Monitoring Phase II Comparative Clinical Trials with Two Endpoints and Penalty for Adverse Events

  • Sotiris BersimisEmail author
  • Athanasios Sachlas
  • Takis Papaioannou


Adverse events in Phase II comparative clinical trials have received limited attention 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 termination 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 proposing 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, satisfying 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.


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 

Mathematics Subject Classification (2010)

60J20 62P10 


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S. Bersimis and A. Sachlas are supported by the Greek General Secretariat for Research and Technology research funding action “ARISTEIA II”. The authors would like to thank the Associate Editor and the two anonymous referees for their constructive comments that helped them to improve the manuscript.


  1. Armitage P, Berry G, Matthews JNS (2002) Statistical methods in medical research. 4nd Ed., Blackell Science LtdGoogle Scholar
  2. Balakrishnan N, Koutras MV (2002) Runs and scans with applications. Wiley, New YorkzbMATHGoogle Scholar
  3. Balakrishnan N, Bersimis S, Koutras MV (2009) Run and frequency quota rules in process monitoring and acceptance sampling. J Qual Technol 41(1):66–81CrossRefGoogle Scholar
  4. Bending JJ, Pickup JC, Keen H (1985) Frequency of diabetic ketoacidosis and hypoglycemic coma during treatment with continuous subcutaneous insulin infusion. Audit of medical care. Am J Med 79(6):685–691CrossRefGoogle Scholar
  5. Bersimis S, Sachlas A, Papaioannou T (2014) Flexible designs for phase II comparative clinical trials involving two response variables. Stat Med 34:197–214MathSciNetCrossRefGoogle Scholar
  6. Bradnock B, Law HT, Roscoe K (1995) A quantitative comparative assessment of the immediate response to high frequency ultrasound and low frequency ultrasound (‘Longwave therapy’) in the treatment of acute ankle sprains. Physiotherapy 82(2):78–84CrossRefGoogle Scholar
  7. Figueroa JJ, Basford JR, Low PA (2010) Preventing and treating orthostatic hypotension as easy as A, B, C. Cleveland Clin J Med 77:298–306CrossRefGoogle Scholar
  8. Glaz J, Naus J, Wallenstein S (2001) Scan statistics. Springer, New YorkCrossRefzbMATHGoogle Scholar
  9. Herrmann N, Szatrowski TH (1982) Small sample properties of asymptotic formulas for expected sample size savings in curtailed binomial tests. Commun Stat C 1:221–245zbMATHGoogle Scholar
  10. Herrmann N, Szatrowski TH (1985) Curtailed binomial sampling procedures for clinical trials with paired data. Control Clin Trials 6:25–37CrossRefGoogle Scholar
  11. Kim K, Tsiatis AA (1990) Study duration for clinical trials with survival response and early stopping rule. Biometrics 46(1):81–92MathSciNetCrossRefzbMATHGoogle Scholar
  12. Kim K, DeMets DL (1992) Sample size determination for group sequential clinical trials with immediate response. Stat Med 11:1391–1399CrossRefGoogle Scholar
  13. Kunz CU, Kieser M (2012) Curtailment in single-arm two-stage phase II oncology trials. Biom J 54(4):445–456MathSciNetCrossRefzbMATHGoogle Scholar
  14. Lan KKG, DeMets DL (1983) Discrete sequential boundaries for clinical trials. Biometrika 70:659–663MathSciNetCrossRefzbMATHGoogle Scholar
  15. Lan KKG, DeMets DL (1989) Changing frequency of interim analysis in sequential monitoring. Biometrics 45:1017–1020CrossRefGoogle Scholar
  16. Leitch JW, Klein GJ, Yee R, Leather RA, Kim YH (1991) Syncope associated with supraventricular tachycardia. an expression of tachycardia rate or vasomotor response?. Circulation 85:1064–1071CrossRefGoogle Scholar
  17. Lou WYW (1996) On runs and longest run tests: a method of finite Markov chain embedding. J Am Stat Assoc 91(436):1595–1601CrossRefzbMATHGoogle Scholar
  18. Lu Y, Jin H, Lamborn KR (2005) A design of phase II cancer trials using total and complete response endpoints. Stat Med 24:3155–3170MathSciNetCrossRefGoogle Scholar
  19. O’Brien PC, Fleming TR (1979) A multiple testing procedure for clinical trials. Biometrics 35:549–556CrossRefGoogle Scholar
  20. O’Connor PW, Li D, Freedman MS, Bar-Or A, Rice GPA, Confavreux C, Paty DW, Stewart JA, Scheyer R (2006) A Phase II study of the safety and efficacy of teriflunomide in multiple sclerosis with relapses. Neurology 66:894–900CrossRefGoogle Scholar
  21. Pocock SJ (1977) Group sequential methods in the design and analysis of clinical trials. Biometrika 64:191–199CrossRefGoogle Scholar
  22. Pryseley A, Tilahun A, Alonso A, Molenberghs G (2010) Using earlier measures in a longitudinal sequence as potential surrogate for a later one. Comput Stat Data Anal 54:1342–1354MathSciNetCrossRefzbMATHGoogle Scholar
  23. Salvan A (1990) Planning sequential clinical trials: a review. Comput Stat Data Anal 9:47–56MathSciNetCrossRefGoogle Scholar
  24. Solomon MJ, Young CJ, Eyers AA, Roberts RA (2002) Randomized clinical trial of laparoscopic versus open abdominal rectopexy for rectal prolapse. Br J Surg 89:35–39CrossRefGoogle Scholar
  25. Suffoletto MS, Dohi K, Cannesson M, Saba S, Gorcsan J (2006) Novel Speckle-tracking radial strain from routine black-and-white echocardiographic images to quantify dyssynchrony and predict response to cardiac resynchronization therapy. Circulation 113:960–968CrossRefGoogle Scholar
  26. Thall PF, Cheng SC (1999) Treatment comparisons based on two-dimensional safety and efficacy alternatives in oncology trials. Biometrics 55:746–753CrossRefzbMATHGoogle Scholar
  27. Thall PF, Wooten LH, Shpall EJ (2006) A geometric approach to comparing treatments for rapidly fatal diseases. Biometrics 62:193–201MathSciNetCrossRefzbMATHGoogle Scholar
  28. Yamanaka R, Abe T, Yajima N, Tsuchiya N, Homma J, Kobayashi T, Narita M, Takahashi M, Tanaka R (2003) Vaccination of recurrent glioma patients with tumour lysate-pulsed dendritic cells elicits immune responses: results of a clinical phase I/II trial. Br J Cancer 89:1172–1179CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Sotiris Bersimis
    • 1
    Email author
  • Athanasios Sachlas
    • 1
  • Takis Papaioannou
    • 1
  1. 1.Department of Statistics & Insurance ScienceUniversity of PiraeusPiraeusGreece

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