Child Abuse, Misdiagnosed by an Expertise Center—Part II—Misuse of Bayes’ Theorem

Abstract

A newborn girl had, from two weeks on, small bruises on varying body locations, but not on her chest. Her Armenian grandmother easily bruised, too. Her mother was diagnosed with hypermobility-type Ehlers-Danlos-Syndrome (hEDS), an autosomal dominant connective tissue disorder, with a 50% inheritance probability. Referral to a University Medical Center located “Dutch Expertise Center for Child Abuse” resulted (prior to consultation) in physical abuse suspicion. Protocol-based skeletal X-rays showed three healed, asymptomatic rib fractures. A protocol-based Bayesian likelihood ratio guesstimation gave 10–100, erroneously used to suggest a 10–100 times likelier non-accidental-than-accidental cause. Foster care placement followed, even in a secret home, where she also bruised, suggesting hEDS inheritance. Correct non-accidental/accidental Bayes’ probability of symptoms is (likelihood ratio) × (physical abuse incidence). From the literature, we derived an infant abuse incidence between about ≈0.0009 and ≈0.0026 and a likelihood ratio of <5 for bruises. For rib fractures, we used a zero likelihood ratio, arguing their cause was birth trauma from the extra delivery pressure on the chest, combined with fragile bones as the daughter of an hEDS-mother. We thus derived a negligible abuse/accidental probability between <5 × 0.0009 <0.005 and <5 × 0.0026 <0.013. The small abuse incidence implies that correctly using Bayes’ theorem will also miss true infant physical abuse cases. Curiously, because likelihood ratios assess how more often symptoms develop if abuse did occur versus non-abuse, Bayes’ theorem then implies a 100% infant abuse incidence (unwittingly) used by LECK. In conclusion, probabilities should never replace differential diagnostic procedures, the accepted medical method of care. Well-known from literature, supported by the present case, is that (child abuse pediatrics) physicians, child protection workers, and judges were unlikely to understand Bayesian statistics. Its use without statistics consultation should therefore not have occurred. Thus, Bayesian statistics, and certainly (misused) likelihood ratios, should never be applied in cases of physical child abuse suspicion. Finally, parental innocence follows from clarifying what could have caused the girl’s bruises (inherited hEDS), and rib fractures (birth trauma from fragile bones).

Child Abuse, Misdiagnosed by an Expertise Center: Part I—Medico-Social Aspects

“…Moreover, rib fractures due to child abuse have been reported as mainly posterior fractures, e.g., Figure 2 of [ 52 ], while they were antero-lateral here. In Part II [ 14 ], we argue from the literature that children of hEDS mothers develop bone fragility, most severe in hEDS children, which is highly likely in our case. We therefore hypothesized that the girl’s rib fractures developed during delivery, as birth trauma due to her weak bones.…”

“…The expertise center pediatricians’ third indicator for child abuse was the large likelihood ratio estimation of 10–100, which was based on data from the literature on bruises and rib fractures. However, we show in Part II [ 14 ] that likelihood ratios only express how much more frequently symptoms develop when abuse actually did occur, compared to a non-abuse cause. It is therefore obvious that a likelihood ratio does not provide the probability that the observed symptoms were caused by abuse.…”

“…The expertise center was consulted again and concluded, with their protocol-based Bayesian likelihood ratios, that this case had a 10–100 times larger probability of having a non-accidental than an accidental cause. In Part II [ 14 ], we show that this conclusion is statistically invalid. Both children were then, by court order, placed in foster care with their grandparents.…”

“…We also wish to express the need for a thorough medical and social assessment in cases where child abuse is suspected. The complexity of the statistical method used, as related to Bayes’ theorem, required a separate Part II [ 14 ], and readability required a forthcoming Part III on the legal and moral aspects. However, the highlights of Parts II and III are summarized in this Part I.…”

“…Essential roles in this case were played by the Dutch Expertise Center for Child Abuse [ 14 , 15 ]), expressed henceforth as “the expertise center”, and three Dutch Child Protection Agencies.…”