Methodol Comput Appl Probab DOI 10.1007/s11009-017-9582-3 Monitoring Phase II Comparative Clinical Trials with Two Endpoints and Penalty for Adverse Events Sotiris Bersimis 1 · Athanasios Sachlas 1 · Takis Papaioannou 1 Received: 21 April 2015 / Revised: 29 February 2016 / Accepted: 14 July 2017 © Springer Science+Business Media, LLC 2017 Abstract Adverse events in Phase II comparative clinical trials have received limited atten- tion in the literature. Bersimis et al. (Stat Med 34:197–214, 2014) in proposed a class of comparative sequential designs with bivariate endpoints, where as a special case, the termi- nation of the clinical trial due to the occurrence of a severe adverse event is treated. In this paper, using the Markov chain embedding technique, we extend this class of designs propos- ing two new designs, which treat cases where the development of an adverse event does not immediately stop the clinical trial, but penalizes appropriately the treatment that caused it. In both designs the penalty can be chosen either by assessing the severity of the adverse event or by optimizing the power. The numerical results show an excellent performance, achieving small expected sample sizes in conjunction with large values for power, satisfy- ing in this way the ethical requirement for small sample sizes and fast decisions in clinical practice. The formulation of the procedure as a stochastic process is elegantly accomplished while it offers the necessary mathematical framework for further generalizing the designs covering more cases such as group sequential designs, etc. Keywords Bivariate sequences of trials · Clinical trials involving two binary endpoints · Markov chain embeddable random variables · Phase II clinical trials · Decision rules · Waiting time distribution · Adverse events · Penalization  Sotiris Bersimis sbersim@unipi.gr Athanasios Sachlas asachlas@unipi.gr Takis Papaioannou takpap@unipi.gr 1 Department of Statistics & Insurance Science, University of Piraeus, 80 Karaoli & Dimitriou str., 185 34, Piraeus, Greece