Master Thesis Research Master of Psychology
Patterns of Aggressive Behavior in Dutch Psychiatric Inpatients with
Psychotic Disorders using Markov Models
Joël Layla Derks, MSc University of Amsterdam
Student number: 10155880
Research group: Clinical Psychology
Supervisor UvA: dr. Lindy-Lou Boyette and dr. Lourens Waldorp Supervisor AMC (external): Jentien Vermeulen, MD
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Patterns of Aggressive Behavior in Dutch Psychiatric Inpatients with Psychotic
Disorders using Markov Models
Joël Layla Derks, MSc
Aggressive behavior is a common problem in psychiatric inpatients and often leads to physical harm to patients and health care professionals. Aggression and measures against aggression (e.g. forced medication, restraint measures) can also be highly emotionally impactful, and even traumatic, for both aggressive patients and their fellow patients (Frueh et al., 2005). Additionally, inpatient aggression can lead to emotional and psychological problems in health care staff (Wildgoose, Briscoe, & Lloyd, 2003), including posttraumatic stress disorder (Needham, Abderhalden, Halfens, Fischer, & Dassen, 2005; Richter & Berger, 2006). Individuals with psychotic disorders are especially at risk for behaving aggressively (Barlow, Grenyer, & Ilkiw‐Lavalle, 2000); Fazel, Långström, & Lichtenstein, 2009; Saha, Chant, & McGrath, 2007).
A number of studies investigated the prevalence of different types of aggression in inpatients with psychotic disorders. According to Kay et al. (1988), aggression can be categorized in four types of aggression: verbal aggression, physical aggression against objects, physical aggression against oneself, and physical aggression against others. These four types of aggression will be further referred to as
verbal aggression, object aggression, auto-aggression and physical aggression. To assess the four types
of aggression in psychiatric patients, Kay et al. developed the Modified Overt Aggression Scale (MOAS) – a modification of the Overt Aggression Scale (Yudofsky et al., 1986).
By reviewing hospital charts of inpatients with first episode psychosis with the MOAS, Foley et al. (2005) found that in the time span of one week, 17% of the patients showed some sort of aggressive behavior. Of these patients, 9% showed verbal aggression, 5% showed object aggression, 4% showed auto-aggression, and 8% showed physical aggression. As the cumulative chance of the occurrence of the different types of aggression is higher than the percentage of patients that were aggressive, we can conclude that some patients showed more than one type of aggression. This raises the question how the different types of aggression are interrelated. Almvik et al. (2000) used the Broset Violence
Objective: Aggression in inpatients with psychotic disorders causes harm to patients and health care professionals. Previous research focused on the incidence and co-occurrence of different types of aggression but lacks insight on how different types of aggression follow one another.
Methods: Aggressive behavior of 120 inpatients with psychotic disorders -admitted to the psychiatric ward of the Academic Medical Centre of Amsterdam (AMC)- was assessed by retrospectively reviewing patients’ charts with the Modified Overt Aggression Scale (MOAS). Behavioral sequences of verbal aggression, physical aggression against objects, physical aggression against oneself and physical aggression against others were analyzed by using Markov models, providing probabilities of transferring from one type of aggression to another.
Results: Markov models showed that when patients
behave aggressively, they are -in the next moment- likely to either show the same type of aggression or to be non-aggressive. They are, however, unlikely to subsequently show another type of aggression. When this does occur, it is most likely to be verbal aggression. Non-aggressive behavior is very unlikely to result in physical aggression or aggression against objects.
Conclusion: This study pioneered in investigating
sequences of aggressive behavior by using Markov models, thereby putting across another perspective on short-term risk assessment of aggressive behavior in patients with psychotic disorders. Markov models could become a simple tool for making quick evidence-based estimations of subsequent aggressive behavior in psychiatric hospitals.
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Checklist (BVC) -a commonly used and well validated screener of inpatient’s aggression in clinical practice (e.g. Abderhalen et al., 2004; Abderhalen et al., 2008)- to show that verbal aggression and object aggression were more prevalent in a group of patients that behaved physically aggressive in comparison to a group of patients that weren't physically aggressive. However, a study on the predictive power of the separate items of the BVC, identified verbal aggression but not object aggression as an evident predictor of physical aggression (Ogloff & Daffern, 2006). Another study found the same result in a 24-hour time frame (Björkdahl, Olsson, & Palmstierna, 2006). Steinert et al. (1999) found that inpatients with psychotic disorders who showed outward directed aggression (i.e. verbal aggression, object aggression, and physical aggression) during their first admission, where more likely than others to behave aggressively during subsequent admissions. Verbal aggression was most strongly related to physical aggression during subsequent admissions. Furthermore, outward directed aggression did not predict auto-aggression during subsequent admissions. Contrary to this finding, several studies in psychiatric populations show that suicide and suicide attempts -extreme manifestations of auto-aggression- correlate positively with physical aggression (e.g. Gvion & Apter, 2011; Keilp et al., 2006; Sher et al., 2005), also in patients with psychotic disorders (Cohen, Lavelle, Rich, & Bromet, 1994; Hunt et al., 2006; Iancu et al., 2010; Suokas et al., 2010; Witt, Hawton, & Fazel, 2014).
Although the co-occurrence of some of the different types of aggression have been studied, not all types of aggression have been investigated in relation to one another, especially in a population of inpatients with psychotic disorders. Furthermore, studies report conflicting results on whether and how the types of aggression are related. This might be explained by the big differences in used research methods. Most studies do not assess all types of aggression by the same means (e.g. self-report, staff report, criminal records, behavioral observations) within the same time scales (e.g. weeks, months, life history). Mostly, large time scales are used. Although these studies provide useful knowledge about relationships between different types of aggression (on the long term), they might not always help health care professionals in making risk assessments of aggression on a day-to-day basis. According to previous research, aggression on day one predicts aggression on day two, but not on day three. This finding stresses the need for reliable short-term predictions of aggression (Clarke, Brown, & Griffith, 2010). More insight on how different types of aggression succeed one another could help health care staff in estimating the risk of subsequent aggressive behavior.
The current study aims to gain a better understanding of aggressive behavior patterns in inpatients with psychotic disorders by analyzing sequences of the four types of aggressive behavior. In order to investigate aggressive behavior sequences of inpatients with psychotic disorders, we retrospectively categorized all reported behavior in the patients' hospital charts by means of the MOAS into one of five states concerning aggression: no aggression, verbal aggression, object aggression, auto-aggression, and physical aggression. Through innovative use of Markov models, we quantified the risk for each type of aggression to take place, based on the type of (aggressive) behavior that took place the previous moment. To our knowledge, no previous studies used Markov models to investigate human (aggressive) behavior. Markov models estimate transition probabilities: the chance of observing a particular behavior given the previous behavior. Markov models thereby enable us to investigate whether and in what frequency different types of aggression follow one another.
Two Markov models were computed. The first model included all aggressive states (including the state of no aggression), thereby showing how observations of no aggression and aggressive observations follow themselves and one another. The second model excluded the state of no aggression, thereby showing how different types of aggression follow one another given that inpatients show some type of aggressive behavior.
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Although aggression has a relatively high prevalence in inpatients with psychotic disorders, we argue that patients are not aggressive for most of the time, even patients that are aggressive most frequently during admission. Therefore, we firstly expected that if a patient is not aggressive, chances are very low that the patient will be aggressive the next moment (i.e. low transition probability of no aggression to all types of aggression). Furthermore, we expect that when a patient is aggressive, chances are high this patient won't be aggressive the next moment (i.e. high transition probability of all types of aggression to no aggression). Second, we expected that the chance that verbal aggression is followed by physical aggression is higher than the chance that object aggression is followed by physical aggression (i.e. the transition probability of verbal to physical aggression is higher than the transition probability from object to physical aggression), as previous research showed that verbal aggression is a stronger predictor of physical aggression than object aggression. We inspected the other transition probabilities (i.e. between verbal aggression, object aggression, auto-aggression and physical aggression) in an exploratory fashion, as findings of previous research are too inconsistent to form valid expectations.
Additionally, the current study investigated exploratory whether substance abuse and gender influence aggressive behavior sequences. Substance abuse is highly prevalent in patients with psychotic disorders (e.g. Bell, Greig, Gill, Whelahan, & Bryson, 2002; Enticott et al., 2008; Kaladjian et al., 2011) and has been related to all types of aggression in both clinical and non-clinical populations, including people with psychotic disorders (Spidel, Lecomte, Greaves, Sahlstrom, & Yuille, 2010; Suokas et al., 2010). Also gender plays a role in the occurrence of aggressive behavior: aggressive behavior is not only found to be generally more prevalent in men than in women, the difference between men and women for physical aggression is found to be greater than for verbal aggression (Archer, 2004; Hyde, 1986).
2. METHODS 2.1 Procedure
The data of this study was collected by means of retrospective chart review of hospital charts of inpatients with psychotic disorders (i.e. schizophrenia; schizophreniform disorder; schizoaffective disorder; brief psychotic disorder; psychotic disorder not otherwise specified (NOS)). Patients were discharged from the open or closed ward of the AMC – a tertiary hospital in the Netherlands – in the years 2014 and 2015. During hospitalization, a psychiatrist, physician or nurse documented detailed information about the patient's behavior in a personal chart, at least three times a day. The occurrence of any aggressive event was always reported in the hospital chart of the concerned patient. The first author of the current study -a psychologist- retrospectively reviewed charts on aggressive events using the MOAS. Charts also contained reports of clinical admission and discharge interviews. A physician -supervised by a psychiatrist- performed the clinical interviews shortly after admission and before discharge. Demographic information and diagnoses according to the Diagnostic and Statistical Manual of Mental Disorders Fourth edition (DSM-IV; American Psychiatric Association, 2000) were derived from these reports. The data of this study was collected as part of a study on patient safety of psychiatric inpatients of the AMC. This study was submitted to the Medical Ethics Committee of the AMC (METC AMC) and was granted exemption of the Dutch Human Research Act (WMO, 1999). We used anonymized data for analysis and reporting.
2.2 Measures
Aggressive behavior during hospitalization was measured by the Modified Overt Aggression Scale (MOAS; Kay et al., 1988), a modification of the Overt Aggression Scale developed by Yudofsky et al.
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(1986). The MOAS is a clinical-based behavior rating scale designed to measure aggressive behavior. The MOAS consists of four scales that represent the aforementioned four types of aggression. By reviewing patient’s charts, the first author retrospectively scored the four scales of the MOAS on at least three occasions per day. For each occasion, the MOAS was used to assess which state of aggressive behavior was present (i.e. verbal aggression, object aggression, auto-aggression, physical aggression or no aggression). If two types of aggression were present in one chart note, this was coded as two occasions, where the first aggressive behavior in time was the first occasion and the second aggressive behavior in time was the second occasion. The scales of the MOAS are constructed as five-point Likert scales, ranging from 0 to 4 where a higher score represents more severe aggressive behavior. For example, a score of 1 on the verbal aggression scale represents "Shouts angrily, curses mildly, or makes personal insults", and a score of 4 represents “Threatens violence toward others or self repeatedly or deliberately”. The scores on the four scales of the MOAS can be used to derive a weighted sum score, that accounts more weight to more severe types of aggression. Kay et al. ranked severity of the four types of aggression in the following order: verbal aggression, object aggression, auto-aggression and physical aggression.
In the current research, only the individual aggression scales and not the sum score were used, as we wished to investigate the individual types of aggression. Because Markov models do not allow to account for severity within each type of aggression, we dichotomized the four scales of aggression. For each scale, a score of 1 or higher indicated aggressive behavior of the corresponding type of aggression. If no score of 1 or higher was present, this was indicative of the state of no aggression.
2.3 Data analysis 2.3.1 Markov models
Markov models assume that a patient is always in one of a finite number of states. In the current study, the states encompass the four types of aggressive behavior and the state of no aggression. Markov models compute transition probabilities between states and within state transition probabilities. A transition probability is the probability of entering a state based on the prior state. For example, a transition probability from verbal aggression to object aggression against objects of 0.4 can be interpreted as a 40% chance that a patient will show object aggression, when the previous state of that patient was verbal aggression. A within state transition probability represents the probability of staying in the same state instead of entering another state.
One four-state Markov model and one three-state Markov model were fitted to the data. The four-state Markov model included the states of verbal aggression, object aggression, physical
aggression and no aggression. Initially, both the four- and three-state Markov models were supposed
to include the state of auto-aggression. However, observations of auto-aggression turned out to be very scarce (0.1% of the observations) and did not lead to reliable model predictions. Therefore, observations of auto-aggression were left out of both models. The four-state Markov model included all observations of patients who behaved aggressive at least at one instance. The three-state Markov model excluded observations of no aggression in order to look more closely to the transitions from one type of aggression to another type of aggression. Therefore, the transition probabilities of the three-state Markov model do not predict the next observation, but predict the next aggressive observation. Additionally, we tested whether the four-state and three-state model fitted better to the data if the covariates gender and substance abuse were added to the model.
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2.3.2 Statistical procedure
For each Markov model, we assumed that all aggressive states were reported in the hospital charts and that thereby each state transition was coded. We added this information in the models by specifying that the time points of our observations reflect the exact times of transition (and no states are possibly left out). We computed the models by means of the msm-package (Jackson, 2011) that operates in the statistical software R (R Development Core Team, 2010). In order to be able to generalize and take subject specific covariates (i.e. substance abuse, gender) into account, we analyzed the Markov model on all patients simultaneously.
The Log Likelihood test and the Akaike information criterion (AIC) were used to compare model fit of the Markov models with and without the covariates of substance abuse and gender. If models did not differ in model fit, the most parsimonious model (i.e. model without covariates) was used for interpretation.
3. RESULTS
3.1 Sample characteristics
In total, the charts of 120 inpatients were reviewed (77 men and 43 women). The mean age was 33.4 ± 12.6. Of the 120 inpatients, 73 were diagnosed with schizophrenia, 4 with schizophreniform disorder, 13 with schizoaffective disorder, 1 with brief psychotic disorder and 29 with psychotic disorder NOS. On average, patients were observed 124.8 ± 107.6 times. In total, 14973 observations were encoded. Of the 120 patients, 55 patients (46%) showed some type of aggression during admission.
Table 1 shows the number of observations per type of aggression in the total sample and in the group
of patients that did show at least one aggressive event. Patients showed aggressive behavior in 3.5% percent of the observations. Verbal aggression was the most prevalent type of aggression and auto-aggression was the least prevalent type of auto-aggression. Patients who showed at least one aggressive event, were aggressive 6.3% percent of the observations.
TABLE 1. Number of observations and percentages per type of aggression
Type of aggression Total sample (N = 14973) Patients with at least one aggressive event (N = 7778)
N % of the total number of observations
N % of the total number of observations No aggression 14452 96.5% 7257 93.3% Verbal 350 2.3% 350 4.5% Object 88 0.6% 88 1.1% Auto-aggression* 10 0.1% 10 0.1% Physical 73 0.5% 73 0.9% Total 14973 100% 7778 100%
Note. The total sample consisted 120 patients, and the patient group with at least one aggressive event
consisted of 55 patients.
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3.2 Markov models
3.2.1 Four-state Markov model: all observations of patients with at least one aggressive event
A four-state Markov model (i.e. no aggression, verbal aggression, object aggression, physical
aggression) was fitted on the 7778 observations of the 55 patients who showed at least one aggressive
event. See Table 2 for the model descriptives and statistics and Figure 1 for the Markov chain with the transition probabilities for the four states. The state to state transition rates and transition probabilities can be found in Appendix A.
Figure 1. Four-state Markov chain with transition probabilities between the states of no aggression, verbal aggression, object aggression and physical aggression. The numbers on the arrows reflect
transition probabilities. object = object aggression, physical = physical aggression, verbal = verbal aggression.
Note. Due to rounding up to two decimals, the sum of all the transition probabilities of one state to
the other states and the within state probability of that state is not always exactly 1.
When evaluating the four-state Markov model, a very high within state transition probability of no aggression was observed (.97), probably resulting from the high number of observations of no
aggression. For any type of aggressive behavior, the probability of subsequent similar aggressive
behavior was nearly a half. Furthermore, transition probabilities from verbal, object and physical
aggression to no aggression were also reasonably high (respectively .44, .36, .40), whereas the
probabilities from no aggression to verbal, object and physical aggression were very small (respectively .002, .00, .00). The transition probability from no aggression to either object or physical aggression approached zero, showing that the chances of no aggression being followed by object or physical
aggression were extremely small. Transition probabilities between verbal, object and physical aggression were quite low (ranging from .03 to .16). In particular, probabilities between object and physical aggression and from verbal aggression to either object or physical aggression were low
(ranging from .03 - .05). Contrary to our expectations, the transition probability from verbal to physical
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TABLE 2. Descriptives and statistics of the four-state Markov model based on 7778 observations
Markov model* df Log Lik. Δdf χ2 p AIC
Four-state model 12 -2209.7 - - - 4443.4
Four-state model with gender 24 -2191.8 12 35.7 <.001 4431.6
Four-state model with substance abuse 24 -2189.6 12 40.2 <.001 4427.2 Four-state model with gender and substance abuse 36 -2172.1 24 75.2 <.001 4416.2
*All models with added covariate(s) are compared to the four-state model without covariates
The covariates of gender and substance abuse were added to the four-state model. See Table
2 for the model descriptives and statistics. The lower AIC of the covariate model and the Log Likelihood
ratio test suggested that adding the covariates to the model resulted in a better model fit.
Although the model with the covariates of gender and substance abuse was significantly better than the model without covariates, differences between transition probabilities of the different models were very small. The different Markov chains per subgroup (males vs. females; substance abusers vs. non substance abusers) can be found in Appendix B. When evaluating the model, two main differences in the transition probabilities of men and women were found. Males (both with and without a diagnosis of substance abuse) had higher transition probabilities from physical aggression to no aggression compared to women (.40; .46 vs. .31; .35), whereas women (both with and without a diagnosis of substance abuse) had a higher transition probability from physical aggression to verbal aggression compared to men (.12; .13 vs. .21; .21). Furthermore, one main difference between patients with and without a diagnosis of substance abuse was found. Patients with a diagnosis of substance abuse (both males and females) had a higher transition probability from verbal aggression to object aggression compared to patients without a substance abuse diagnosis (.08; .12 vs. 0.02; 0.03).
3.2.2. Three-state Markov model: aggressive observations of patients with at least one aggressive event
A three-state Markov model (i.e. verbal aggression, object aggression, physical aggression) was fitted on the 502 observations of aggressive behavior (i.e. 343 observations of verbal aggression, 87 observations of object aggression and 72 observations of physical aggression). See Table 3 for the model descriptives and statistics and Figure 2 for the Markov chain with the transition probabilities for the three states. The state to state transition rates and transition probabilities can be found in
Appendix A.
Figure 2. Three-state Markov chain with transition probabilities between the states of verbal aggression, object aggression and physical aggression. Numbers on the arrows reflect transition
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When evaluating the three-state Markov model, within state probabilities of verbal, object and
physical aggression were the highest in the model (respectively .83, .55, .48). Transition probabilities
from object and physical aggression to verbal aggression were reasonably high (respectively .34, .44), whereas the probabilities from verbal aggression to object and physical were fairly small (respectively .09, .08). Also, transition probabilities between object and physical aggression were quite small (.11 from object aggression to physical aggression; .08 from object aggression to physical aggression). Contrary to our expectations, the transition probability from verbal to physical aggression was smaller than the transition probability from object to physical aggression.
TABLE 3. Descriptive statistics of the four-state Markov model based on 502 observations
Markov model* df Log Lik. Δdf χ2 p AIC
Three-state model 6 -440.4 - - - 892.8
Three-state model with gender 12 -435.4 6 10.1 .119 894.7
Three-state model with substance abuse 12 -431.8 6 17.6 .008 887.5
Three-state model with gender and substance abuse 18 -428.0 12 24.8 .016 892.1
*All models with added covariate(s) are compared to the three-state model without covariates Again, the covariates of gender and substance abuse were added to the model. See Table 3 for the model descriptives and statistics. The small difference in AIC and the non-significant Log Likelihood ratio test suggested that adding gender to the model did not result in a better fit. The lower AIC of the model with substance abuse and the Log Likelihood ratio test suggested that adding substance abuse to the model resulted in a better model fit. Adding both gender and substance abuse to the model resulted in a better fit according to the Log Likelihood ratio test. However, the model with two covariates had a higher AIC than the model with only substance abuse as a covariate. Therefore, we decided to choose the most parsimonious model with the lowest AIC: the three-state model with substance abuse as a covariate. Overall, differences between the transition probabilities of substance abusers and non-substance abusers were very small. The different Markov chains per subgroup (substance abusers vs. non substance abusers) can be found in Appendix C. Two main differences in the transition probabilities of patients with and without a diagnosis of substance abuse were observed. Patients with a diagnosis of substance abuse had a higher transition probability from verbal aggression to object aggression (.18 vs. .06) and a lower within state probability of verbal aggression compared to patients without a diagnosis of substance abuse (.74 vs. .86).
3.2.3 All observations of all patients
Originally, we planned to compute another Markov model on the observations of all patients. However, there was not enough variance to compute the model, as almost all the observations consisted of events that involved no aggression (96.5 % of the observations).
4. DISCUSSION
The aim of this study was to model behavior patterns of types of aggression in inpatients with psychotic disorder. For patients with psychotic disorders who showed aggression at least once, the four-state Markov model showed that patients with psychotic disorders were very unlikely (3%) to behave aggressively if they weren't aggressive the previous moment. This can be explained by the low incidence of aggression overall: patients showed aggressive behavior at only 7% of the observations. In the rare case that non-aggressive behavior was followed by aggressive behavior, this aggression was
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almost always verbal aggression. Thus, non-aggressive behavior was very unlikely to be followed by object or physical aggression. When verbal aggression occurred, chances were still quite small that object or physical aggression followed verbal aggression (4%; 4%). Chances were also small that patients went from object aggression to physical aggression and vice versa (5%; 3%). When patients showed aggressive behavior, they were most likely to show the same type of aggression the next moment (42-47%), although they were almost as likely to behave non-aggressively the next moment (36-44%). In conclusion, the model indicates that when patients with psychotic disorders behave aggressively, they are likely to either show the same type of aggression or to be non-aggressive the next moment. They are, however, unlikely to show another type of aggression the next moment. These findings are in line with research of Steinert et al. (1999) that showed that aggression can predict subsequent aggression. Where Steinert et al. (1999) showed that this was the case for subsequent admissions, the current study showed this is also true for very short time intervals. The current findings also provide additional knowledge about the relationship between the different types of aggression: each type of aggressive behavior is likely to follow itself but unlikely to follow another type of aggression.
The three-state Markov model gives a closer look on how likely the different types of aggression are to follow one another by filtering out all observations where no aggression occurred. Notably, most of the observations in this model were of verbal aggression (68%). Therefore, the chances were high (83%) that patients with psychotic disorders were verbally aggressive if they were verbally aggressive at the previous aggressive observation. The high incidence of verbal aggression also explains the finding that patients were unlikely to go from verbal aggression to object or physical aggression (9%; 8%) and that patients were quite likely to go from object or physical aggression to verbal aggression (34%; 44%). However, object and physical aggression were more likely to be succeeded by itself (55%; 58%). Patients were unlikely to go from object aggression to physical aggression and vice versa (8%; 11%). Thus, the model indicates that patients with psychotic disorders are inclined to show the same type of aggression consecutively, even so when this aggression is intermitted by periods of time where aggression is absent. Furthermore, patients with psychotic disorders are likely to go from object or physical aggression to verbal aggression, but object and physical aggression are not likely to precede one another.
With respect to the covariates of gender and substance abuse, we found that gender and diagnosis of substance abuse improved the model fit of the four-state model. This indicates that men and women and substance abusers and non-substance abusers show different patterns of aggressive behavior. The three-state model showed that only substance abuse improves the fit of the model, indicating that only substance abusers and non-substance abusers show different patterns of aggressive behavior. The finding that gender plays a role in the four-state model but not in the three-state model indicates that the differences between males and females are most profound in the transition from and to the state of no aggression. Overall, the differences between the models with and without covariates are too small to draw valid conclusions about differences in transition probabilities. The results do however support the idea that gender and substance abuse play a role in aggression in patients with psychotic disorders, but the specific interplay between these covariates and aggression sequences remain to be investigated in further detail. Larger subgroups of males and females and substance abusers and non-substance abusers might make differences between the groups more apparent.
Contrary to our expectations, the transition probability from verbal to physical aggression was smaller than the transition probability from object to physical aggression. This suggests that object aggression is a stronger indicator of subsequent physical aggression than verbal aggression. This
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finding seems to contradict previous research that indicates that verbal aggression is a more evident predictor of physical aggression in comparison to object aggression (Björkdahl, Olsson, & Palmstierna, 2006; Ogloff & Daffern, 2006). The incidence of verbal aggression was substantially higher than the incidence of object and physical aggression, inherently making the transition probabilities from verbal aggression to other types of aggression smaller. Looking at the number of transitions from verbal to physical aggression and object to physical aggression, we found that there were more instances where physical aggression was preceded by verbal aggression than by object aggression. This is probably why the previous mentioned studies found verbal aggression to be a better predictor of physical aggression than object aggression. However, the higher transition probabilities between object and physical aggression indicate that when object aggression is observed physical aggression is more likely to occur than when verbal aggression is observed. Thus, object aggression is a more specific but less common predictor of physical aggression than verbal aggression.
This finding shows how the use of Markov models can put across a different perspective on the short-term complex interactions of aggressive behavior. Markov models provide the probability that a type of aggression will occur based only on the previously observed type of aggression, and thereby forms short-term predictions of subsequent aggressive behavior. Prior research into prediction of aggression mostly looked at longer periods of time. Hence, both techniques provide unique information about aggressive behavior patterns.
An important limitation of the current study is the retrospective assessment of aggressive behavior. Although mental health care staff is obliged to report every aggressive incident, patients charts are not designed to assess aggressive behavior and might lead to underestimation of the incidence of aggression. Recall bias may have especially influenced the reported incidence of less severe types of aggression (i.e. verbal aggression) as staff members might attribute less importance to these behaviors. On the other hand, research shows that when nurses are asked to actively report aversive events, events are ten times less likely to be detected than when medical charts are reviewed (Classen et al., 2011). Another limitation involves the chart reviewing process. Charts were only reviewed by one person that was aware of the hypothesis of the study. However, the MOAS has been found to have a high inter-rater reliability (0.85-0.98; Kay, Wolkenfeld, & Murrill, 1988; Spidel et al., 2010; Steinert, Sippach, & Gebhardt, 2000) and the high number of observations per patient and the complexity of the statistical procedure underlying the hypothesis made it less likely that the data was biased by the reviewer. Another shortcoming in the reviewing was that we dichotomized the scales of the MOAS, therefore not taking severity of aggression into account. We deliberately chose not to include severity of aggression as this would result in a very complex Markov model with 13 states (i.e. three levels of severity for each type of aggression plus the state of no aggression) and 169 transition probabilities. As this is the first study using Markov models in aggressive behavior, we decided that a less complex model would be more interpretable at this stage and more useful in clinical practice. Lastly, we did not have enough observations of auto-aggressive behavior to include auto-aggression in the Markov models. Future research could focus on replicating the current study in a larger patient sample from multiple health care centers, therefore including more (auto-)aggressive events. A larger dataset would also enable to look in more detail to the influence of severity of aggression and the influence of gender and substance abuse on aggression. Furthermore, a multicenter study would make generalizations to other health care institutions more valid.
In conclusion, the current study investigated sequences of aggressive behavior in inpatients with psychotic disorders by making innovative use of Markov model techniques. We found that inpatients with psychotic disorders show very little aggression overall. When patients do behave aggressively, they are likely to either show the same type of aggression or to be non-aggressive the
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next moment. They are, however, unlikely to show another type of aggression subsequently. Furthermore, non-aggressive behavior is very unlikely to be followed by object or psychical aggression and object and physical aggression are unlikely to precede one another. When the Markov chains of the current study are replicated in a larger sample in multiple health care centers, they can serve as a simple tool for evidence-based risk assessment of subsequent aggressive behavior in psychiatric hospitals that treat inpatients with psychotic disorders.
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Appendix A. Tables of transition rates and transition probabilities from state to state
TABEL A.1. Transition rates between the stages of for the four-state model. Type of aggression From
no aggr. verbal object physical
To no aggr. 6923 232 32 25
verbal 213 74 32 31
object 30 19 21 9
physical 37 25 3 8
No aggr. = no aggression
Note. The transition rate is the number of instances where a patients went from one state to
another.
TABEL A.2. Probability matrix: transition probabilities between the stages of for the four-state model
Type of aggression From
no aggr. verbal object physical
To no aggr. .970 .023 .004 .003
verbal .443 .472 .044 .042
object .363 .113 .474 .050
physical .398 .157 .026 .419
No aggr. = no aggression
TABLE A.3. Transition rates between the stages of for the three-state model. Type of aggression From
verbal object physical
To verbal 230 46 38
object 36 29 14
physical 45 7 12
Note. The transition rate is the number of instances where a patients went from one state to
another.
TABLE A.4. Probability matrix: transition probabilities between the stages of for the three-state model
Type of aggression From
verbal object physical
To verbal .821 .099 .080
object .334 .562 .104
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Appendix B. Four-state Markov chains of males and females with and without a diagnosis of substance abuse
Figure A.1. Four-state Markov chain of male patients with a diagnosis of substance abuse.
Figure A.2. Four-state Markov chain of male patients without a diagnosis of substance abuse.
Figure A.3. Four-state Markov chain of female patients with a diagnosis of substance abuse.
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Appendix C. Three-state Markov chains of patients with and without a diagnosis of substance abuse
Figure B.1. Three-state Markov chain of patients with a diagnosis of substance abuse.
