The R package $\texttt{ebmstate}$ for disease progression analysis under empirical Bayes Cox models

Abstract

The software package $\texttt{mstate}$, in articulation with the package $\texttt{survival}$, provides not only a well-established multi-state survival analysis framework in R, but also one of the most complete, as it includes point and interval estimation of relative transition hazards, cumulative transition hazards and state occupation probabilities, both under clock-forward and clock-reset models; personalised estimates, i.e. estimates for an individual with specific covariate measurements, can also be obtained with $\texttt{mstate}$ by fitting a Cox regression model. The new R package $\texttt{ebmstate}$, which we present in the current paper, is an extension of $\texttt{mstate}$ and, to our knowledge, the first R package for multi-state model estimation that is suitable for higher-dimensional data and complete in the sense just mentioned. Its extension of $\texttt{mstate}$ is threefold: it transforms the Cox model into a regularised, empirical Bayes model that performs significantly better with higher-dimensional data; it replaces asymptotic confidence intervals meant for the low-dimensional setting by non-parametric bootstrap confidence intervals; and it introduces an analytical, Fourier transform-based estimator of state occupation probabilities for clock-reset models that is substantially faster than the corresponding, simulation-based estimator in $\texttt{mstate}$. The present paper includes a detailed tutorial on how to use our package to estimate transition hazards and state occupation probabilities, as well as a simulation study showing how it improves the performance of $\texttt{mstate}$.