The Markov Model for Survival Trials

The Markov model for designing survival trials was introduced in 1986, initially for sample size/power for a comparison of proportions, and in 1988 for the logrank statistic. The approach has been cited extensively, is available in commercial software. Also presented are the Markov approaches to group-sequential and conditional power, retaining all of the features of the fixed-design model. Through simulations it has been shown to outperform the Schoenfeld proportional hazards approach even in proportional hazards settings. Estimates apply to all weighted versions of the logrank, as well as to the Restricted Mean Survival Time approach to survival analyses. The advantage of greatest importance is for non-proportional hazards, addressing time dependent rates of failure, loss to follow-up, non-compliance, and staggered entry; again, extensively simulation-verified. The Markov model appears to strike fear into the hearts of many otherwise very strong statisticians; in reality, it is a far simpler approach. While some equations are needed, a large focus here is on heuristic explanations, which, hopefully, will allay such fears. Some common misconceptions, such as the event-driven trial, will be discussed.