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• Is Bayes' statistics sensitive enough to assess physical child abuse? Comment to: "Implementation of the Dutch expertise centre for child abuse: descriptive data from the first 4 years"
  Martin van Gemert
  Published on: 6 June 2023

• Published on: 6 June 2023

  Is Bayes' statistics sensitive enough to assess physical child abuse? Comment to: "Implementation of the Dutch expertise centre for child abuse: descriptive data from the first 4 years"

  • Martin van Gemert, Emeritus Professor of medical physics Amsterdam UMC, the Netherlands

  Martin JC van Gemert,*1 Marianne Vlaming,2 Peter J van Koppen,3 Aeilco H Zwinderman,4 HA Martino Neumann5

  1Department of Biomedical Engineering & Physics, Amsterdam University Medical Centers, location AMC, University of Amsterdam, Amsterdam, The Netherlands
  2Private Practice, Criminal Psychology and Law, Doetinchem, The Netherlands
  3Department of Criminal Law and Criminology, Faculty of Law, VU University Amsterdam, The Netherland
  4Department of Clinical Epidemiology & Bio-Statistics, Amsterdam University Medical Centers, location AMC, University of Amsterdam, Amsterdam, The Netherlands
  5ZBC-Multicare, Hilversum-The Netherlands

  Van Rijn et al1 described the implementation and first output data of the Dutch expertise centre for child abuse (LECK: Landelijk Expertise Centrum Kindermishandeling). LECK's methodology aims to be easily accessible for giving anonymous advice when health care professionals suspect potential cases of physical child abuse.1 LECK physicians do not see the patient nor talk to the parents and are neither involved in further treatment or follow-up. LECK works with Bayes' statistics,2,3 and uses likelihood ratios, part of Bayes' theorem, in their conclusions.1

  Bayes' theorem, named after the 18th century English statistician, philosopher and Presbyterian minister Thomas Bayes,2,3 updates the relative probability of an hypothesis (here, physical child abuse caused the symptoms),...

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  Martin JC van Gemert,*1 Marianne Vlaming,2 Peter J van Koppen,3 Aeilco H Zwinderman,4 HA Martino Neumann5

  1Department of Biomedical Engineering & Physics, Amsterdam University Medical Centers, location AMC, University of Amsterdam, Amsterdam, The Netherlands
  2Private Practice, Criminal Psychology and Law, Doetinchem, The Netherlands
  3Department of Criminal Law and Criminology, Faculty of Law, VU University Amsterdam, The Netherland
  4Department of Clinical Epidemiology & Bio-Statistics, Amsterdam University Medical Centers, location AMC, University of Amsterdam, Amsterdam, The Netherlands
  5ZBC-Multicare, Hilversum-The Netherlands

  Van Rijn et al1 described the implementation and first output data of the Dutch expertise centre for child abuse (LECK: Landelijk Expertise Centrum Kindermishandeling). LECK's methodology aims to be easily accessible for giving anonymous advice when health care professionals suspect potential cases of physical child abuse.1 LECK physicians do not see the patient nor talk to the parents and are neither involved in further treatment or follow-up. LECK works with Bayes' statistics,2,3 and uses likelihood ratios, part of Bayes' theorem, in their conclusions.1

  Bayes' theorem, named after the 18th century English statistician, philosopher and Presbyterian minister Thomas Bayes,2,3 updates the relative probability of an hypothesis (here, physical child abuse caused the symptoms), as more evidence becomes available (expressed in the form of a likelihood ratio). The updated outcome, the relative probability of the hypothesis being true if the symptoms are present, is given by the product of likelihood ratio and physical child abuse incidence,4 where the likelihood ratio expresses how more frequent the symptoms develop if abuse indeed occurred versus the non-abuse situation.

  We previously estimated the Dutch incidence of physical child abuse for infants as about 0.0026.4 For older Dutch children it is likely that the physical abuse incidence decreases even further, based on the yearly published child abuse data for USA children.5

  Implication of these exceedingly low physical abuse incidences is that Bayesian statistics predicts a virtually zero probability for USA and Dutch children that physical abuse-mimicking-symptoms are indeed caused by physical abuse. Nevertheless, LECK claims the use of Bayes' theorem, e.g. in its first 4 years in 761 cases.1 The solution to this conundrum is given in the Abstract of their paper,1,4 that LECK "works with Bayes' theorem and uses likelihood ratios in their conclusions." Even though they correctly explained Bayes' theorem in words,1 we showed4 that LECK literally used the likelihood ratio to represent the probability that the observed symptoms are due to physical abuse. That invalid use of Bayes' theorem obviously produces physical abuse probabilities that can be orders of magnitude too large, not only for <1 year old infants,4 but also for all other child ages.

  A Bayesian probability of >3 that observed symptoms could be physical abuse-related, a minimum value of possible statistical significance, requires likelihood ratios of approximately >1,200 for children below 1 year, >2,700 for 1-8 year old children, and >4,500 for 11-18 year old children, which numbers are far beyond any reasonable likelihood ratio.

  In conclusion, Bayes' theorem, when correctly used (which obviously should occur), includes such exceedingly low physical abuse incidences, that this statistical method is too insensitive to assess potential physical child abuse cases convincingly, not only in the USA and the Netherlands, but possibly also worldwide. Finally, LECK creates by their approach an unsafe situation Finally, LECK creates by its approach an unsafe situation for e.g. Dutch parents when presenting their child that has a rare or inheritable medical disorder that gives symptoms mimicking child abuse.4 Such a methodology will likely increase the number of invalid physical child abuse convictions, including the number of temporary as well as permanent foster care placements.4 In our opinion, therefore, LECK should refrain from applying Bayesian statistics in cases of child abuse suspicion and use differential diagnostic procedures, the general accepted medical method of care.

  REFERENCES
  1. van Rijn RR, Affourtit MJ, Karst WA, Kamphuis M, de Bock LC, van de Putte E. Implementation of the Dutch Expertise Centre for Child Abuse: descriptive data from the first 4 years. BMJ Open 2019;9:e031008 (1-7).
  2. Bayes T. An Essay Toward Solving a Problem in the Doctrine of Chances. Philosoph Trans Roy Soc London 1764;53:370-418.
  3. https://en.wikipedia.org/wiki/Bayesian statistics.
  4. van Gemert MJC, Zwinderman AH, van Koppen PJ, Neumann HAM, Vlaming M. Child Abuse, misdiagnosed by an Expertise Center. Part II. Misuse of Bayes' Theorem. Children 2023;10(5):(1-11).
  5. US Department of He

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  Conflict of Interest:
  None declared.

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