Existing multi-state models are restricted either by the 'plug-in' parameters that can be estimate, or the dependence on the bootstrap for variance estimation. Our objective is to develop an efficient algorithm and implementation for 'plug-in' maximum likelihood estimation for parametric and smooth penalised Markov multi-state models. For methods, we restrict our attention to smooth parametric and penalised transition intensities for multi-state Markov models. We propose a new algorithm that uses a system of ordinary differential equations to calculate the parameters and their gradients, with standard errors calculated using the delta method. The algorithm supports 'plug-in' parameter estimation for state occupancy probabilities, transition probabilities, length of stay, relative survival, screening sensitivity, utilities, costs, net monetary benefit and their linear combinations. We provide an implementation in R that allows for a wide range of parametric and penalised survival models. Using simulations, we demonstrate good coverage for a range of transition intensity models. We apply these methods to an earlier multi-state analysis of the Rotterdam Breast Cancer Data and extend the analysis to include regression standardisation. In conclusion, we have provided a broad framework for 'plug-in' parameter estimation for Markov multi-state models with smooth transition intensities. These methods have applications to a range of disciplines, including epidemiology and health economics.
3 Ottobre 2025, ore 12
Mark Clements
Karolinska Institutet, Sweden
In person: Room 34 (4th floor) building CU002 Scienze Statistiche
Webinar: https://uniroma1.zoom.us/j/83625004899?pwd=bXCtz0mp759PUh2lkqT0BUoVa0Uegg.1
ID riunione: 836 2500 4899
Passcode: 123456