Purpose: Markov models are widely employed in cost-effectiveness analyses of healthcare interventions. Although nearly all of the models are formulated in discrete time, continuous-time Markov (CTM) models, which evaluate time as a continuous variable and allow transitions to occur at any instance, offer more realistic representation of most medical problems. Wide application of CTM modeling for medical decision making is hampered by theoretical and computational complexities.
Method: We reviewed methods from continuous-time stochastic process literature and implemented time-dependency and cohort methods to continuous-time modeling for this purpose. We considered several real and hypothetical examples, and demonstrated the similarities and differences between CTM and discrete-time Markov (DTM) analytically and numerically. One example was a simple survival model of individuals with constant annual mortality rate. We also applied CTM models to a published cost-effectiveness analysis.
Result: As an approximation of the continuous phenomenon of death, the DTM model always underestimates life-expectancy. For instance, if the cycle length of the DTM model is one year and annual mortality rate is 0.1, the DTM model underestimates life expectancy by almost half a year. Use of 'work-around-methods' such as half-cycle correction or trapezoidal rule improves, but does not eliminate, the approximation. Although the incremental cost per quality-adjusted life year (QALY) calculated from the published study can be close for DTM and CTM models, discrepancies in QALY and costs were often large.
Conclusion: The choice of DTM chain with a long cycle length can lead to misleading conclusions. It is often more natural and accurate to formulate medical problems in continuous time and model them using a CTM. The feasibility of this approach was established.
Candidate for the Lee B. Lusted Student Prize Competition