Ahmed M. Bayoumi, MD, MSc, St. Michael's Hospital, University of Toronto, Toronto, ON, Canada
Although a Markov state cycle diagram efficiently and elegantly displays the structure of a Markov state transition model, such figures become unwieldy if the number of states or the number of transitions is large. We developed a method of displaying Markov state cycle diagrams on a computer based on extensible markup language (XML) representations of decision trees. Our method builds on previous work which defined an XML structure for describing decision trees. We wrote an HTML application that converts decision trees from Decision Maker or TreeAge text format into XML format and subsequently display the children (states) of a Markov node a computer screen using Scalable Vector Graphics (SVG), another XML-based technology for displaying 2-dimensional graphics. XML and SVG are open standards of the World Wide Web Consortium. Each state was represented by an ellipse containing the state name, transitions were represented by arrows between states, and a side window displayed path, binding and variable information for each state as it is selected. Clicking on each ellipse displayed the allowable transitions from that state, the bindings at that node, and variable values at that state. Clicking while holding the control key displayed the allowable transitions to that state from other states. Selecting an arrow (representing transitions) displayed all pathways in the tree from the first state to the second. The program incorporated binding of Markov state names. Options include the ability to move states, hide states, control the graphical display properties, and save the modified graphic displays as SVG files. The main limitation is the considerable memory requirement for very large trees (several hundred nodes). Dynamic Markov state transition diagrams illustrate the potential for developing applications that exploit the potential for standardized XML descriptions of decision trees. Because users can interact with the Markov state cycle diagrams to explore state transition models in detail, such approaches have the potential to assist with debugging and increase the transparency of complicated Markov models.