A quantum-like model of homeopathy clinical trials: importance of in situ randomization and unblinding
Received16 November 2012
revised28 January 2013
accepted20 February 2013
20 December 2017 (online)
Background: The randomized controlled trial (RCT) is the ‘gold standard’ of modern clinical pharmacology. However, for many practitioners of homeopathy, blind RCTs are an inadequate research tool for testing complex therapies such as homeopathy.
Methods: Classical probabilities used in biological sciences and in medicine are only a special case of the generalized theory of probability used in quantum physics. I describe homeopathy trials using a quantum-like statistical model, a model inspired by quantum physics and taking into consideration superposition of states, non-commuting observables, probability interferences, contextuality, etc.
Results: The negative effect of blinding on success of homeopathy trials and the ‘smearing effect’ (‘specific’ effects of homeopathy medicine occurring in the placebo group) are described by quantum-like probabilities without supplementary ad hoc hypotheses. The difference of positive outcome rates between placebo and homeopathy groups frequently vanish in centralized blind trials. The model proposed here suggests a way to circumvent such problems in masked homeopathy trials by incorporating in situ randomization/unblinding.
Conclusion: In this quantum-like model of homeopathy clinical trials, success in open-label setting and failure with centralized blind RCTs emerge logically from the formalism. This model suggests that significant differences between placebo and homeopathy in blind RCTs would be found more frequently if in situ randomization/unblinding was used.
- 1 Maddox J. When to believe the unbelievable. Nature 1988; 333: 787.
- 2 Brien S., Lachance L., Prescott P., McDermott C., Lewith G. Homeopathy has clinical benefits in rheumatoid arthritis patients that are attributable to the consultation process but not the homeopathic remedy: a randomized controlled clinical trial. Rheumatology (Oxford) 2011; 50: 1070-1082.
- 3 Milgrom L.R., Chatfield K. “It's the consultation, stupid!” … Isn't it?. J Altern Complement Med 2011; 17: 573-575.
- 4 The end of homoeopathy. [Editorial] Lancet 2005; 366: 690.
- 5 Vandenbroucke J.P. Homoeopathy and “the growth of truth”. Lancet 2005; 366: 691-692.
- 6 Shang A., Huwiler-Muntener K., Nartey L. et al. Are the clinical effects of homoeopathy placebo effects? Comparative study of placebo-controlled trials of homoeopathy and allopathy. Lancet 2005; 366: 726-732.
- 7 Walach H., Jonas W., Lewith G. Are the clinical effects of homoeopathy placebo effects?. Lancet 2005; 366: 2081 author reply 2083–2086.
- 8 Fisher P., Berman B., Davidson J., Reilly D., Thompson T. Are the clinical effects of homoeopathy placebo effects?. Lancet 2005; 366: 2082-2083 author reply 2083–2086.
- 9 Ludtke R., Rutten A.L. The conclusions on the effectiveness of homeopathy highly depend on the set of analyzed trials. J Clin Epidemiol 2008; 61: 1197-1204.
- 10 Milgrom L.R. Gold standards, golden calves, and random reproducibility: why homeopaths at last have something to smile about. J Altern Complement Med 2009; 15: 205-207.
- 11 Weatherley-Jones E., Thompson E.A., Thomas K.J. The placebo-controlled trial as a test of complementary and alternative medicine: observations from research experience of individualised homeopathic treatment. Homeopathy 2004; 93: 186-189.
- 12 Fisher P. Entangled, or tied in knots?. Homeopathy 2004; 93: 171-172.
- 13 Belon P., Cumps J., Ennis M. et al. Inhibition of human basophil degranulation by successive histamine dilutions: results of a European multi-centre trial. Inflamm Res 1999; 48 (Suppl. 01) S17-S18.
- 14 Benveniste J., Davenas E., Ducot B., Cornillet B., Poitevin B., Spira A. L'agitation de solutions hautement diluées n'induit pas d'activité biologique spécifique. C R Acad Sci II 1991; 312: 461-466.
- 15 Davenas E., Beauvais F., Amara J. et al. Human basophil degranulation triggered by very dilute antiserum against IgE. Nature 1988; 333: 816-818.
- 16 Davenas E., Poitevin B., Benveniste J. Effect of mouse peritoneal macrophages of orally administered very high dilutions of silica. Eur J Pharmacol 1987; 135: 313-319.
- 17 Walach H., Jonas W.B., Ives J., van Wijk R., Weingartner O. Research on homeopathy: state of the art. J Altern Complement Med 2005; 11: 813-829.
- 18 Hyland M.E. Extended Network Generalized Entanglement Theory: therapeutic mechanisms, empirical predictions, and investigations. J Altern Complement Med 2003; 9: 919-936.
- 19 Milgrom L.R. Patient–practitioner–remedy (PPR) entanglement. Part 1: a qualitative, non-local metaphor for homeopathy based on quantum theory. Homeopathy 2002; 91: 239-248.
- 20 Walach H. Magic of signs: a non-local interpretation of homeopathy. Br Hom J 2000; 89: 127-140.
- 21 Weingartner O. What is the therapeutically active ingredient of homeopathic potencies?. Homeopathy 2003; 92: 145-151.
- 22 Walach H., von Stillfried N. Generalised Quantum Theory – basic idea and general intuition: a background story and overview. Axiomathes 2011; 21: 185-209.
- 23 Walach H. Generalized entanglement: a new theoretical model for understanding the effects of complementary and alternative medicine. J Altern Complement Med 2005; 11: 549-559.
- 24 Walach H. Entanglement model of homeopathy as an example of generalized entanglement predicted by weak quantum theory. Forsch Komplementarmed Klass Naturheilkd 2003; 10: 192-200.
- 25 Bruza P., Busemeyer J.R., Gabora L. Introduction to the special issue on quantum cognition. J Math Psychol 2009; 53: 303-305.
- 26 Mogiliansky A.L., Zamir S., Zwirn H. Type indeterminacy: a model of the KT(Kahneman–Tversky)-man. J Math Psychol 2009; 53: 349-361.
- 27 Pothos E.M., Busemeyer J.R. A quantum probability explanation for violations of ‘rational’ decision theory. Proc Biol Sci 2009; 276: 2171-2178.
- 28 Khrennikov A. Quantum-like model of cognitive decision making and information processing. Biosystems 2009; 95: 179-187.
- 29 Khrennikov A. Quantum-like brain: “Interference of minds”. Biosystems 2006; 84: 225-241.
- 30 Busemeyer J.R., Wang Z., Townsend J.T. Quantum dynamics of human decision-making. J Math Psychol 2006; 50: 220-241.
- 31 Khrennikov A.Y., Haven E. Quantum mechanics and violations of the sure-thing principle: the use of probability interference and other concepts. J Math Psychol 2009; 53: 378-388.
- 32 Conte E., Todarello O., Federici A., Vitiello T., Lopane M., Khrennikov A. et al. A preliminary evidence of quantum like behavior in measurements of mental states. Khrennikov A.Yu. Quantum Theory: Reconsideration of Foundations. Series Mathematical Modelling in Physics, Engineering, and Cognitive Sciences. vol. 10 2004. Växjö: Växjö University Press; 679-702 Available from: http://xxx.lanl.gov/abs/quant-ph/0307201.
- 33 Atmanspacher H., Filk T., Romer H. Quantum Zeno features of bistable perception. Biol Cybern 2004; 90: 33-40.
- 34 Scarani V., Suarez A. Introducing quantum mechanics: one-particle interferences. Am J Phys 1998; 66: 718-721.
- 35 Walach H. Entangled – and tied in knots! Practical consequences of an entanglement model for homeopathic research and practice. Homeopathy 2005; 94: 96-99.
- 36 Mollinger H., Schneider R., Loffel M., Walach H. A double-blind, randomized, homeopathic pathogenetic trial with healthy persons: comparing two high potencies. Forsch Komplementarmed Klass Naturheilkd 2004; 11: 274-280.
- 37 Walach H., Möllinger H., Sherr J., Schneider R. Homeopathic pathogenetic trials produce more specific than non-specific symptoms: results from two double-blind placebo controlled trials. J Psychopharmacol 2008; 22: 543-552.
- 38 Schiff M. The memory of water: homoeopathy and the battle of ideas in the new science. London: Thorsons Publishers; 1998.
- 39 Benveniste J. Ma vérité sur la mémoire de l'eau. Paris: Albin Michel; 2005.
- 40 Beauvais F. Emergence of a signal from background noise in the “memory of water” experiments: how to explain it?. Explore (NY) 2012; 8: 185-196.
- 41 Beauvais F. Memory of water and blinding. Homeopathy 2008; 97: 41-42.
- 42 Beauvais F. L'Âme des Molécules – Une histoire de la “mémoire de l'eau”. Collection Mille Mondes 2007. ISBN: 978-1-4116-6875-1 Available from: http://www.mille-mondes.fr.
- 43 Jonas W.B., Ives J.A., Rollwagen F. et al. Can specific biological signals be digitized?. FASEB J 2006; 20: 23-28.
- 44 Poitevin B., Davenas E., Benveniste J. In vitro immunological degranulation of human basophils is modulated by lung histamine and Apis mellifica . Br J Clin Pharmacol 1988; 25: 439-444.
- 45 Sainte-Laudy J., Belon P. Inhibition of basophil activation by histamine: a sensitive and reproducible model for the study of the biological activity of high dilutions. Homeopathy 2009; 98: 186-197.
- 46 Beauvais F. Description of Benveniste's experiments using quantum-like probabilities. J Sci Explor 2013; 27: 43-71.
- 47 Aspect A., Dalibard J., Roger G. Experimental test of Bell's inequalities using time-varying analyzers. Phys Rev Lett 1982; 49: 1804-1807.