RT Journal Article
T1 A Procedure for Deriving Formulas to Convert Transition Rates to Probabilities for Multistate Markov Models.
A1 Jones, Edmund
A1 Epstein, David
A1 García-Mochón, Leticia
K1 Markov model
K1 spreadsheet
K1 transition probabilities
K1 transition rates
AB For health-economic analyses that use multistate Markov models, it is often necessary to convert from transition rates to transition probabilities, and for probabilistic sensitivity analysis and other purposes it is useful to have explicit algebraic formulas for these conversions, to avoid having to resort to numerical methods. However, if there are four or more states then the formulas can be extremely complicated. These calculations can be made using packages such as R, but many analysts and other stakeholders still prefer to use spreadsheets for these decision models. We describe a procedure for deriving formulas that use intermediate variables so that each individual formula is reasonably simple. Once the formulas have been derived, the calculations can be performed in Excel or similar software. The procedure is illustrated by several examples and we discuss how to use a computer algebra system to assist with it. The procedure works in a wide variety of scenarios but cannot be employed when there are several backward transitions and the characteristic equation has no algebraic solution, or when the eigenvalues of the transition rate matrix are very close to each other.
YR 2017
FD 2017-04-05
LK http://hdl.handle.net/10668/11056
UL http://hdl.handle.net/10668/11056
LA en
DS RISalud
RD Apr 8, 2025