SemiMarkovModel$get_populations()
Returns
A numeric vector of populations, named with state names.
Method get_cycle()
Gets the current cycle number.
Usage
SemiMarkovModel$get_cycle()
Returns
Current cycle count, as an integer.
Method get_tcycle()
Gets the cycle duration.
Usage
SemiMarkovModel$get_tcycle()
Returns
Current cycle duration, as a difftime object.
Method get_elapsed()
Gets the current elapsed time.
Usage
SemiMarkovModel$get_elapsed()
Details
The elapsed time is defined as the difference between the
current time in the model and an index time used as the reference
time for applying discounting. By default the elapsed time starts at
zero. It can be set directly by calling reset. It is incremented
after each call to cycle by the cycle duration to the time at the
end of the cycle (even if half cycle correction is used). Thus, via the
reset and cycle methods, the time of each cycle relative
to the discounting index and its duration can be controlled arbitrarily.
Returns
Elapsed time as an R difftime object.
Method tabulate_states()
Tabulation of states
Usage
SemiMarkovModel$tabulate_states()
Details
Creates a data frame summary of each state in the model.
Returns
A data frame with the following columns:
- Name
State name
- Cost
Annual cost of occupying the state
- Utility
Incremental utility associated with being in the state.
Method cycle()
Applies one cycle of the model.
Usage
SemiMarkovModel$cycle(hcc.pop = TRUE, hcc.cost = TRUE, hcc.QALY = TRUE)
Arguments
hcc.popDetermines the state populations returned by this
function. If FALSE, the end of cycle populations apply; if TRUE the
mid-cycle populations and time apply. The mid-cycle populations are
taken as the mean of the start and end populations and the discount
time as the mid-point. The value of this parameter does not affect the
state populations or elapsed time passed to the next cycle or available
via get_populations; those are always the end cycle values.
hcc.costDetermines the state occupancy costs returned by this
function and the time at which the cost discount is applied to the
occupancy costs and the entry costs. If FALSE, the end of cycle
populations and time apply; if TRUE the mid-cycle populations and time
apply, as per hcc.pop. The value of this parameter does not affect
the state populations or elapsed time passed to the next cycle or
available via get_populations; those are always the end cycle
values.
hcc.QALYDetermines the incremental quality adjusted life years
returned by this function and the time at which the utility discount is
applied. If FALSE, the end of cycle population and reference time are
applied to the utilities of each state; if TRUE the mid-cycle populations
and time are applied to the state utilities. The value of this parameter
does not affect the state populations or elapsed time passed to the next
cycle or available via get_populations; those are always the
end cycle values.
Returns
Calculated values, one row per state, as a data frame with the
following columns:
StateName of the state.
CycleThe cycle number.
TimeClock time in years of the end of the cycle.
PopulationPopulations of the states; see hcc.pop.
OccCostCost of the population occupying the state for
the cycle. Discounting and half cycle correction is applied, if those
options are set. The costs are normalized by the model population. The
cycle costs are derived from the annual occupancy costs of the
MarkovStates.
EntryCostCost of the transitions into the state
during the cycle. Discounting is applied, if the option is set.
The result is normalized by the model population. The cycle costs
are derived from Transition costs.
CostTotal cost, normalized by model population.
QALYQuality adjusted life years gained by occupancy of
the states during the cycle. Half cycle correction and discounting are
applied, if these options are set. Normalized by the model population.
Method cycles()
Applies multiple cycles of the model.
Usage
SemiMarkovModel$cycles(
ncycles = 2L,
hcc.pop = TRUE,
hcc.cost = TRUE,
hcc.QALY = TRUE
)
Arguments
ncyclesNumber of cycles to run; default is 2.
hcc.popDetermines the state populations returned by this
function. If FALSE, the end of cycle populations apply; if TRUE the
mid-cycle populations and time apply. The mid-cycle populations are
taken as the mean of the start and end populations and the discount
time as the mid-point. The value of this parameter does not affect the
state populations or elapsed time passed to the next cycle or available
via get_populations; those are always the end cycle values.
hcc.costDetermines the state occupancy costs returned by this
function and the time at which the cost discount is applied to the
occupancy costs and the entry costs. If FALSE, the end of cycle
populations and time apply; if TRUE the mid-cycle populations and time
apply, as per hcc.pop. The value of this parameter does not affect
the state populations or elapsed time passed to the next cycle or
available via get_populations; those are always the end cycle
values.
hcc.QALYDetermines the incremental quality adjusted life years
returned by this function and the time at which the utility discount is
applied. If FALSE, the end of cycle population and reference time are
applied to the utilities of each state; if TRUE the mid-cycle populations
and time are applied to the state utilities. The value of this parameter
does not affect the state populations or elapsed time passed to the next
cycle or available via get_populations; those are always the
end cycle values.
Details
The starting populations are redistributed through the
transition probabilities and the state occupancy costs are
calculated, using function cycle. The end populations are
then fed back into the model for a further cycle and the
process is repeated. For each cycle, the state populations and
the aggregated occupancy costs are saved in one row of the
returned data frame, with the cycle number. If the cycle count
for the model is zero when called, the first cycle reported
will be cycle zero, i.e. the distribution of patients to starting
states.
Returns
Data frame with cycle results, with the following columns:
CycleThe cycle number.
YearsElapsed time at end of cycle, years
CostCost associated with occupancy and transitions between
states during the cycle.
QALYQuality adjusted life years associated with occupancy
of the states in the cycle.
<name>Population of state <name> at the end of
the cycle.
Method modvars()
Find all the model variables in the Markov model.
Usage
SemiMarkovModel$modvars()
Details
Returns variables of type ModVar that have been
specified as values associated with transition rates and costs and
the state occupancy costs and utilities.
Returns
A list of ModVars.
Method modvar_table()
Tabulate the model variables in the Markov model.
Usage
SemiMarkovModel$modvar_table()
Returns
Data frame with one row per model variable, as follows:
DescriptionAs given at initialization.
UnitsUnits of the variable.
DistributionEither the uncertainty distribution, if
it is a regular model variable, or the expression used to create it,
if it is an ExprModVar.
MeanMean; calculated from means of operands if
an expression.
EExpectation; estimated from random sample if expression,
mean otherwise.
SDStandard deviation; estimated from random sample if
expression, exact value otherwise.
Q2.5p=0.025 quantile; estimated from random sample if
expression, exact value otherwise.
Q97.5p=0.975 quantile; estimated from random sample if
expression, exact value otherwise.
EstTRUE if the quantiles and SD have been estimated by
random sampling.
Method clone()
The objects of this class are cloneable with this method.
Usage
SemiMarkovModel$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
Author(s)
Andrew J. Sims andrew.sims@newcastle.ac.uk
References
Beck JR and Pauker SG. The Markov Process in Medical Prognosis.
Med Decision Making, 1983;3:419–458.
Briggs A, Claxton K, Sculpher M. Decision modelling for health economic
evaluation. Oxford, UK: Oxford University Press; 2006.
Fleurence RL and Hollenbeak CS. Rates and probabilities in economic
modelling. PharmacoEconomics, 2007;25:3–6.
Jones E, Epstein D and García-Mochón L. A procedure for deriving
formulas to convert transition rates to probabilities for multistate
Markov models. Medical Decision Making 2017;37:779–789.
Miller DK and Homan SM. Determining transition probabilities: confusion
and suggestions. Medical Decision Making 1994;14:52-58.
O'Mahony JF, Newall AT, van Rosmalen J. Dealing with time in health
economic evaluation: methodological issues and recommendations for
practice. PharmacoEconomics 2015;33:1255–1268.
Sonnenberg FA, Beck JR. Markov models in medical decision making: a
practical guide. Medical Decision Making, 1993:13:322.
Welton NJ and Ades A. Estimation of Markov chain transition probabilities
and rates from fully and partially observed data: uncertainty
propagation, evidence synthesis, and model calibration.
Medical Decision Making, 2005;25:633-645.
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| SemiMarkovModel | R Documentation |
A semi-Markov model for cohort simulation
Description
An R6 class representing a semi-Markov model for cohort simulation.
Details
A class to represent a continuous time semi-Markov chain, modelled using cohort simulation. As interpreted in rdecision, semi-Markov models may include temporary states and transitions are defined by per-cycle probabilities. Although used widely in health economic modelling, the differences between semi-Markov models and Markov processes introduce some caveats for modellers:
If there are temporary states, the result will depend on cycle length.
Transitions are specified by their conditional probability, which is a per-cycle probability of starting a cycle in one state and ending it in another; if the cycle length changes, the probabilities should change, too.
Probabilities and rates cannot be linked by the Kolmogorov forward equation, where the per-cycle probabilities are given by the matrix exponential of the transition rate matrix, because this equation does not apply if there are temporary states. In creating semi-Markov models, it is the modeller's task to estimate probabilities from published data on event rates.
The cycle time cannot be changed during the simulation.
Graph theory
A Markov model is a directed multidigraph permitting loops (a loop multidigraph), optionally labelled, or a quiver. It is a multidigraph because there are potentially two edges between each pair of nodes {A,B} representing the transition probabilities from A to B and vice versa. It is a directed graph because the transition probabilities refer to transitions in one direction. Each edge can be optionally labelled. It permits self-loops (edges whose source and target are the same node) to represent patients that remain in the same state between cycles.
Transition rates and probabilities
Why semi-Markov?
Beck and Pauker (1983) and later Sonnenberg and Beck (1993) proposed the use of Markov processes to model the health economics of medical interventions. Further, they introduced the additional concept of temporary states, to which patients who transition remain for exactly one cycle. This breaks the principle that Markov processes are memoryless and thus the underlying mathematical formalism, first developed by Kolmogorov, is not applicable. For example, ensuring that all patients leave a temporary state requires its transition rate to be infinite. Hence, such models are usually labelled as semi-Markov processes.
Rates and probabilities
Miller and Homan (1994) and Fleurence & Hollenbeak (2007) provide advice
on estimating probabilities from rates. Jones (2017) and Welton (2005)
describe methods for estimating probabilities in multi-state,
multi-transition models, although those methods may not apply to
semi-Markov models with temporary states. In particular, the
"simple" equation, p = 1-e^{-rt} (Briggs 2006) applies only in a
two-state, one transition model (O'Mahony 2015).
Uncertainty in rates
In semi-Markov models, the conditional probabilities of the transitions
from each state are usually modelled by a Dirichlet distribution. In
rdecision, create a Dirichlet distribution for each state and
optionally create model variables for each conditional probability
(\rho_{ij}) linked to an applicable Dirichlet distribution.
Super classes
rdecision::Graph -> rdecision::Digraph -> SemiMarkovModel
Methods
Public methods
Inherited methods
rdecision::Graph$degree()rdecision::Graph$edge_along()rdecision::Graph$edge_at()rdecision::Graph$edge_index()rdecision::Graph$edge_label()rdecision::Graph$edges()rdecision::Graph$graph_adjacency_matrix()rdecision::Graph$has_edge()rdecision::Graph$has_vertex()rdecision::Graph$is_simple()rdecision::Graph$neighbours()rdecision::Graph$order()rdecision::Graph$size()rdecision::Graph$vertex_along()rdecision::Graph$vertex_at()rdecision::Graph$vertex_index()rdecision::Graph$vertex_label()rdecision::Graph$vertexes()rdecision::Digraph$arrow_source()rdecision::Digraph$arrow_target()rdecision::Digraph$as_DOT()rdecision::Digraph$as_gml()rdecision::Digraph$digraph_adjacency_matrix()rdecision::Digraph$digraph_incidence_matrix()rdecision::Digraph$direct_predecessors()rdecision::Digraph$direct_successors()rdecision::Digraph$is_acyclic()rdecision::Digraph$is_arborescence()rdecision::Digraph$is_connected()rdecision::Digraph$is_polytree()rdecision::Digraph$is_tree()rdecision::Digraph$is_weakly_connected()rdecision::Digraph$paths()rdecision::Digraph$topological_sort()rdecision::Digraph$walk()
Method new()
Creates a semi-Markov model for cohort simulation.
Usage
SemiMarkovModel$new( V, E, tcycle = as.difftime(365.25, units = "days"), discount.cost = 0, discount.utility = 0 )
Arguments
VA list of nodes (
MarkovStates).EA list of edges (
Transitions).tcycleCycle length, expressed as an R
difftimeobject.discount.costAnnual discount rate for future costs. Note this is a rate, not a probability (i.e. use 0.035 for 3.5%).
discount.utilityAnnual discount rate for future utility. Note this is a rate, not a probability (i.e. use 0.035 for 3.5%).
Details
A semi-Markov model must meet the following conditions:
It must have at least one node and at least one edge.
All nodes must be of class
MarkovState;All edges must be of class
Transition;The nodes and edges must form a digraph whose underlying graph is connected;
Each state must have at least one outgoing transition (for absorbing states this is a self-loop);
For each state the sum of outgoing conditional transition probabilities must be one. For convenience, one outgoing transition probability from each state may be set to NA when the probabilities are defined. Typically, probabilities for self loops would be set to NA. Transition probabilities in
Ptassociated with transitions that are not defined as edges in the graph are zero. Probabilities can be changed between cycles.No two edges may share the same source and target nodes (i.e. the digraph may not have multiple edges). This is to ensure that there are no more transitions than cells in the transition matrix.
The node labels must be unique to the graph.
Returns
A SemiMarkovModel object. The population of the first
state is set to 1000 and from each state there is an equal
conditional probability of each allowed transition.
Method set_probabilities()
Sets transition probabilities.
Usage
SemiMarkovModel$set_probabilities(Pt)
Arguments
PtPer-cycle transition probability matrix. The row and column labels must be the state names and each row must sum to one. Non-zero probabilities for undefined transitions are not allowed. At most one
NAmay appear in each row. If an NA is present in a row, it is replaced by 1 minus the sum of the defined probabilities.
Returns
Updated SemiMarkovModel object
Method transition_probabilities()
Per-cycle transition probability matrix for the model.
Usage
SemiMarkovModel$transition_probabilities()
Returns
A square matrix of size equal to the number of states. If all states are labelled, the dimnames take the names of the states.
Method transition_cost()
Return the per-cycle transition costs for the model.
Usage
SemiMarkovModel$transition_cost()
Returns
A square matrix of size equal to the number of states. If all states are labelled, the dimnames take the names of the states.
Method get_statenames()
Returns a character list of state names.
Usage
SemiMarkovModel$get_statenames()
Returns
List of the names of each state.
Method reset()
Resets the model counters.
Usage
SemiMarkovModel$reset( populations = NULL, icycle = 0L, elapsed = as.difftime(0, units = "days") )
Arguments
populationsA named vector of populations for the start of the state. The names should be the state names. Due to the R implementation of matrix algebra,
populationsmust be a numeric type and is not restricted to being an integer. If NULL, the population of all states is set to zero.icycleCycle number at which to start/restart.
elapsedElapsed time since the index (reference) time used for discounting as an R
difftimeobject.
Details
Resets the state populations, next cycle number and elapsed time
of the model. By default the model is returned to its ground state (zero
people in the all states; next cycle is labelled
zero; elapsed time (years) is zero). Any or all of these can be set via
this function. icycle is simply an integer counter label for each
cycle, elapsed sets the elapsed time in years from the index time
from which discounting is assumed to apply.
Returns
Updated SemiMarkovModel object.
Method get_populations()
Gets the occupancy of each state.
Usage
SemiMarkovModel$get_populations()
Returns
A numeric vector of populations, named with state names.
Method get_cycle()
Gets the current cycle number.
Usage
SemiMarkovModel$get_cycle()
Returns
Current cycle count, as an integer.
Method get_tcycle()
Gets the cycle duration.
Usage
SemiMarkovModel$get_tcycle()
Returns
Current cycle duration, as a difftime object.
Method get_elapsed()
Gets the current elapsed time.
Usage
SemiMarkovModel$get_elapsed()
Details
The elapsed time is defined as the difference between the
current time in the model and an index time used as the reference
time for applying discounting. By default the elapsed time starts at
zero. It can be set directly by calling reset. It is incremented
after each call to cycle by the cycle duration to the time at the
end of the cycle (even if half cycle correction is used). Thus, via the
reset and cycle methods, the time of each cycle relative
to the discounting index and its duration can be controlled arbitrarily.
Returns
Elapsed time as an R difftime object.
Method tabulate_states()
Tabulation of states
Usage
SemiMarkovModel$tabulate_states()
Details
Creates a data frame summary of each state in the model.
Returns
A data frame with the following columns:
- Name
State name
- Cost
Annual cost of occupying the state
- Utility
Incremental utility associated with being in the state.
Method cycle()
Applies one cycle of the model.
Usage
SemiMarkovModel$cycle(hcc.pop = TRUE, hcc.cost = TRUE, hcc.QALY = TRUE)
Arguments
hcc.popDetermines the state populations returned by this function. If FALSE, the end of cycle populations apply; if TRUE the mid-cycle populations and time apply. The mid-cycle populations are taken as the mean of the start and end populations and the discount time as the mid-point. The value of this parameter does not affect the state populations or elapsed time passed to the next cycle or available via
get_populations; those are always the end cycle values.hcc.costDetermines the state occupancy costs returned by this function and the time at which the cost discount is applied to the occupancy costs and the entry costs. If FALSE, the end of cycle populations and time apply; if TRUE the mid-cycle populations and time apply, as per
hcc.pop. The value of this parameter does not affect the state populations or elapsed time passed to the next cycle or available viaget_populations; those are always the end cycle values.hcc.QALYDetermines the incremental quality adjusted life years returned by this function and the time at which the utility discount is applied. If FALSE, the end of cycle population and reference time are applied to the utilities of each state; if TRUE the mid-cycle populations and time are applied to the state utilities. The value of this parameter does not affect the state populations or elapsed time passed to the next cycle or available via
get_populations; those are always the end cycle values.
Returns
Calculated values, one row per state, as a data frame with the following columns:
StateName of the state.
CycleThe cycle number.
TimeClock time in years of the end of the cycle.
PopulationPopulations of the states; see
hcc.pop.OccCostCost of the population occupying the state for the cycle. Discounting and half cycle correction is applied, if those options are set. The costs are normalized by the model population. The cycle costs are derived from the annual occupancy costs of the
MarkovStates.EntryCostCost of the transitions into the state during the cycle. Discounting is applied, if the option is set. The result is normalized by the model population. The cycle costs are derived from
Transitioncosts.CostTotal cost, normalized by model population.
QALYQuality adjusted life years gained by occupancy of the states during the cycle. Half cycle correction and discounting are applied, if these options are set. Normalized by the model population.
Method cycles()
Applies multiple cycles of the model.
Usage
SemiMarkovModel$cycles( ncycles = 2L, hcc.pop = TRUE, hcc.cost = TRUE, hcc.QALY = TRUE )
Arguments
ncyclesNumber of cycles to run; default is 2.
hcc.popDetermines the state populations returned by this function. If FALSE, the end of cycle populations apply; if TRUE the mid-cycle populations and time apply. The mid-cycle populations are taken as the mean of the start and end populations and the discount time as the mid-point. The value of this parameter does not affect the state populations or elapsed time passed to the next cycle or available via
get_populations; those are always the end cycle values.hcc.costDetermines the state occupancy costs returned by this function and the time at which the cost discount is applied to the occupancy costs and the entry costs. If FALSE, the end of cycle populations and time apply; if TRUE the mid-cycle populations and time apply, as per
hcc.pop. The value of this parameter does not affect the state populations or elapsed time passed to the next cycle or available viaget_populations; those are always the end cycle values.hcc.QALYDetermines the incremental quality adjusted life years returned by this function and the time at which the utility discount is applied. If FALSE, the end of cycle population and reference time are applied to the utilities of each state; if TRUE the mid-cycle populations and time are applied to the state utilities. The value of this parameter does not affect the state populations or elapsed time passed to the next cycle or available via
get_populations; those are always the end cycle values.
Details
The starting populations are redistributed through the
transition probabilities and the state occupancy costs are
calculated, using function cycle. The end populations are
then fed back into the model for a further cycle and the
process is repeated. For each cycle, the state populations and
the aggregated occupancy costs are saved in one row of the
returned data frame, with the cycle number. If the cycle count
for the model is zero when called, the first cycle reported
will be cycle zero, i.e. the distribution of patients to starting
states.
Returns
Data frame with cycle results, with the following columns:
CycleThe cycle number.
YearsElapsed time at end of cycle, years
CostCost associated with occupancy and transitions between states during the cycle.
QALYQuality adjusted life years associated with occupancy of the states in the cycle.
<name>Population of state
<name>at the end of the cycle.
Method modvars()
Find all the model variables in the Markov model.
Usage
SemiMarkovModel$modvars()
Details
Returns variables of type ModVar that have been
specified as values associated with transition rates and costs and
the state occupancy costs and utilities.
Returns
A list of ModVars.
Method modvar_table()
Tabulate the model variables in the Markov model.
Usage
SemiMarkovModel$modvar_table()
Returns
Data frame with one row per model variable, as follows:
DescriptionAs given at initialization.
UnitsUnits of the variable.
DistributionEither the uncertainty distribution, if it is a regular model variable, or the expression used to create it, if it is an
ExprModVar.MeanMean; calculated from means of operands if an expression.
EExpectation; estimated from random sample if expression, mean otherwise.
SDStandard deviation; estimated from random sample if expression, exact value otherwise.
Q2.5p=0.025 quantile; estimated from random sample if expression, exact value otherwise.
Q97.5p=0.975 quantile; estimated from random sample if expression, exact value otherwise.
EstTRUE if the quantiles and SD have been estimated by random sampling.
Method clone()
The objects of this class are cloneable with this method.
Usage
SemiMarkovModel$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
Author(s)
Andrew J. Sims andrew.sims@newcastle.ac.uk
References
Beck JR and Pauker SG. The Markov Process in Medical Prognosis. Med Decision Making, 1983;3:419–458.
Briggs A, Claxton K, Sculpher M. Decision modelling for health economic evaluation. Oxford, UK: Oxford University Press; 2006.
Fleurence RL and Hollenbeak CS. Rates and probabilities in economic modelling. PharmacoEconomics, 2007;25:3–6.
Jones E, Epstein D and García-Mochón L. A procedure for deriving formulas to convert transition rates to probabilities for multistate Markov models. Medical Decision Making 2017;37:779–789.
Miller DK and Homan SM. Determining transition probabilities: confusion and suggestions. Medical Decision Making 1994;14:52-58.
O'Mahony JF, Newall AT, van Rosmalen J. Dealing with time in health economic evaluation: methodological issues and recommendations for practice. PharmacoEconomics 2015;33:1255–1268.
Sonnenberg FA, Beck JR. Markov models in medical decision making: a practical guide. Medical Decision Making, 1993:13:322.
Welton NJ and Ades A. Estimation of Markov chain transition probabilities and rates from fully and partially observed data: uncertainty propagation, evidence synthesis, and model calibration. Medical Decision Making, 2005;25:633-645.
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