Traumatic Head Injury and the Diagnosis of Abuse: A Cluster Analysis

We applied 3 different cluster algorithms to sort PediBIRN patients into distinct cohorts. We then compared the frequency of prospectively defined clinical findings across clusters defined by each algorithm and by the presence or absence of the triad. Additionally, we compared the cluster partitions with each other, pairwise, to assess their similarity.

The PediBIRN patient population used for this secondary analysis includes 500 children aged <3 years hospitalized between 2010 and 2013 across 18 PICUs for management of acute, symptomatic, and traumatic closed cranial or intracranial injury identified by computed tomography (CT) scan or MRI from the PediBIRN derivation and validation studies.^35,36  Eligible children were enrolled consecutively by each participating center. Children with preexisting brain abnormalities and children injured in motor vehicle collisions were excluded. All 500 children in the PediBIRN database were included in cluster analysis.

For each qualifying patient, PediBIRN investigators captured prospective data regarding patients’ symptoms, clinical and imaging findings, historical features, local diagnostic impression, and the decision to report the case to children’s protective services.^35,36  Explanations of terms were incorporated into the data collection tool; for instance, encephalopathy was defined as “clear impairment or loss of consciousness.” During the PediBIRN derivation study of 209 patients at 14 sites, a second physician independently entered the same data points for 20% of patients at each individual site.³⁵  Data used in cluster analysis met the following criteria: the variable possessed sufficient interrater reliability, as evidenced by a κ score >0.6 in the derivation study, and the variable described an objective feature, such as symptoms, examination findings, radiologic findings, and clinical course. Data elements that reflected some subjective assessment, such as consistency of provided history, final diagnostic impression, or child protective services reporting decisions, were not used in cluster analysis but were analyzed when comparing the resulting clusters.

Throughout the article, we will use the word “cluster” to indicate a group of patients identified by 1 of the 3 cluster algorithms, “partition” as a verb to indicate the process of dividing patients into clusters by 1 of the 3 cluster algorithms, and “partition” as a noun to indicate the structure of clusters across the entire research cohort developed by 1 of the 3 cluster algorithms. The 500 PediBIRN patients were partitioned by using 3 different cluster analysis algorithms: K-means clustering, divisive hierarchical clustering, and agglomerative hierarchical clustering.³⁴  Cluster analysis was performed in the statistical package R, version 3.6.2, by using the “pam,” “diana,” and “hclust” commands.³⁷  Because data included predominantly dichotomous but also continuous data, Gower's method for measuring distance was used for cluster algorithms.³⁸ 

The K-means algorithm requires that the statistician specify the number of desired clusters. K-means clustering was applied, specifying 2 through 10 clusters, producing 9 separate partitions. The resulting 9 partitions were then evaluated by 2 methods, silhouette width and gap statistic, to determine which single K-means partition had the best mathematical characteristics.^34,39  The optimal cluster number was chosen such that silhouette width was maximized and gap statistic was maximized and within 1 SD of the next larger number of clusters. In divisive and agglomerative hierarchical clustering the “complete” or “farthest neighbor” method was used. The divisive and agglomerative clustering algorithms each produce a tree of clusters and subclusters. The level in each tree producing a cluster number matching the optimized K-means partition was chosen for analysis, 1 partition for divisive hierarchical clustering and 1 partition for agglomerative hierarchical clustering.

We also divided the cohort into 2 groups by the presence or absence of the triad. For this process, we defined the triad as the presence of any SDH(s) or fluid collection(s), acute encephalopathy before admission, and RH(s) described by an ophthalmologist as dense, extensive, covering a large surface area and/or extending to the ora serrata (extensive RH). As discussed in the literature, the triad does not distinguish nuances in subdural collections, encephalopathy, or RH. The PediBIRN data set did not collect data on lesser degrees of RH. As such, our operational definition of the triad, within this data set, is more restrictive than the triad discussed in critical literature.

We performed 2 additional statistical analyses after partition into 2 clusters. For each algorithm’s partition, we compared the relative frequencies of clinical variables between the clusters. Significance was determined by χ² tests or Fisher’s exact tests, as appropriate, in which the Haldane-Anscombe correction was applied if any cell count was 0. Strength of association was determined by odds ratios (ORs) with 95% confidence intervals (CIs). This was done both for variables used to partition the clusters and for select variables not used in cluster analysis.

We also analyzed the relationship between the partitions developed by each algorithm and by the triad. Contingency tables were created to analyze patient sorting into the resulting clusters. Similarity between resulting partitions was assessed for significance by χ² analysis and for strength by the accuracy of 1 partition at predicting a comparison partition. Treating physicians’ determination of abuse likelihood was dichotomized (definite and/or probable AHT versus undetermined or definite and/or probable non-AHT).

The 9 separate results, created by using the K-means algorithm specifying 2 through 10 clusters, were each evaluated by the silhouette and the gap-statistic methods. The K-means result in which the statistician specified 2 clusters had the best mathematical characteristics. The silhouette width of this solution was 0.22, and the gap statistic was 0.48.

To compare the results of divisive and agglomerative hierarchical analysis to the results of the K-means results, the 2-cluster partitions of the hierarchical algorithms were chosen for further analysis. Silhouette widths and gap statistics are provided here, for description, but were not used in choosing the 2 cluster solutions for these algorithms. The silhouette width for partition into 2 clusters by the divisive hierarchical algorithm was 0.38, and the gap statistic was 0.23. For partition by the agglomerative hierarchical algorithm, silhouette width was 0.35, and the gap statistic was 0.23. Although physicians’ final diagnosis of definitive or probable AHT was not used in developing any partition, it was substantially associated (P < .001 and OR>10) with 1 of the clusters produced by each algorithm, which we will refer to as cluster 1. We will refer to the cluster that did not associate with physician-diagnosed AHT as cluster 2.

The triad, by design, divides the population into 2 clusters. The cluster that manifested the triad also associated strongly to physicians’ final diagnosis of definitive or probable AHT and will be referred to as cluster 1. We will refer to individual clusters by the partition method and their numerical label (K-means 1, K-means 2, divisive 1, divisive 2, agglomerative 1, agglomerative 2, triad 1, and triad 2)

The within-algorithm comparisons of cluster 1 with cluster 2 (K-means 1 with K-means 2, divisive 1 with divisive 2, agglomerative 1 with agglomerative 2, and triad 1 with triad 2) produced informative results. Most variables occurred with significantly greater frequency (P < .05) in 1 of the clusters for each of the 3 mathematical algorithms. (Table 1) Variables making the most substantial contribution to differentiating clusters (P < .001 and OR > 10 or <0.1 in all 3 algorithms) were imaging patterns indicating brain hypoxemia-ischemia in any distribution; acute encephalopathy before admission, encephalopathy lasting >24 hours, and encephalopathy lasting >24 hours with subsequent deterioration; respiratory compromise before admission; the presence of SDH or fluid collection; and ophthalmologist-confirmed retinoschisis.

By definition, clinical encephalopathy, SDH or fluid collection, and extensive RH made a substantial contribution (P < .001 and OR > 10 or <0.1) to partitioning by the triad. There were differences between partition by the triad and partition by the K-means, divisive, and agglomerative algorithms. Imaging indications of parenchymal brain injury and retinoschisis had lower ORs in partition by the triad than the 3 cluster algorithms. The duration of encephalopathy differed. Brief encephalopathy that resolved before admission associated statistically with the triad-1 cluster but was nonsignificant in the K-means partition and associated with the divisive 2 and agglomerative 2 clusters. Other differences in encephalopathy duration and SDH distribution may be seen in Table 1.

The ages of the children in the K-means 1 cluster of the K-means partition were slightly younger (mean 8.61 vs 10.39 months) than those in the K-means 2 cluster (P = .046) (Table 2). There was no statistically significant difference in mean age between divisive 1 and divisive 2, agglomerative 1 and agglomerative 2, and triad 1 and triad 2. The ability to walk or cruise was not statistically different between clusters 1 and 2 in any partition.

When variables not used in the cluster algorithms were analyzed, there were significant differences between clusters 1 and 2, as defined by each of the 3 algorithms and by the triad (Table 3). For each algorithm and for the triad, caregiver admission of abuse, physician-identified changes in the reported clinical history, and physician-identified developmental inconsistencies in reported child behavior were all significantly more frequent in cluster 1. Independently witnessed unintentional injury was significantly less frequent in cluster 1. Caregiver admission of abuse had a substantial (P < .001 and OR > 10) relationship to being in the K-means 1 cluster. Independently witnessed unintentional injury had a substantial (P < .001 and OR < 0.10) relationship to being in the triad-2 cluster.

Pairwise comparisons of 6 combinations between the 3 algorithms or the triad revealed significant similarities in their partitions, each achieving a χ² <0.001. (Table 4) The K-means and divisive hierarchical algorithms were the most closely related, with an accuracy of 94.8% in predicting one another. All 3 mathematical algorithms agreed in the assignment of 87.8% of patients, 122 to cluster 1 and 317 to cluster 2.

The evidence base for diagnosing AHT in children with neurotrauma relies on a series of case-control studies and meta-analyses of those studies.^14–30  Cohorts of AHT cases have been separated from controls by various methods: physician diagnosis,^15,16,22  consensus opinion of a multidisciplinary team,^{14,17,18,22,23,26,28,29}  predefined criteria designed to avoid indicators under study,^{14,19–21 ,29}  and confessed abuse versus a public non-AHT event.²²  Results of the various methods have been consistent, lending strength to the findings. Some authors have pointed to circularity inherent in some of these methods, dismissing the literature as invalid.³¹  Cluster analysis uses an entirely different approach, identifying divisions in a body of data by the mathematical distribution of data points. By applying cluster analysis to a cohort of children with neurotrauma, excluding data referencing physician diagnosis or judgements of historical consistency, we have sorted patients without this circularity.³⁴ 

The results of 3 mathematical cluster analyses indicate that the population of children with neurologic injury admitted to a PICU has at least 2 distinguishable subpopulations. As a correlate, these results reject that the objective clinical presentations of these children occur across a spectrum of severity, without clear division, or in random combinations of findings without pattern. Cluster results are generally considered appropriate when silhouette width is >0.2 and are considered strong when silhouette width is >0.6.³⁴  Each of the 3 algorithms we deployed generated 2-cluster results with a silhouette width >0.2, each partition pair correlated with a χ² <0.001 and accuracy >88%, and all agreed on the assignment of 87.8% of patients, indicating that partition was justifiable and robust. Although partition implies that a latent factor operated to produce 2 subpopulations within the PediBIRN cohort, our cluster results alone do not reveal that the difference was AHT.

For each algorithm, children in cluster 1 manifested significantly increased rates of SDH other than unilateral contact SDH, acute encephalopathy that did not resolve within 24 hours, extensive RH, retinoschisis, abuse-associated fractures on skeletal survey, concerning traumatic skin findings, and laboratory or imaging indications of intraabdominal injury. By contrast, children in cluster 2 manifested high rates of findings that indicate impact to the head: skull fracture, epidural hemorrhage, and extracranial craniofacial injury. It bears repeating that partition into clusters 1 and 2 made no reference to physicians’ diagnosis of AHT or any research definition of AHT. And yet, mathematical partition based on objective, reliably determined clinical variables replicated the results of decades of literature on the characteristics of children with AHT.^14–30  By replicating the segregation of clinical findings in the case-control literature, the cluster analyses demonstrate that the division of cases from controls reflected natural latent divisions in the larger population of young children with neurotrauma. The fact that these differences extended beyond neurologic and eye findings to include skeletal fractures, skin injuries, and visceral injuries supports the inference that inflicted trauma was closely related to the latent variable responsible for partition.

Given that partition into clusters 1 and 2 replicates clinical associations found by researchers into the characteristics of children with AHT, it is unsurprising that partition was significantly associated with clinical diagnosis of AHT by treating physicians. We suspect that diagnosing physicians applied the very case-control studies we have previously referenced in their clinical determinations. Physicians also appear to have considered nuances and findings not used by the clustering algorithms when making their diagnoses, diagnosing both AHT and non-AHT within clusters 1 and 2 of each algorithm. This is consistent with the finding that silhouette width never exceeded 0.6 for any cluster algorithm, indicating that the 2 clusters are not highly discreet.

Authors who have questioned the existing literature guiding diagnosis of AHT have also suggested that research should rely on confession to identify children with AHT.³¹  We treated both confessions and the observations of independent witnesses as subjective and not susceptible to reliability testing, excluding consideration of these variables by the cluster algorithms. Despite this, when there was an admission of AHT, it associated with cluster 1, and when there was an independent witness to an unintentional injury, it associated with cluster 2. Viewed another way, nonmedical, firsthand witness data agreed with cluster partition and with AHT characteristics identified in decades of literature and in our 3 mathematical partitions.

Final, interesting outcomes were age and developmental differences between clusters. Much earlier research into characteristics of AHT have found children with AHT to be significantly younger than those in comparison groups.^{14,17–19 ,22,23,25–28 ,30}  Only 1 of the clusters, K-means 1, had a significant association with age, based on a difference of 1.78 months, with a P of .046. The ability to walk or cruise was not statistically different between clusters 1 and 2 of any algorithm. It follows that physiologic and developmental variables related to age and maturity are unlikely to be responsible for other differences between cluster pairs.

We began this study to see whether a noncircular research method, blind to issues of abuse, would replicate the clinical associations found in the case-control literature that references a determination of abuse in its methods. What we found was not only that it did but that the clinical findings making the most contribution to partition were encephalopathy, SDH, and retinal injury. This immediately called to mind the triad of findings that some authors have asserted are both poorly supported by research literature and heavily relied on by physicians to diagnose AHT.^31–33  For this reason, we looked at partition by the closest surrogate we could construct for this triad. The partition by these criteria was statistically similar to the partitions derived by the 3 mathematical algorithms, with sorting accuracies of 80.0% to 83.6%. Furthermore, many of the associations with extracephalic findings attributable to abuse, and with available firsthand reports of abuse or unintentional injury, were preserved in this partition. As such, it is unsurprising that the triad, when incorporating the additional component of requiring that RHs be “dense, extensive and covering a large surface area or extending to the ora serrata,” has a high specificity for physicians’ diagnosis of AHT (98.0%), although a modest sensitivity (47.8%) and accuracy (73.2%). The triad, too, appears to reflect a natural division in the population of children with neurologic injury, reflective of a latent variable that is related to the diagnosis of AHT.

We have identified several limitations to this study. The data used in cluster analysis were captured in a PICU setting on patients with acute symptomatic injury. It is unknown if the results would have been the same in a non-PICU setting or in children with nonacute intracranial injury. Bias may be introduced in ascertainment of certain findings. All patients had a history, physical examination, and head imaging by CT or MRI. Retinal examination and skeletal survey were performed at physicians’ discretion, and thus the absence of fractures and RHs could have been the result of omitted rather than normal ophthalmologic or radiologic examinations. Among the 500 patients, 322 patients underwent both skeletal survey and retinal examination, and 109 patients underwent neither evaluation. Retinoschisis was the only inconsistently ascertained finding that had a substantial (P < .001 and OR > 10) association with cluster 1 and only occurred in 30 cases. Thus, the variables that most substantially contributed to partition were universally assessed, and the influence of ascertainment bias appears to be minimized. Finally, the variables captured in the study were chosen as relevant to child abuse. It is conceivable that the inclusion of other variables might have produced different results.

When mathematical clustering methods based solely on objectively and reliably ascertained clinical variables were used to analyze a cohort of young children with neurologic injury, 2 subpopulations emerged. One of these subpopulations was characterized by an elevated prevalence of imaging patterns indicating brain hypoxemia-ischemia, SDH other than unilateral contact SDH, retinal findings, extracephalic injuries, the absence of clear evidence of head impact, caregiver admission of AHT, and physician-identified inconsistencies in provided trauma histories. These differences replicate differences previously found in case-control literature as distinguishing AHT, differences that treating physicians appeared to view as highly informative to the diagnosis of AHT. We conclude that there are aspects unique to AHT that produce discernible subpopulations and that the division of cases from controls in previous research on AHT reflected a natural division in the larger cohort. Partition of these same patients by the presence or absence of a proposed triad of findings produces similar results and is likely related to the same latent factor. These results support the preponderant diagnostic practices in the pediatric community. By arriving at similar results through very different methods, this study validates previous literature and should strengthen physician’s confidence in the current diagnostic paradigm and their presentation of that paradigm in court.

The authors acknowledge and thank the remaining PediBIRN investigators who helped to capture the data used in this secondary analysis: Bruce E. Herman, MD, and Antoinette Laskey, MD, MPH (Primary Children's Medical Center, Salt Lake City, UT); Douglas F. Willson, MD, and Robin Foster, MD (The Children’s Hospital of Richmond, Richmond, VA); Veronica Armijo-Garcia, MD, and Sandeep K. Narang, MD, JD (University of Texas Health Sciences Center at San Antonio, San Antonio, TX); Christopher Carroll, MD (Connecticut Children’s Medical Center, Hartford, CT); Deborah A. Pullin, BSN, APRN (Dartmouth-Hitchcock Medical Center, Lebanon, NH); Jeanine M. Graf, MD, and Reena Isaac, MD (Texas Children’s Hospital, Houston, TX); Terra N. Frazier, DO, and Kelly Tieves, MD (Children’s Mercy Hospital, Kansas City, MO); Edward Truemper, MD, and Suzanne Haney, MD (Children's Hospital of Omaha, Omaha, NE); Kerri Weeks, MD, and Lindall E. Smith, MD (Wesley Medical Center, Wichita, KS); Renee A. Higgerson, MD, and George A. Edwards, MD (Dell Children's Medical Center of Central Texas, Austin, TX); Nancy S. Harper, MD, FAAP and Karl L. Serrao, MD, FAAP, FCCM (Driscoll Children's Hospital, Corpus Christi, TX); Andrew Sirotnak, MD, Joseph Albietz, MD, and Antonia Chiesa, MD (Children’s Hospital Colorado, Denver, CO); Christine McKiernan, MD (Baystate Medical Center, Springfield, MA); Mark S. Dias, MD (Penn State College of Medicine, Hershey, PA); Michael Stoiko, MD, Debra Simms, MD, FAAP, and Sarah J. Brown, DO, FACOP, FAAP (Helen DeVos Children's Hospital, Grand Rapids, MI); Amy Ornstein, MD, FRCPC (IWK Health Centre, Halifax, Nova Scotia); and Phil Hyden, MD (Children’s Hospital of Central California, Madera, CA)

AHT

abusive head trauma

CI

confidence interval

CT

computed tomography

OR

odds ratio

PediBIRN

Pediatric Brain Injury Research Network

RH

retinal hemorrhage

SDH

subdural hemorrhage