The basic methods of decision analysis,
including calculation of expected values and
sensitivity analysis, are deterministic.
There is no randomness in these types of model
calculations; during each calculation, each model
parameter uses its specified point value. If an
analysis is repeated using the same parameters, the
results will be unchanged.
In contrast, there are many situations where introducing
a random, or stochastic, element into some
part of the analysis can be useful. In these situations,
Monte Carlo simulation can be applied.
Probabilistic Sensitivity Analysis (Sampling)
Monte Carlo simulation refers to the use of random
numbers in evaluating a model. Perhaps the most
frequent application of Monte Carlo simulation in
TreeAge Pro is as a form of sensitivity analysis.
Like regular (deterministic) sensitivity analysis,
Monte Carlo simulation also recalculates a model
multiple times. Monte Carlo simulation can update
any number of parameters between model recalculations,
assigning values that are randomly sampled
from probability distributions. This use of Monte
Carlo simulation is referred to as probabilistic sensitivity
analysis.
One advantage of probabilistic sensitivity analysis
is that all parameter uncertainties can be incorporated
into an analysis (see section on nonlinearity,
below). Sampling parameter values from probability
distributions (rather than from a simple range
defined by upper and lower bounds) places greater
weight on likely combinations of parameter values,
and simulation results quantify the total impact of
uncertainty on the model, in terms of the confidence
that can be placed in the analysis results.
Nonlinearity
In some models, calculating an expected value
based on the mean value of an uncertain parameter
(i.e., using roll back) is equivalent to randomly
sampling many values for the uncertain parameter
from its probability distribution, recalculating the
model for each sample, and taking the average.
However, this is not the case with all models and
all parameters.
If, for example, a distribution is used to define an
uncertain component of a probability or utility
function, you may find that the “expected value” of
the model calculated using the parameter’s mean
value will differ from the average of many recalculations
of the model using sampled values for the
uncertain parameter. In these cases, the simulation
average value is the better “expected value” for the
model (and therefore simulation would be the preferred
means of analyzing the model).
EVPI/Value of Information Analysis
Monte Carlo simulation can be used to perform
various kinds of “value of information” analysis.
The Analysis > Expected Value of Perfect Information
command in TreeAge Pro calculates the difference
between the baseline expected value of a decision,
and the expected value when a chance node is
temporarily shifted to the left of the decision. In a
Monte Carlo simulation, the calculation of EVPI is
done differently.
For example, if the optimal strategy changes for
different sampled parameter values, then there is
some benefit to having “perfect information” about
the uncertainty prior to the decision. The average of
the values of the best option from each recalculation
is the expected value with perfect information;
it will either be equal to or greater than the best
average value for any single alternative. Calculating
the difference gives the expected value of perfect
information.
TreeAge Pro v2005 added an EVPI report and chart
to the Monte Carlo simulation window’s Graph
popup menu.
TreeAge Pro also includes an option to do two
levels (nested loops) of parameter sampling during
simulation, in order to do robust EVPI-type simulation.
This may be required to get an accurate
EVPI when there is nonlinearity in the model, as
described above. The “information” parameter is
sampled in the top-level, outside loop; for each
sample value, the model is reevaluated using an
inner loop (a simulation of N iterations which samples
the remaining uncertainties).
Microsimulation (First-Order Trials)
In TreeAge Pro, Monte Carlo simulation includes
two distinct features, which may be used separately
or in combination: sampling parameter
values, described above (sometimes called second-order
simulation); and running random trials (also
called first-order simulation, microsimulation, or a
random walk). These two kinds of simulation correspond
roughly to two categories of uncertainty
— second-order, parameter uncertainty versus
first-order uncertainty (variability among individuals,
or over time) — and have different applications
and methods.
The last step in each iteration of a second-order
simulation is recalculating the model. The most
efficient way to perform this recalculation is using
expected value calculations, but it is also possible
to use first-order simulation as a means of approximating
an expected value.
First-order simulation trials can be used to model
the variability in individual outcomes, visualized
in a decision tree as the branches of a chance node.
Simulation trials use random numbers to select a
single path through the tree, following one branch
at each chance node, with higher probability events
being more likely. Running 100 first-order simulation
trials results in a list of 100 individual outcomes
(e.g., profit equals $150, $175, $0, $550, -
$50, and so on), with some chance of repeating outcomes.
As more individual trials are run through a
decision tree, the average outcome should approach
the regular expected value calculation. (Increasing
the numbers of trials will also result in a standard
deviation for the simulation that should converge
on the expected value form of standard deviation.)
First-order trials have somewhat limited use with
most models (with the major exception of Markov
models). One possible use of simulation trials in
a regular tree is to replace any chance node with a
parameterized probability distribution (e.g., sampling
an outcome from a normal distribution, or any
other continuous or discrete sampling distribution).
For example, in the investment decision tree, the
risky investment’s chance node could be replaced
with a distribution representing either a continuous
range of outcomes, or a discrete distribution just
like the existing three-branch chance node. This
can also be accomplished without simulation trials,
using TreeAge Pro’s DistKids( ) function.
Elsewhere in This Section
> Decision Analysis and Decision Trees
> Markov Models - State Transition Models
> Discrete Event Simulation Models
> Cost-Effectiveness Analysis
Learn
how TreeAge Pro users are using decision analysis. >