Transposed Markov Matrix as a New Decision Tool of How to Choose among Competing Investment Options in Academic Medicine
Medical institutions face the challenge of promoting excellence in a variety of competing focus areas, such as grants, publications, income, research, faculty, variety, patient care and teaching. A transposed Markov chain is used analyse the interactions between the various focus areas and their transition towards steady-state. In contradistinction with a regular Markov chain, in the transposed chain used for the present analysis, the sum of inputs (rather than outputs) of each individual state is 100%, whereas the outputs are left to assume any possible value. The mathematics of calculating the steady state conditions of a transposed Markov matrix are similar to those of a regular Markov matrix. The analysis shows that a focus area more dependent on other areas is also more likely to lose its investment, whereas largely self-reliant areas will generate the largest return. Full strength of all academic focus areas can be achieved only by investments in all areas. In academic systems with one or several exclusively self-reliant focus areas, only investment in these particular areas will invigorate the system, as all other investments are bound to dissipate over time. The newly developed decision tool of a transposed Markov matrix could be helpful in stochastic modelling of medical phenomena.