The prevalence of mental disorders and patterns of comorbidity within a large sample of mentally ill prisoners: A network analysis

Background. Comorbidity has profound implications in both the clinical field and research, yet little is known about the prevalence and structure of comorbid mental disorders. This article aims not only to present data on the prevalence of mental disorders and comorbidity, but also to explore relationships between comorbid mental disorders by using a network approach. Methods. Data used in this cross-sectional study are part of a prospective cohort study within penitentiary psychiatric centers (PPCs) in the Netherlands. It includes DSM diagnoses of 5,257 unique male patients incarcerated in one of the PPC's. Prevalence rates of mental disorders and comorbidity were calculated, the network of comorbid DSM diagnoses was constructed using regression coefficients. Results. Schizophrenia spectrum and substance-related disorders were most prevalent within this sample (56.7 and 43.1%, respectively), and over half of all patients were diagnosed with a comorbid disorder (56.9%). Four distinctive groups of disorders emerged from the network analysis of DSM diagnoses: substance use, impulsivity, poor social skills, and disruptive behaviors. Psychotic disorders were considered as a separate group as it was unconnected to other disorders. Conclusions. Comorbid mental disorders can be described, at least in part, as connected networks. Underlying attributes as well as direct influences of mental disorders on one another seem to be affecting the presence of comorbidity. Results could contribute to the understanding of a possible causal relation between psychopathology and criminal behavior and the development of treatment programs targeting groups of disorders.


Introduction
Comorbidity, defined as the co-occurrence of two or more psychiatric disorders [1], is a widespread phenomenon within the clinical practice of psychiatry and psychology. Previous studies indicated high rates of comorbidity in various populations with mental illness. The United States National Comorbidity Survey found that 56% of adults with a Diagnostic and Statistical Manual of Mental Disorders (DSM) diagnosis at some point in their lives had also been diagnosed with another mental disorder [2].
Clinical effects of comorbidity are profound. Comorbidity has negative effects on the progression of a disorder, the severity of symptoms [3][4][5][6], and treatment outcome [7,8], and is associated with more antisocial behavior [3,9]. Patients with comorbid mental disorders experience more functional disability [4,10], less social competence [6,11], and higher public service utilization [6,12]. Comorbidity also causes multiple complications for research. For example, restricting a study to "pure cases" (i.e., subjects with only one mental disorder) limits the generalizability and ability to detect correlates of mental disorders. Furthermore, studying samples with a target disorder, and disregarding the presence of comorbid disorders, compromises the interpretation of all results as the confounding influence of comorbid mental disorders is not considered [13].
Although complications associated with comorbidity are evident, current psychiatric classification systems such as the DSM or International Classification of Diseases still describe mental disorders as discrete conditions with little respect to the overlap in symptoms of various mental disorders. Different approaches to understanding and classifying psychopathology have been proposed. Among them is the common cause hypothesis, in which comorbidity is explained as the effect of a latent attribute [14]. Studies using latent class analysis have yielded distinctive profiles of comorbidity [13,15]. However, the common cause hypothesis does not allow for a direct relationship between the observable indicators, and it is questionable whether this is plausible [14]. Consider, for example, the relationship between insomnia and psychiatric disorders, that is, insomnia can lead to depression, anxiety, or even psychosis. It seems that the relationship between mental disorders could also emerge as a result of direct influences they impose on each other.
To define and analyze relationships between various mental disorders, without postulating the existence of a common cause, Cramer et al. [14] proposed a network approach to comorbidity. Based on network models of depression and anxiety, they argue that it "generates realistic hypotheses about pathways to comorbidity, overlapping symptoms, and diagnostic boundaries, that are not naturally accommodated by latent variable models" (p. 33).
Currently, around 585,000 individuals are incarcerated in European prisons, of which 10,000 are incarcerated in the Netherlands [16]. The Netherlands has one of the lowest incarceration rates in Europe, with 50 detainees per 100,000 inhabitants [16,17]. This is a much lower rate than the European average of 118.5 [16] and comparable to, for example, Sweden and Finland [17]. Around 60% of the total Dutch prison population has been diagnosed with a mental disorder [17]. As noted before, comorbidity is associated with more antisocial behavior, and it has been suggested that psychiatric patients with multiple disorders are at a higher risk of being incarcerated [18,19]. Prevalence rates of comorbidity as high as 90% in prisons seem to support this notion. Combinations of schizophrenia and bipolar disorder with antisocial personality and substance use disorders (SUD) are common within this population [3], although comorbidity research has been limited in this population [20].
The aim of this study is to present data on the prevalence of mental disorders and comorbidity in a large sample of mentally ill prisoners (n = 5,257). To take into consideration comorbidity, we also model a network of DSM diagnoses and their relations to each other and explore the possibility of underlying attributes and direct relations between mental disorders. This study will provide a better understanding of serious mental illness and the structure of comorbidity within a forensic population.

Penitentiary psychiatric centers and the National Database PPC
The data used in this study were collected in the four penitentiary psychiatric centers (PPC) in the Netherlands. PPCs are facilities within the Dutch criminal justice system equipped to house detainees who are incapable of functioning within a regular prison regime due to their mental state and need specialized psychiatric care [21].
Since May 1, 2013, the PPCs are required to systematically gather information on all patients admitted to the PPC, resulting in the National Database PPC. The database contains diagnostic information, demographic patient characteristics, and criminal records, as well as information on clinical symptoms. The data are used for policymaking and evaluation of the effectiveness of treatment offered to patients. This study uses data collected within the clinical practice and comprises secondary analyses of these data for scientific research.

Ethical considerations
The secondary usage of anonymized data for scientific research, as presented in this paper, was authorized by the Dutch Ministry of Justice and Security. Additionally, the Ethics Committee of the Department of Law and Criminology, Vrije Universiteit Amsterdam, approved this study.

Participants
This study includes data of all 9,057 patients detained in the four PPCs in the Netherlands between May 1, 2013, and June 2, 2019. In case of multiple admittances of the same person, which is not unusual in this population, data gathered during the most recent admittance was included in the study. Removing data of 3,271 previous admissions resulted in a sample of 5,786 unique subjects. Given possible gender differences in diagnosis and comorbidity [22], only male patients were included in this study, resulting in a final sample size of 5,257 patients. Offenses committed by this sample are omnifarious, ranging from felony drug charges to homicide.

DSM diagnosis
Upon admittance to the PPC, both a psychiatrist and a psychologist conduct an independent primary interview with the patient. The final DSM diagnosis is the result of a consensus diagnosis between these two professionals. As of January 1, 2017, the DSM-IV is replaced by the DSM-5 to classify the presence of a mental disorder. For a detailed description on the merging of DSM-IV and DSM-5 diagnoses, see Appendix A.
All diagnoses were used to establish the prevalence of mental disorders, including a "deferred diagnosis" either on axis I, axis II, or both. Diagnoses were deferred when it was not possible to conclude a diagnosis, whereas the presence of a mental illness seems likely. To make no assumptions about the presence of a mental disorder [21], we excluded deferred diagnoses from calculations on the prevalence of comorbidity, resulting in a sample size of n = 5,133 of comorbidity assessment.
The numerous DSM diagnoses had to be categorized for the network analysis, retaining both clinical relevance and an adequate sample size. See Appendix A for a detailed account of this categorization. Categories with an insufficient sample size (n < 20) that could not be merged without compromising clinical relevance were excluded from the network analysis. Some patients (n = 68) were exclusively diagnosed with disorders belonging to these small categories, resulting in exclusion. Data of 5,065 patients were included in the network analysis.

Statistical analyses
Descriptive statistics and prevalence rates were calculated using SPSS (v24; IBM, Armonk, NY). Network analyses were conducted in R.
Because of the binary nature of the data, the IsingFit package [23] was used to estimate the network parameters. Based on logistic regressions, the best-fitting function was selected using the extended Bayesian information criterion (EBIC), which has shown to estimate the most relevant features of a network successfully. To ensure the sparsity of the network and to cope with the problem of multicollinearity and multiple testing, all regression coefficients are penalized using eLasso, resulting in more conservative network structures. The hyperparameter, which determines the strength of this extra penalty, was set to 0.25 [24,25].
The resulting matrix was plotted using qGraph [26]. The network nodes represent categories of DSM diagnoses. The edges represent the reciprocal relations (AND rule) between the DSM diagnoses (i.e., the presence of comorbidity between diagnoses). Only positive estimates were included in the model to clearly describe patterns of comorbidity between diagnoses, as these relations are indicated by the positive edges. In the visualization of the network, the Fruchterman-Reingold algorithm was used, which places strongly connected nodes close to each other [25,27].
Possible clinical phenotypes, indicated by groups of nodes clustering together, were investigated using the Walktrap algorithm, which has shown to perform well in psychological networks [28].

Prevalence of mental illness and comorbidity
Prevalence rates of mental disorders are displayed in Table 1. Prevalence rates of comorbidity rates found in this sample are displayed in Table 2. In total, 56.9% of the patients had one or more comorbid diagnoses.

Network of DSM diagnosis
The final network model (see Figure 1) included DSM data of 5,065 patients in 31 categories of mental disorders. Thick edges represent strong correlations. Node names and sample sizes are listed in the legend. The network shows 18 connected categories and reveals four communities of mental disorders (connected groups of diagnostic categories).

Clusters of comorbidity
The largest community is formed by alcohol use, cannabis use, opioid use, and stimulant use disorders, and neurocognitive disorders. It accounts for 26.9% of all observations of DSM diagnoses within the network. This substance use group represents excessive substance use and its probable neurocognitive consequences. Both cannabis use disorders and stimulant use disorders are connected to antisocial personality disorder (ASPD). Furthermore, stimulant use disorder is connected to the node that represents attention-deficit/ hyperactivity disorder (ADHD), forming a bridge to the second group.
The second group is defined as the impulsivity group, accounting for 12.9% of all observations. It includes ASPD, narcissistic personality disorder, ADHD, borderline personality disorder, and polysubstance use. Besides high levels of impulsivity, this group includes patients portraying a lifetime pattern of antisocial behaviors. Polysubstance use forms a bridge to the third group by correlating with other and cluster B personality disorders. Another bridge to the third group is formed by the connections between ADHD and both autism spectrum disorders (ASDs) and other personality disorders.
The third group accounts for 12.5% of all observations and includes ASDs, cluster B personality disorders, cluster C personality disorders, other personality disorders, paraphilia, and pedophilia. This group might experience eccentric sexual preferences and could be expected to portray below-average social skills. Therefore, it is deemed the poor social skills group. It connects to the impulsivity group through several edges, including connections with ADHD, a disorder also often characterized by difficulties in social interactions.
The last connected group is the disruptive behaviors group and contains intellectual disabilities and disruptive, impulse-control, and conduct disorders. Intellectual disabilities connect to the poor social skills group via ASDs. The disruptive behaviors group could be characterized by many behavioral problems, most likely starting from a young age. The group's connection to ASD seems to support this, as ASDs have an early onset and individuals with these disorders often portray disruptive behaviors. The group constitutes 4.3% of all observations. Finally, several nodes remain unconnected within the network. Schizophrenia spectrum and other psychotic disorders contain the largest amount of all observations (30.1%) within the network. It is therefore viewed at the level of a community and defined as the psychotic disorders group.
The five described diagnostic groups sum up to 86.7% of all observed DSM diagnoses. The remaining nodes that are unrelated to the network represent 13.3%. European Psychiatry 3

Discussion
The results of this study revealed high levels of comorbidity within a sample of mentally ill prisoners. Taken together, 56.9% of the patients had one or more comorbid diagnoses. These results are in line with the sparse previous research on the prevalence rates of comorbidity within correctional settings [20,22], where it should be noted that these rates strongly vary across countries and specific settings. For example, in an older study in Quebec, Canada, researchers found that 386 of the 495 interviewed male prisoners suffered from a comorbid mental disorder, ranging from 84 to 94% for specific disorders [3]. High rates of comorbid mental disorders were also found in Chilean prisoners, where the highest rate of comorbid disorders (92%) was found for major depressive disorders [29]. Last, in their systematic review, Fazel and Seewald found ranges of 20-44% for the co-occurrence of substance misuse in prisoners with mental illness [20]. Our study presents a novel approach for modeling DSM diagnoses and comorbidity within this complex sample. Results of the network analysis show four distinctive diagnostic communities and one substantial distinctive unconnected diagnostic category. The finding that various addictive disorders tend to cluster together in the substance use group is not surprising. Studies have demonstrated high rates of comorbid SUDs [30], and its presence increases the risk of having another addictive disorder [31]. The connections between opioid, stimulant, and cannabis disorder are interesting, as these substances have an opposite effect. A possible explanation could be that one tries to attenuate vigorous effects of one drug with another [32]. In addition, the relationship between substance use and criminal behavior is a well-established one [33,34]. Consequently, the prevalence rates of SUD within prison samples are high [35,36], as was found in this study (43.1%).
The impulsivity group is described as impulsive and externalizing. Previous research indicates a relationship between ADHD and cluster B personality disorders [37,38] and increased rates of substance abuse in both disorders [38][39][40]. It has been proposed that the relation between ADHD and substance use is, partially, mediated by the presence of antisocial disorders [38]. In the current network, both ADHD and ASPD are "bridge-connections" to the substance Table 2. Prevalence rates of comorbid mental disorders in a sample of mentally ill offenders. use group and are also connected to each other. The connection of ADHD to stimulant use is interesting, as stimulants have been proposed to be used as self-medication by individuals with ADHD [41]. Finally, the strong connection between antisocial and narcissistic personality disorders should be noted. The disorders have shown many similarities and have been questioned as discrete conditions [42]. It is not hard to imagine how an individual belonging to the impulsivity group would be at risk of portraying criminal behavior given the described interplay of impulsivity, substance use, and antisocial personality structures.
The poor social skills group is defined as a group of belowaverage social skills and patients portraying eccentric sexual behaviors. The group shows the strongest correlations between the diagnostic categories it includes, which may be explained by the overlap in diagnostic criteria for personality disorders in the DSM-IV [43]. Of much interest is the connection between the cluster C personality disorders and the presence of a pedophilic disorder. These personality disorders seem to describe a shy and socially isolated sex offender, which may limit them in establishing intimate relationships [44], perhaps resulting in gravitation toward younger children. Also interesting is the connection between sexual disorders and ASDs. Unfortunately, not much is known about the possible relation between paraphilia, including pedophilia, and ASDs, but some research found some deviant sexual behaviors in young males with an ASD [45]. It seems that there are possible connections between sexual offending and mental disorders that are relevant to explore. Besides the obvious risk of criminal offending related to certain sexual dysfunctions, limited social skills have also been related to criminal offending [46]. The current results underline the possible importance of improving the social skills of the offenders within this group. It should be noted that this group also includes a small sample of cluster B personality disorders, a condition not usually described by substandard social skills. Given its position close to the impulsivity group, it is a bridge-connection to this group.
The disruptive behavior group is characterized by the presence of many behavioral problems, including aggressive and destructive behaviors. Previous research has indicated that individuals with an intellectual disability showed increased prevalence rates of ASDs and conduct disorders [47], and both connections are also found in the current model. Aggression and criminal behavior are associated with both intellectual disabilities in adults [48] and history of conduct disorder in patients with a severe mental illness [49]. When considering direct relationships between mental disorders, one could contemplate whether disruptive, impulse-control, and conduct disorders are, in some way, an expression of intellectual disabilities.
Finally, the most prevalent is the psychotic disorder group (56.7%). High rates of psychotic disorders in prison samples have been found by previous studies [20,21] and have been related to criminal [50][51][52] and often violent behavior [50,[53][54][55]. It should be noted that the psychotic disorder group is not connected to other diagnostic categories within the network model, even though a comorbid SUD is very common in psychotic disorders [22,52,56] and is seen as a major risk factor of violent behavior in psychotic individuals [57].
The five groups indicate that comorbidity is not only influenced by latent constructs, as is proposed by the common cause hypothesis. Although latent constructs could be derived from the findings of this study, it also shows how comorbidity can be a result of direct effects that various mental disorders impose on one another. The described groups provide a first step in the development of clinical phenotypes of mentally ill offenders based on their comorbid psychopathology.

Limitations
It should be noted that possible associations and patterns of comorbidity exist that are not represented in this sample or network. For example, a relation between the psychotic disorder group and the substance use group was expected. One explanation for its absence could be that clinical professionals are inclined to underdiagnose comorbid mental illness next to a psychotic disorder, as the presence of a florid psychosis may interfere with the diagnostic process. The high prevalence of deferred diagnoses (38.3%) seems to support this notion. Similar explanations could be possible for other absent connections.
The data used in this study are part of a large and unique cohort of mentally ill prisoners and are an accurate representation of the clinical practice. The data could, however, possibly obscure certain expected connections and prevalence rates. The absence of structurally gathered data for research purposes, for example, by using the Structured Clinical Interview for DSM-IV, is a significant limitation in this study.
An alternative explanation for the absence of expected relations between mental disorders is the conservative method of modeling. The use of eLasso highly penalizes connections in the network, and only reciprocal relations were included. Networks of the data modeled with more lenient methods indicated more connections, among them a connection between the psychotic disorder group and substance use group. However, a conservative method of modeling was deemed more fitting, given the exploratory nature of this study.

Future research
This study is a first attempt at modeling the structure of the comorbidity of DSM diagnoses of this complex sample by using a network analysis approach. Future research should focus on replication, optimization, and expansion of possible clinical phenotypes based on psychopathology, preferably using data gathered for research purposes. The development of clinical phenotypes is of great importance for the prevention of criminal behavior by mentally ill offenders as they could provide information about risk factors of criminal behavior associated with mental illness. This information could provide markers for early identification of individuals at risk of portraying criminal behavior as a consequence of the structure of their (comorbid) mental disorders.
Comorbidity has profound clinical effects. Treatment of clusters of psychopathology, taking into account interactions between comorbid disorders, may yield more results in improving mental health and reducing recidivism rates of mentally ill offenders. More knowledge on the structure of comorbidity is needed to develop treatment programs effectively targeting multiple disorders, or clinical phenotypes. This would not only benefit the forensic field, but also the field of psychiatry as a whole.
Financial Support. This research received no specific grant from any funding agency, commercial, or not-for-profit sectors.
Conflict of Interest. The authors declare that no conflicts of interest exist.
Data Availability Statement. The authors received permission from the Dutch Ministry of Justice and Security to access the data used in this study. However, they are unable to share the data as they are not the data custodians.

European Psychiatry 5
ICD-9 code referenced to fundamentally different descriptions of mental disorders within the versions of the DSM, we indicated to which version of the DSM the ICD-9 code included in the category refers. Thus, resulting in the following 31 categories: Tobacco use disorders (n = 17) 305.10 Tobacco use disorder. Nicotine dependence. Finally, three categories of mental disorders were excluded for other reasons than small sample size. ICD-9 codes 292.89 and 292.90 reference to a variety of substance-induced disorders. It was not possible to trace back to what specific description of mental disorders the codes had referenced to when diagnosed. Because of the diffuse character of the resulting category, it was excluded from further analysis. The category "Unspecified mental disorders" was excluded because of its indistinct nature; it provides no information on specific symptoms or behaviors related to the category. Keeping in mind the aim of the current study, to provide possible clinical phenotypes of psychopathology within this population, the variable would not have contributed to this goal.