8.1 Multi-attribute weighted costs

TreeAge Pro provides access to an unlimited number of payoff/reward sets. In Multi-Attribute calculations (refer to the Changing Calculation methods and using different Payoffs section for details), this means that all enabled payoffs can be combined using a weighting function — i.e., a set of numeric or variable weights corresponding to pay off or Markov reward sets.

Under the Cost-Effectiveness calculation method, TreeAge Pro allows you to use a weighted cost function in the same way; up to all enabled payoff sets (less one for effectiveness) can be combined as the net cost component of CE calculations.

Using a weighted cost function in a cost-effectiveness model may facilitate clearer identification of the parts of a complex cost formula (for example, drug costs, hospital costs, and inpatient costs). It also makes it easier to switch between CEA using a single cost component, and CEA using different combinations of cost components.

Multi-attribute weighted costs: an example

In simple trees, simple numeric values were assigned to each terminal node’s cost payoff. In most models, however, cost payoffs or rewards will be more complicated. The tutorial from the Building Formulas Using Variables and Functions Chapter includes an example tree in which a more realistically complex cost formula is used. The "Cost Formula" tree uses variables to represent the components of a cost formula. In the tutorial, the Simple calculation method was used, but the same issues apply to cost calculations under the Cost-Effectiveness calculation method.

Instead of representing the costs of hospitalization, surgery/drugs, prosthetics, and physical therapy as components of a single payoff (#1 in the example), each of these components can instead be placed in a separate payoff (i.e., #3-#6). Under the Multi-Attribute calculation method or the Cost-Effectiveness calculation method with multi-attribute costs, a simple weighting function could be used to recombine the component variables into a single cost calculation.

To see how the multi-attribute cost weightings work, open the Health Care tutorial example model CE Cost Formula.trex. This is a CE version of the tutorial example tree "Cost Formula".

If you look at the payoffs for a terminal node, you will see that the current calculation preferences are using the Total_Cost variable for cost calculations, which in turn combines several separate measurements of cost. If you change the number of enabled payoffs through the Tree Preferences, it is also possible to see that four other payoffs (#3 through #6) have been assigned the individual components of the Total_Cost formula. These separate payoff values can be used for multi-attribute weighted cost calculations.

Before making any changes to the tree, perform a cost-effectiveness analysis at the decision node. Later, after changing the payoff calculation preferences in the tree, we can re-run the analysis and compare the results to ensure that no errors were made.

Now, modify the Calculation Method preferences to use a multi-attribute cost formula, combining the four cost components already in payoffs #3 through #6.

To set up a weighted multi-attribute cost function:

  • Choose Tree > Tree Preferences from the menu or press the F11 key to open the Tree Preferences Dialog.

  • Navigate to the category Calculation > Payoffs.

  • Note that the number of enabled payoffs to 6.

  • Navigate to the category Calculation > Calculation Method.

  • Change the Active Method to Multi-Attribute.

  • Navigate to the category Calculation > Calculation Method > Cost-Effectiveness > Multi-Attribute.

  • Enter a weight of 0 for the Cost payoff and weights of 1 for each payoff that represents a component of the overall cost (payoffs 3-6).

  • Note that the box corresponding to the effectiveness payoff should be left blank (along with any unneeded payoffs). See below.

  • Click OK to save the Tree Preferences.

Note that variables could have been entered for each weight instead of 1. This would provide greater flexibility, including the ability to run sensitivity analysis on the weight variables.

If using variables for weights, those variables must be defined in the tree; they are then calculated dynamically when analyses are run.

Run another Cost-Effectiveness Analysis to ensure that the results are the same. They should be since the weighted multi-attribute costs mimic the original cost formula for the variable Total_Cost.

Note that a version of this model with the multi-attribute changes is also available - the Health Care tutorial example model: CE Cost Formula - MultiAttribute.trex.

Notes on using multi-attribute costs in CE trees

When weighted, multi-attribute costs are in use in a cost-effectiveness model. Terminal nodes will display the weighted cost payoff formula in brackets; nodes in a Markov model will display separate Markov information line items for each cost reward set.

Multi-attribute cost payoff expressions

To turn off the display of multi-attribute payoff expressions, open the Display > Terminal Nodes preferences category inside Tree Preferences, and uncheck the option labeled Display payoff names.

If you do not enter terminal node payoff expressions for each active cost attribute (i.e., each payoff that is enabled and has an assigned multi-attribute weight), calculation errors will occur. If you enter a weight for the payoff set currently assigned to effectiveness, it is simply ignored during cost calculations. If you leave a weight blank, it evaluates to 0. If you subsequently reduce the number of enabled payoffs in the Calculation Method preferences, any disabled payoffs will be excluded from the weighted cost calculation.

The same weighting function will apply if the calculation method is changed to Multi-Attribute, instead of Cost-Effectiveness.

Markov CE models using multi-attribute costs

Just as with regular trees, Markov models can use the Multi-Attribute calculation method or the Cost-Effectiveness calculation method with the multi-attribute cost preferences described above.

TreeAge Pro calculates each Multi-Attribute (or Cost-Effectiveness with multi-attribute costs) Markov process in a single pass, with the cost weighting done during the Markov process, as well as using either the reward set #1 termination condition (for Multi-Attribute) or the CE termination condition. See the Health Care tutorial example model “Multi Cost Markov”.

See the subsequent chapters on Markov modeling later in the manual for more details.