The MARKOV Process Approach to Survival Analysis

Sample size calculation using Markov chains for a one-arm study of heroin administration routes

Sample size calculations for trials with time-to-event outcomes are usually based on the assumption that an event - prototypically death in survival analysis - occurs only once per sample unit. However, events like changes in disease status or switches between treatment modalities may repeat over time. In trials with such outcomes, standard sample size formulae derived from the classical survival time models are not applicable. Instead, modeling the repeating transition events must precede the actual sample size calculation. Markov chains are an obvious choice to model transitions. Accordingly, in order to determine the sample size for a one-arm feasibility and acceptability study of a new drug intake route, we model switches of administration routes by a homogeneous finite-state, higher-order Markov chain. Assumptions about its transition matrix translate into multinomial distributions of the preferred administration routes at given points in time. From these distributions, the required sample size can then be calculated according to the study's specific question. In this manuscript, we first introduce the method for the case of drug intake preferences, before we briefly discuss how the proposed method can also be used for power-based sample size calculation in multi-arm trials.