# Markov Chain Simulation for Health Economics

This web-based tool allows the user to model the transition of a population of patients through a series of health states that are followed over time, which may include for example: living with a particular disease; having a treatment; being cured; having complications; or becoming deceased. These states are connected so that in any one time-step (typically using a cycle time of one year), there is a probability of a patient staying in their existing state or moving to a different one, and it is possible to move between specified health states in either direction. In this way it is possible to model either the progression of a chronic disease, which may includes worsening or improvement (such as the appearance or healing of a wound) or the consequences of treatment of an acute condition (such as surgery and its possible complications and follow-up). Cost and quality of life incurred in each cycle are added up incrementally as the model progresses.

Features

• The number of states may be chosen between 2 and 5. These are shown on separate web-pages as bubble diagrams. States may be joined up graphically by mouse-clicking to add arrows in either direction between states.
• Transition probabilities between states are entered.
• Relevant data are entered for each state: the annual cost of being in the state, quality of life (measured as a utility between 0.00 and 1.00) in that state. In addition, in the first cycle a different cost or utility may be specified.
• The model can be run for a specified number of cycles (time step measure in years) and for a specified size of population.
• The model may be run either with a single set of data or as a comparison, where one model (Base case) is compared side by side with another (Innovation) with the same number of states, where any of the connections and their probabilities and state data (costs and/or utilities) may be different between the two models. This allows an innovation to be compared to the Base case (incumbent) technology.
• The model includes discounting, where the value of costs and utilities are reduced each year according to a fixed percentage, as the model proceeds into the future. A typical discounting percentage (as used by NICE) is 3.5% and so, in this case, a cost of £100 in year one is reduced to £100 divided by 1.035 in year two, by £100 divided by 1.0352 in year three, and so on. Likewise a utility of 0.8 in year one is reduced to 0.8 divided by 1.035 in year two.
• The model may be solved in one of two ways: analytically using a Cohort method which provided a single answer, or run probabilistically using a Monte Carlo simulation method which provides a distribution of answers around a mean which is the same mean as the answer found in the Cohort method.

Outputs

After the model (or pair of models) is run for a population of patients, for example 10,000 patients for 20 cycles, it is possible to see:

• Average cost per patient accrued over the time of the model, calculated by adding up the costs of each patient living in each health state. In the case of the Monte Carlo simulation, the maximum and minimum costs are also found.
• Average patient benefit accrued, calculated from the utility in each year, expressed as Quality Adjusted Life Years (QALYs). In the case of the Monte Carlo simulation, the maximum and minimum QALY of the patient population is also found.
• In the case of comparison of two models the Incremental Cost Effectiveness Ratio (ICER), the difference in costs divided by difference in QALYs, is calculated.
• The average costs and utilities versus time (number of cycles elapsed) are shown graphically, comparing total costs and utilities between Base Case and Innovation.

MATCH Markov Chain Simulation for Health Economics(link to secure portal) 