Cookies on this website

We use cookies to ensure that we give you the best experience on our website. If you click 'Accept all cookies' we'll assume that you are happy to receive all cookies and you won't see this message again. If you click 'Reject all non-essential cookies' only necessary cookies providing core functionality such as security, network management, and accessibility will be enabled. Click 'Find out more' for information on how to change your cookie settings.

Existing methods for fitting continuous time Markov models (CTMM) in the presence of covariates suffer from scalability issues due to high computational cost of matrix exponentials calculated for each observation. In this article, we propose an optimization technique for CTMM which uses a stochastic gradient descent algorithm combined with differentiation of the matrix exponential using a Padé approximation. This approach makes fitting large scale data feasible. We present two methods for computing standard errors, one novel approach using the Padé expansion and the other using power series expansion of the matrix exponential. Through simulations, we find improved performance relative to existing CTMM methods, and we demonstrate the method on the large-scale multiple sclerosis NO.MS data set.

Original publication




Journal article



Publication Date



Continuous-time Markov model, Multiple sclerosis, Multistate model, Padé, Scalable optimization, approximation