32.1 Creating and referencing distributions

Before you can run PSA on a model, you must first create parameter distributions and reference them within the model. In this section, we will add distributions to the Healthcare Tutorial example model Markov-PSA-PreSetup.trex.

This section will go through the manual method to create and reference parameter distributions in the model. You can also use the Wizard which "Adds PSA for variable" which is described in the next section: Creating and referencing distributions - using the Wizard

The example model contains many parameter inputs. We will focus on seven of these inputs – adding and referencing distributions for each.

We will start with the parameter input cLocal1, which has the base case value 20,000. We will create a Gamma distribution to represent uncertainty for this input. Gamma distributions can be defined using parameters Alpha and Lambda, but commonly they are instead defined using a mean and standard deviation, as we will do now.

Create a distribution

  • Choose Views > Distributions from the menu to open the Distributions View.

  • In the Distributions View toolbar, click the "+" icon to create a new distribution. The Add/Change Distribution dialog will open.

  • Enter the new distribution's properties:

    • Choose distribution type Gamma.

    • Enter the distribution name dist_cLocal1.

    • Click on the Parameters dropdown and change the selection from Default to From Mean and Std Dev.

      • Enter the Mean 20,000

      • Enter the Standard Deviation 500

    • Leave 'override mean' blank.

    • Leave the sampling rate as "Resample per EV...", which will sample for each model calculation.

  • Examine the probability density graph to understand the range of values that will be sampled from this distribution.

  • Click OK to save the new distribution. It will be added to the list in the Distributions View.

When you run PSA, a distribution sample will be used for each model calculation. When you run a single analysis (like base case), the mean from the distribution will be used. Note that the override mean entry allows you to use a different value (i.e. not the mean) for non-PSA model analyses.

Alternative parameter options are available for many statistical packages like SAS and Stata. Refer to the Distribution Parameters from Statistical Packages section for details on using these.

We have now created the distribution, but it must be referenced from the model before it has an impact on the calculations.

Reference the distribution(s) in the model

Distributions will not affect analysis results until they are referenced within the model. You can reference them directly in the model as entries for probabilities, costs and utilities. However, we recommend you continue to reference variables for these inputs and set the root node definition for each variable equal to its associated distribution. This provides additional flexibility for your analyses in the following way:

  • Base case results – use the mean value from the distribution (or the override mean value)

  • Deterministic Sensitivity Analysis – uses the range defined for the input variable

  • Probabilistic Sensitivity Analysis – uses samples from the distribution

To reference the distribution through the variable:

  • Open the Variables View.

  • Set the root definition of cLocal1 to dist_cLocal1.

We can then repeat these two steps for each parameter we want to include in the PSA, in this case a total of 7 parameters and distributions.

Whilst we provide sufficient details above to create and use distributions to run PSA, more details about distributions can be found in the section: Distributions: creating, editing and using.