Stochastic Trees and the StoTree modeling software

(May 2007)

Stochastic trees are an innovative tool we developed for modeling decisions involving long-term consequences, and in particular for modeling medical treatment decision problems. Stochastic trees are hybrids of continuous-time Markov chains and a decision trees. Like decision trees, stochastic trees may be rolled back to recover optimal decisions.

• To open (or download) an introductory Powerpoint presentation on stochastic trees, click (or right click) here (and choose Save Link As… or Save Target As… from the resulting pop-up menu).
• To open (or download) an introductory Word article on stochastic trees, click (or right click) here (and choose Save Link As… or Save Target As… from the resulting pop-up menu).

StoTree is a graphical modeling interface for the formulation and solution of multi-factor stochastic trees. StoTree is designed for the Microsoft Excel environment. Operating in a spreadsheet environment, the StoTree user can access all the usual spreadsheet features in addition to those of StoTree. The user composes a desired model graphically and next specifies parameters such as rates, probabilities, tolls, costs and quality coefficients. The user concludes by using the rollback features in StoTree to calculate average quantities of interest such as mean quality adjusted life years or average costs.

StoTree 4 is the most recent version of StoTree. It is an Excel spreadsheet (.xls suffix) compatible with later versions of Excel including Office XP. Like all versions of StoTree, this version calculated expected QALYs and costs. One-way sensitivity analysis and probabilistic sensitivity analysis capabilities are included. The major enhancement of version 4 over version 3 is the ability to calculate population equilibria (including steady-state probabilities). All versions of StoTree have been developed in a Windows environment, and are not guaranteed to function under a MacIntosh operating system.

To download a self-extracting zip file containing StoTree 4 (3.191 Mb, Version 4a, August 2006), do the following:

· Right click here and choose Save Link As… or Save Target As… from the resulting pop-up menu. (Do not perform the usual left click - your browser may attempt to open the file remotely.) Documentation is included with this download.

· Find the file you downloaded to your computer. It is a self-extracting zip file named StoTree4aZipped.exe. Double-click on the file. The WinZip self-extractor will indicate that it will unzip to folder c:, and you should not change this. Click on Unzip, and the folder StoTree will be extracted to the c:\ directory on your computer. Make sure all StoTree files unzip to c:\StoTree in this way, or you will not be able to access the enclosed help files.

· To start StoTree, find the Excel workbook StoTree4a.xls in the directory c:\StoTree, and double click to have Excel open this workbook. Older version 3f of StoTree is also available in this zip file.

You may also download two illustrative applications:

• Matchar and Pauker (1986) constructed a Markov model of the treatment of transient ischemic attack. We have reformulated their model using StoTree. To download a spreadsheet containing this stochastic tree model, right click here: MatcharPauker.xls
• Chang, Pellissier and Hazen (1996) used StoTree to formulate a stochastic tree model of the decision to undergo total hip replacement. (R.W. Chang, J.M. Pellissier and G.B. Hazen, "A Cost-Effectiveness Analysis of Total Hip Arthroplasty for Osteoarthritis of the Hip", Journal of the American Medical Association 275 (1996) 858-865). To download a spreadsheet containing this stochastic tree model, right click here: THAUtility.xls

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StoTree Overview

Via point-and-click operations in StoTree, the user can create nodes, name and position them as he likes, and connect nodes with either stochastic or chance arcs, to which he may attach any desired label.. Arcs may be drawn in any of the four compass directions. This process is illustrated in the diagrams that follow. Each worksheet in the Excel workbook to which nodes have been added is regarded by StoTree as a factor in a multi-factor stochastic tree. Graphical capabilities not shown below include subtree copy and paste, node and arc deletion, and tree redraw.

(a) The Excel environment and the StoTree toolbar. The user has just clicked on the Add Node button in the upper-right portion of the toolbar. StoTree will convert the worksheet to a stochastic factor and label it as active.	(b) The Add Node dialog appears. The user chooses to create a new node and types the node name "My Node".
(c) StoTree creates the node and gives it the name "My Node". The stochastic factor is now active but the user may de-activate it should the need arise.	(d) The user has created a second node and now wishes to connect the two nodes with a stochastic arc. He first selects the two nodes, and then clicks on one of the Add Arc buttons in the StoTree toolbar
(e) StoTree connects the two nodes with a stochastic arc and places below the arc a blank textbox into which the user may type whatever label he desires.	(f) The user has typed "Trans Rate" into the arc-labeling textbox.

Once the user has specified the graphical structure, he can associate numerical parameters with nodes and arcs. Parameters for arcs consist of probabilities for chance arcs, rates for stochastic arcs, and tolls for either type of arc. Node parameters consist of a quality or cost rate, and a discount rate. Arc parameters can depend on the state of other factors. The user may also add one or more triggers on any arc, which force transitions in other specified factors when that arc is traversed. All of these features are accessed via dialog boxes called up from the StoTree toolbar.

Here for example are two component factors of the stochastic tree THAUtility.xls we have used to model the decision to undergo total hip replacement. These are screen captures from this Excel workbook.

Functional Status

Prosthesis Status

The rollback algorithm used by StoTree