Article critique: Binary logistic Regression

published: 12 June 2018

doi: 10.3389/fpsyt.2018.00258

Frontiers in Psychiatry | 1 June 2018 | Volume 9 | Article 258

Edited by:

Meichun Mohler-Kuo,

University of Applied Sciences and

Arts of Western Switzerland,


Reviewed by:

Eric Noorthoorn,

GGNet Mental Health Centre,


Raoul Borbé,

Universität Ulm, Germany


Florian Hotzy

[email protected]

Specialty section:

This article was submitted to

Public Mental Health,

a section of the journal

Frontiers in Psychiatry

Received: 08 November 2017

Accepted: 24 May 2018

Published: 12 June 2018


Hotzy F, Theodoridou A, Hoff P,

Schneeberger AR, Seifritz E, Olbrich S

and Jäger M (2018) Machine

Learning: An Approach in Identifying

Risk Factors for Coercion Compared

to Binary Logistic Regression.

Front. Psychiatry 9:258.

doi: 10.3389/fpsyt.2018.00258

Machine Learning: An Approach in
Identifying Risk Factors for Coercion
Compared to Binary Logistic

Florian Hotzy1*, Anastasia Theodoridou1, Paul Hoff1, Andres R. Schneeberger2,3,4,

Erich Seifritz1, Sebastian Olbrich1 and Matthias Jäger1

1 Department for Psychiatry, Psychotherapy and Psychosomatics, University Hospital of Psychiatry Zurich, Zurich,

Switzerland, 2 Psychiatrische Dienste Graubuenden, Chur, Switzerland, 3 Universitaere Psychiatrische Kliniken Basel,

Universitaet Basel, Basel, Switzerland, 4 Department of Psychiatry and Behavioral Sciences, Albert Einstein College of

Medicine, New York, NY, United States

Introduction: Although knowledge about negative effects of coercive measures in

psychiatry exists, its prevalence is still high in clinical routine. This study aimed at define

risk factors and test machine learning algorithms for their accuracy in the prediction of

the risk to being subjected to coercive measures.

Methods: In a sample of involuntarily hospitalized patients (n = 393) at the University

Hospital of Psychiatry Zurich, we analyzed risk factors for the experience of coercion

(n = 170 patients) using chi-square tests and Mann Whitney U tests. We trained machine

learning algorithms [logistic regression, Supported Vector Machine (SVM), and decision

trees] with these risk factors and tested obtained models for their accuracy via five-fold

cross validation. To verify the results we compared them to binary logistic regression.

Results: In a model with 8 risk-factors which were available at admission, the SVM

algorithm identified 102 out of 170 patients, which had experienced coercion and 174

out of 223 patients without coercion (69% accuracy with 60% sensitivity and 78%

specificity, AUC 0.74). In a model with 18 risk-factors, available after discharge, the

logistic regression algorithm identified 121 out of 170 with and 176 out of 223 without

coercion (75% accuracy, 71% sensitivity, and 79% specificity, AUC 0.82).

Discussion: Incorporating both clinical and demographic variables can help to estimate

the risk of experiencing coercion for psychiatric patients. This study could show that

trained machine learning algorithms are comparable to binary logistic regression and

can reach a good or even excellent area under the curve (AUC) in the prediction of

the outcome coercion/no coercion when cross validation is used. Due to the better

generalizability machine learning is a promising approach for further studies, especially

when more variables are analyzed. More detailed knowledge about individual risk factors

may help to prevent the occurrence of situations involving coercion.

Keywords: coercion, seclusion, restraint, coercive medication, involuntary hospitalization, machine learning

mailto:[email protected]

Hotzy et al. Machine Learning and Coercion


The use of coercive measures (e.g., seclusion, physical and
mechanical restraint, forced medication) in psychiatric patients is
a massive invasion in their integrity and freedom. As a result, the
usage of coercion is controversially discussed since the beginning
of modern psychiatry and certain approaches have tried to reduce
its rates (1). Although some of those approaches were successful,
there are still many patients in which coercion is used. Often the
usage of coercion seems necessary when the patients are a danger
for themselves or for others due to an underlying psychiatric
disorder (2, 3). These situations are always associated with an

ethical dilemma. On one side coercion shall help to protect the
patient’s or other’s integrity (2, 3). On the other hand it restricts
the freedom of the person which is one of the basic human rights
(4). Being a threat to oneself or others may have different reasons
in psychiatric patients. In some situations patients are delusional
and feel threatened by others which leads to the reaction to
protect themselves and can result in threats to other patients or
staff (5). Also in situations where the patients are threatening
themselves or have suicidal ideations caused by the symptoms
of their psychiatric disorder, coercive measures might become
necessary to secure the patients survival.

The use of coercion distinguishes psychiatry from other
medical disciplines where informed patients can decide to accept
or reject a specific measure. Psychiatry at one hand aims to help

the patients to develop a self-determined life without burden of
psychiatric symptoms. On the other hand psychiatry is legally
determined to reject the patients freedom to move (involuntary
hospitalization) but also the freedom to reject a specific measure
(forced medication, physical or mechanical restraint, seclusion)
if harm to self or others has to be disrupted.

It is obvious that such situations are challenging for the
patients but also for the therapeutic team. Those challenges
were topic of previous studies where it was shown that patients
who experienced coercive measures often describe feelings of
helplessness (6, 7), fear (8), anger (9, 10) and humiliation

(11). Due to that, some patients stated to avoid searching for
psychiatric help in a crisis (12, 13). On the other hand there
were some patients who retrospectively agree with the coercive
measure (7, 9) and state that they would like to be forced into
treatment again in the case of a future crisis (14). These contrary
findings underline the controversy of this topic.

It was the goal of earlier studies to understand which patients
experience coercion and to characterize their clinical, but also
their socioeconomic features. Gaining better understanding of
risk factors to experience coercion was thought to be helpful in
the development of therapeutic strategies for patients at risk and
thus, to reduce the prevalence of coercion.

During the last years specialized psychiatric intensive care
units (PICU) had been the center of extensive research and it
could be shown that some patient characteristics are associated
with the transfer from a general psychiatric unit to a PICU
and with the usage of coercion on these specialized wards
(15). Furthermore psychotic disorders were shown to be
frequently associated with coercion (16–24). Also personality
disorders (25, 26), substance-use-related disorders (19) and

mental retardation (25) were found to be associated with
coercion. A history of aggression (16–18, 22, 23, 25, 27–
29) was frequently found to be associated with coercion and
violence/threats were described to be the second most frequent
reasons after agitation/disorientation for the usage of coercion
(30). Patients with a history of former voluntary and/or
involuntary commitments (IC) and frequent hospitalizations
(16–20, 24) and those with longer duration of hospitalizations
(31) were also described to experience coercion more often.
Those factors were described nearly uniformly throughout
literature. Whereas other factors like male (20, 23–25, 32, 33)
and female gender (22, 29) or younger (19, 20, 23, 25, 28, 29,
32, 33) and older age (22, 24) were controversially associated
with coercion in different study sites. These inconsistent findings
impede the definition of risk-factors which are independent of
specific countries. The inconsistencies between study sites were
discussed to be caused by cultural influences, organizational
factors, societal factors, the clinic-culture or a combination (34,
35). Besides that, one has to bear in mind that prior studies
followed different methodological approaches to analyze data
which additionally limits the comparability between different
study sites. Some studies used descriptive approaches (16, 32)
or group comparisons with binominal, non-parametric tests or
ANOVA (17–20, 22–24, 26, 29, 30). To describe risk factors
regression analysis was frequently used (19–21, 23, 26, 28, 29, 31,
33) and some studies extended their findings with an estimation
of the area under the curve (AUC) (23). One study used a
latent class analysis (LCA) which is capable of detecting the
presence of groups in individuals with relatively homogeneous
clinical courses (25). Another study used Multilevel random
effects modeling (27). Only a few studies tried to describe the
potency of specific risk factors to affect the outcome coercion/no
coercion. Furthermore, the description of the specificity and
sensitivity of the statistical models is scarce. One study which
followed this approach described an acceptable AUC for one
model using bivariate analysis (23). Another study found that
with the included parameters only a limited prediction of patients
at risk was possible (31). Thus, besides the analysis of risk factors
at our study site, the second aim of this study was to find statistical
approaches with a good balance in their specificity and sensitivity
and prediction accuracy for the outcome “coercion/no coercion”
in psychiatric inpatients. Furthermore we wanted to analyze the
risk factors for their weights in affecting the outcome coercion/no

In today’s psychiatric research machine learning is an
emerging methodology. It is connoted with a great potential
for innovation and paradigm shift as the algorithms facilitate
integration of multiple measurements as well as allow objective
predictions of previously “unseen” observations. We used this
new approach to train and compare models with parameters
available at admission and after discharge. To test for the
hypothesis that machine learning algorithms are effective in the
prediction of the outcome coercion/no coercion in psychiatric
patients we compared binary regression analysis to the machine
learning algorithms according to their sensitivity, specificity,
accuracy, and AUC. Furthermore, we used machine learning to
weight the included predictors for their potency in affecting the

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Hotzy et al. Machine Learning and Coercion

outcome coercion/no coercion. For the comparison of the two
approaches we analyzed clinical data of involuntarily hospitalized
patients at the University Hospital of Psychiatry Zurich and built
two groups depending on the outcome Coercion/No Coercion.


The study was reviewed and approved by the Cantonal Ethics
Commission of Zurich, Switzerland (Ref.-No. EK: 2016-00749,
decision on 01.09.2016). Commitment documents as well as
the medical records of patients involuntarily hospitalized at
the University Hospital of Psychiatry Zurich during a 6-month
period from January first to June 30, 2016 were analyzed.

N = 16 wards of the University Hospital of Psychiatry Zurich
with a total of 252 beds were included. The clinic provides mental
health services for a catchment area of 485,000 inhabitants.

Study Sample
No exclusion criteria were defined. We screened a comprehensive
cohort of all patients admitted voluntarily and involuntarily to
the University Hospital of Psychiatry Zurich during a 6-month
period from January first to June 30, 2016 (n = 1,699 patients).
For the analysis we included involuntarily committed patients
(n = 577) and voluntarily committed patients who were retained
at a later stage during their hospitalization and then changed to
the legal status of involuntary hospitalization (n = 35).

Selection of Predictor Variables
Selection of predictor variables for “training” an algorithm
in machine learning is challenging. We used a recommended
method and searched the literature databases for variables
which were already described to be associated with the usage
of coercion: Psychiatric diagnosis (16–24), aggressive behavior
(16–18, 22, 23, 25, 27–30), former voluntary or involuntary
commitment (IC) and frequent hospitalizations (16–20, 24),
gender (20, 22–25, 29, 32, 33), and age (19, 20, 22, 23,
25, 28, 29, 32, 33) were identified as variables of interest.
We searched the routine documentation in the electronic
medical files of the patients for these variables. The medical
files include documentation about the socio-demographic
parameters, admission circumstances, prescribed medication,
documentation of coercive measures, and treatment planning. As
there was no standardized assessment for aggression we searched
which indirect information could be used and found IC due to
danger to others and involvement of police in the admission
process as indirect markers for aggressive behavior. Furthermore
we included the procedural aspects abscondence, appeal to
the court, duration until day passes, duration of IC, duration
of hospitalization into analysis. When patients are exposed to
coercive medication mostly antipsychotics or benzodiazepines
are used. We were interested if the patients, exposed to coercion
differed from those without coercion according to their regular
prescribed medication during hospitalization. Thus, we searched
the medical files for the prescription of medication classes
(antipsychotics, antidepressants, benzodiazepines, and others).

Analysis and Machine Learning
We conducted analysis with MATLAB (MATLAB and Statistics
Toolbox Release 2012b, The MathWorks, Inc., Natick,
Massachusetts, United States.) and SPSS 23.0 (IBM Corp.
Released 2011. IBM SPSS Statistics for Windows, Version 23.0.
Armonk, NY: IBM Corp.) for Windows.

In a first step we compared patients with/without experience
of coercion. We used cross-tabulation with chi-square tests for
categorical variables. Due to the non-normal distribution we
used Mann–Whitney tests for numeric variables. Variables that
differed between both groups in bivariate analyses were included
as potential risk factors in multivariate analysis. To analyze the
impact of the risk factors on the outcome coercion/no coercion
binary logistic regression analysis was used with coercion/no
coercion as the dependent variable. The goodness of fit of the
binary logistic regression model was assessed by the receiver
operating characteristic (ROC) curve method. The AUC served
as the criterion to determine the level of discrimination.
Discrimination was deemed acceptable at AUC values between
0.7 and 0.79, excellent at values between 0.8 and 0.89, and
outstanding at values over 0.9 (23). The specificity and sensitivity,
positive predictive value (PPV) and negative predictive value
(NPV) were calculated from the results of the different models.

Because of multiple comparisons Bonferroni’s adjustments
were made to prevent Type I error inflation (α = 0.05/5 = 0.01).

In a second step we tested the hypothesis that machine
learning algorithms can be used to predict the outcome.
Again the outcome of coercion/no coercion was used as
dependent variable. Because the outcome was already defined,
supervised learning algorithms [Logistic regression, supported
vector machine (SVM), and bagged trees algorithms] were used.
We used cross-validation to test the trained model. The training
set was divided in 5 equal sized subsets with one part being
used to train a model and the other four subsets to evaluate
the accuracy of the learnt model (five-fold cross validation). The
error rate of each subset was an estimate of the error rate of
the classifier. Cross-validation is used in machine learning to
establish the generalizability of an algorithm to new or previously
“unseen” subjects. The validity of the algorithms in predicting
the outcome coercion from no coercion was evaluated using
prediction accuracy, sensitivity, specificity, positive predictive
value (PPV) and negative predictive value (NPV). In this
study, sensitivity and specificity represented correctly predicted
occurrence of coercion (true positives) and correctly predicted
lack of coercion (true negatives), respectively.

Logistic Regression
The classifier models the class probabilities as a function of the
linear combination of predictors. Logistic regression utilizes a
typical linear regression formulation.

Support Vector Machines (SVM)
This technique separates data by a hyperplane, trying to
maximize the margin and creating the maximum distance
between the hyperplane and the values which lie on each side.
The higher this distance gets the better is the reduction of the
expected generalization error.

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Hotzy et al. Machine Learning and Coercion

SVM are robust in dealing with large numbers of features
included because only those features which lie on the margin
of the hyperplane are included. If data are non-linear and
separation is not possible on one hyperplane, SVM can create
more dimensional hyperplanes in a higher dimensional feature
space. SVM methods are binary. So in the case of this study
where we compared the patient group with/without coercion no
dummy-variables had to be created for the response-feature.

Decision Trees
Decision trees classify instances by sorting them based on feature
values. The nodes represent instances in the feature to be
classified and the branches represent values that the node can
become. The instance which divides the training data in the best
way is selected as the root node. Than the instance which best
divides this feature is chosen and so on. There are many ways to
select the instance which is best at dividing data. It is possible to
train ensembles of regression trees. They combine results from
many weak learners into one high-quality ensemble model and
are potent in the analysis of skewed data.

In generally, methods like SVMs and neural networks perform
well with balanced continuous and multi-dimensional features
whereas logic-based systems like decision trees or rule learners
perform better with discrete/categorical variables.

SVMs are potent in dealing with large data which increase
their prediction accuracy. These techniques can also work in
the case of multi co-linearity and non-linear relationships. Logic
based systems like decision trees are easier to interpret than

Imbalance Problem
Class imbalance where the number of patients in one class
(e.g., no coercion) exceeds the patients in the other class (e.g.,
coercion) is a common problem in machine learning. A typical
machine learning algorithm trained with an imbalanced data set
would assign new observations to the majority class (e.g., no
coercion) (36). In this study we met this problem by creating
an artificial group with balanced distribution of the outcome
(coercion/no coercion). We assigned random numbers to the
cohort of 612 patients which were involuntary hospitalized
during the study period. We selected those patients without
documentation of coercion during their hospitalization and
sorted them by ascending numbers. We then excluded the first
half of this group of patients. Thus, we conducted the analysis
with 393 patients (no coercion: n = 223, coercion: n = 170). In
those patients who experienced coercion, at least one coercive
measure (e.g., seclusion, coercive medication, restraint alone, or
in combination) was used during hospitalization.


Comparison Between Groups of Patients
With/Without Coercion During Involuntary
Being a threat to others (72%) or self and others (20%)
were the most frequent reasons for the usage of coercion.
Clinical aspects like a higher CGI at admission, psychotic or

personality disorders, the prescription of antipsychotics and
benzodiazepines, harm to others or harm to self and others
before admission, and male gender were significantly associated
with the usage of coercion. From the procedural side being
retained, police involvement at admission, the number of
former admissions, a history of IC, a longer duration until
patients were allowed for day passes, duration until revocation
of involuntary hospitalization and duration of hospitalization,
appeal for prolongation from the clinic but also appeal for early
discharge from the patient were significantly associated with the
use of coercion. We found an association between a secondary
diagnosis of a substance-use-related disorder and coercion which
was not significant (for details see Tables 1, 2).

Age at admission (Mann–Whitney U: 17454.000, Z: −1.346,
p = 0.178, n = 393) and Nationality did not differ significantly
between the groups [χ2

= 6.466, p = 0.373, n = 393].

Also we found no significant group difference for skills in
German language, which is the official language in the state of
Zurich, [χ2 = 0.384, p = 0.825, n = 393] and educational-level

= 8.285, p = 0.218, n = 393].

Two Models to Predict the Outcome
Coercion/No Coercion
The main question of this study was to find models with a good
accuracy in the prediction of the outcome coercion/no coercion.
With a supervised learning technique a predictive model can be
tested for both, input and output data. We trained and tested
two models for their accuracy in the prediction of the outcome
coercion/no coercion. For comparison we computed the same
two models in binary logistic regression.

The first model included data which were available at hospital
admission. In the second model we included variables which are
available after a whole course of hospitalization. We hypothesized
this second model to have higher prediction accuracy. The
variables included in both models are shown in Table 3.

Binary logistic regression in SPSS and logistic regression in
ML had the same results for B, SE, and p. This is comprehensible
as logistic regression utilizes a typical linear regression
formulation. The calculation of the coefficients/weights is
different between both approaches and led to different results.
Details are shown in Table 4.

The machine learning algorithms (Quadratic SVM, Ensemble
RUSBoosted Trees and Logistic regression) predicted the
outcome parameters (coercion/no coercion) with a balanced
accuracy ranging from 66.5 to 69% (the quadratic SVM algorithm
identified 102 out of 170 patients which experienced coercion)
in the model with 8 parameters and 71.5–76% in the model
with 18 parameters. In contrast the binary logistic regression in
SPSS had a balanced accuracy of 68.5% in the 8 item model and
78.5% in the 18 item model. In the 18 item model the logistic
regression algorithm identified 121 out of 170 patients which
experienced coercion (sensitivity). This resulted in an accuracy of
75%. The binary logistic regression of SPSS identified 124 out of
170 patients which experienced coercion and was more potent in
predicting those who did not experience coercion (187 out of 223
patients). This resulted in an accuracy of 78.5%.The Quadratic

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Hotzy et al. Machine Learning and Coercion

TABLE 1 | Comparison of socio-demographic and clinical aspects in patients with/without coercion.

Total (n = 393) No Coercion Coercion χ2 d.f.* P-value

N % N % N %

Gender 7.858 1 0.003

Male 204 52 102 46 102 60

Female 189 48 121 54 68 40

Reason for IC 50.253 3 <0.001 Harm to self 193 49 143 64 50 29 Harm to others 87 22 29 13 58 34 Harm to self and others 101 26 44 20 57 34 Other 12 3 7 3 5 3 ICD-10 primary diagnosis 59.746 6 <0.001 Organic disorder (F0) 71 18 44 20 27 16 Substance use disorder (F1) 49 13 37 17 12 7 Psychotic disorder (F2) 159 40 70 31 89 52 Affective disorder (F3) 51 13 31 14 20 12 Neurotic disorder (F4) 37 10 36 16 1 1 Personality disorder (F6) 13 3 1 1 12 7 Other 13 3 4 1 9 5 ICD-10 secondary F1 diagnosis 4.695 1 0.021 No 307 78 183 82 124 73 Yes 86 22 40 18 46 27 CGI at admission 28.857 3 <0.001 1–2 5 1 5 2 0 0 3–4 18 5 15 7 3 2 5–6 161 41 108 48 53 31 7–8 209 53 95 43 114 67 Police involved at admission 11.978 1 <0.001 No 257 65 162 73 95 56 Yes 136 35 61 27 75 44 Antipsychotics 50.147 1 <0.001 No 78 20 72 32 6 3 Yes 315 80 151 68 164 97 Benzodiazepines 25.006 1 <0.001 No 92 23 73 33 19 11 Yes 301 77 150 67 151 89 Retainment 19.167 1 <0.001 No 362 92 217 97 145 85 Yes 31 8 6 3 25 15 Former IC 22.197 1 <0.001 No 206 52 140 63 66 39 Yes 187 48 83 37 104 61 Abscondence No 317 81 195 87 122 72 15.203 1 <0.001 Yes 76 19 28 13 48 28 Appeal for prolongation of IC 17.063 1 <0.001 No 354 90 213 95 141 83 Yes 39 10 10 5 29 17 Appeal for early discharge 14.257 1 <0.001 No 320 81 196 88 124 73 Yes 73 19 27 12 46 27 Rehospitalization during 6 months 12.951 1 <0.001 No 267 68 168 75 99 58 Yes 126 32 55 25 71 42 CGI, Clinical Global Impression; IC, Involuntary Commitment. Chi-square test reveals significant differences between an involuntarily hospitalized cohort of patients which experienced coercion and those which did not experience coercion. Frontiers in Psychiatry | 5 June 2018 | Volume 9 | Article 258 Hotzy et al. Machine Learning and Coercion TABLE 2 | Comparison of socio-demographic and clinical aspects in patients with/without coercion. Coercion Mann–Whitney U Z Sig No Yes Min Mean Median Max Min Mean Median Max Number of former admissions 0 4 0 69 0 9 2 67 12468.500 −4.831 <0.001 Duration until revocation of IC 0 79 16 10 1 31 25 230 10937.500 −7.189 <0.001 Duration of hospitalization 0 138 22 13 1 37 31 245 11383.000 −6.789 <0.001 Duration until day passes 0 109 10 5 0 18 11 161 12468.500 −5.822 <0.001 IC, Involuntary Commitment. Mann–Whitney U-Test reveals significant differences in procedural aspects of the cohort with compared to the cohort without coercion during hospitalization. TABLE 3 | Included predictors in both models. 8 item model 18 item model 1. Gender 1. Gender 2. Reason for IC 2. Reason for IC 3. Police involved at admission 3. Police involved at admission 4. ICD-10 primary diagnosis 4. ICD-10 primary diagnosis 5. ICD-10 secondary F1 diagnosis 5. ICD-10 secondary F1 diagnosis 6. Former admissions 6. Former admissions 7. Former IC 7. Former IC 8. CGI at admission 8. CGI at admission 9. Retainment 10. Antipsychotics 11. Benzodieazepines 12. Appeal for early discharge 13. Appeal for prolongation of IC 14. Abscondence 15. Duration until day passes 16. Duration until revocation of IC 17. Duration of hospitalization 18. Rehospitalization during 6 months IC, Involuntary Commitment, CGI, Clinical Global Impresssion. SVM was able to predict 185 out of 223 patients without coercion and had less potency in predicting the outcome coercion (117 out of 170 patients). For details see Table 5. Due to inconsistent findings in literature we also created two models which did not include the variables gender and substance- use-related disorders as co-diagnosis (which was not significantly associated in our bivariate analyses). The results were comparable but not as robust as the 8 and 18 item model. They are shown in Table 6. Weighting of Risk Factors to Experience Coercion In a next step we analyzed the relevance of each variable in the prediction of the outcome coercion/no coercion. We compared the weights of the included variables between logistic regression in ML and binary logistic regression. We analyzed the relevance of predictor variables in distinguishing the outcome coercion/no coercion. Positive coefficients or weighting factors were assigned to an increase in coercion for the 8 and 18 item models. In the model with 8 items the CGI at admission had the highest weight. In ML this was followed by the reason for IC, former IC and a police involvement at admission. In binary logistic regression the second weighted predictor was former IC followed by reason for IC and police involvement at admission. In the 18 item model retainment was the highest weighted predictor. In ML this was followed by duration until revocation of IC, reason for IC at admission and prescription of antipsychotic medication. In binary logistic regression antipsychotic medication was weighted after retainment, followed by appeal for early discharge and the prescription of benzodiazepines. In both models female gender was negatively weighted. For details see Figure 1. DISCUSSION This study could show that machine learning algorithms can predict the outcome of coercion/no coercion in a patient group with a good accuracy and have some advantages compared to binary logistic regression which also appeared to have a good accuracy. All algorithms achieved greater than chance (50%) accuracy in distinguishing patients with coercion from those without coercion. We could verify the hypothesis that a model with a higher number of variables (including variables which occur during the course of hospitalization) was more potent in the prediction of the outcome coercion/no coercion. The AUC was acceptable in the model with 8 items with values from 0.73 to 0.75. In the model with 18 items the AUC reached values from 0.78 to 0.86 which implies excellent results in 2 out of 4 algorithms. In the model with 8 items quadratic SVM had the best accuracy whereas binary logistic regression had the best accuracy in the 18 item model. All the included algorithms had a good balance of specificity and sensitivity. Although the binary logistic regression appeared to have a slightly better AUC than the machine learning algorithms the machine learning algorithms appear to have an advantage. By using cross validation the training data are divided into a set of data where the model is trained and another k (in this study k = 5) sets of data where the trained model is validated. Thus, the accuracy of the trained model is verified in data sets which are independent of the trained data. This allows better generalizability for the prediction Frontiers in Psychiatry | 6 June 2018 | Volume 9 | Article 258 Hotzy et al. Machine Learning and Coercion TABLE 4 | Findings of binary logistic regression and ML logistic regression. Factor B* SE* P* tSTAT** 95% CI for Exp b*** Lower Exp B Upper 8 ITEM MODEL Gender −0.432 0.235 0.066 −1.838 0.41 0.649 1.029 Former admissions 0.011 0.01 0.279 1.084 0.991 1.011 1.032 Former IC 0.591 0.256 0.021 2.310 1.094 1.806 2.982 Reason for IC 0.493 0.127 <0.001 3.878 1.276 1.636 2.099 Police involved at admission 0.466 0.244 0.056 1.910 0.988 1.594 2.571 CGI at admission 0.929 0.205 <0.001 4.521 1.692 2.532 3.787 ICD-10 primary diagnosis 0.098 0.067 0.141 1.473 0.968 1.104 1.258 ICD-10 secondary F1 diagnosis 0.206 0.279 0.46 0.739 0.711 1.229 2.124 18 ITEM MODEL Gender −0.655 0.281 0.02 −2.330 0.3 0.52 0.901 Former admissions 0.012 0.012 0.321 0.991 0.989 1.012 1.036 Former IC −0.122 0.312 0.696 −0.391 0.481 0.885 1.631 Retainment 2.142 0.56 <0.001 3.824 2.841 8.514 25.518 Reason for IC 0.556 0.157 <0.001 3.552 1.283 1.744 2.371 Police involved at admission 0.753 0.303 0.013 2.483 1.172 2.123 3.848 Rehospitalization during 6 months 0.127 0.301 0.672 0.424 0.63 1.136 2.048 Antipsychotics 1.569 0.5 0.002 3.138 1.802 4.802 12.795 Benzodieazepines 0.764 0.348 0.028 2.197 1.086 2.148 4.248 Duration until day passes 0.016 0.011 0.155 1.423 0.994 1.016 1.039 ICD-10 primary diagnosis 0.16 0.085 0.059 1.892 0.994 1.174 1.386 Abscondence −0.038 0.367 0.918 −0.103 0.469 0.963 1.978 Duration until revocation of IC 0.053 0.015 <0.001 3.581 1.024 1.054 1.085 Duration of hospitalization −0.014 0.01 0.142 −1.469 0.968 0.986 1.005 Appeal for prolongation of IC −0.369 0.584 0.527 −0.633 0.22 0.691 2.17 Appeal for early discharge 0.823 0.344 0.017 2.391 1.16 2.278 4.471 CGI at admission 0.483 0.238 0.043 2.027 1.016 1.621 2.587 ICD-10 secondary F1 diagnosis 0.24 0.319 0.451 0.754 0.681 1.272 2.374 *Binary logistic regression and ML logistic regression, **ML logistic regression, ***Binary logistic regression. accuracy because it was tested on “new” data. This is different from conventional binary logistic regression where all data are used in one analysis and generalizability is limited. The fact that the models can predict the occurrence of coercion/no coercion with a good accuracy of 69% in the model with 8 parameters and even more in the model with 18 parameters underlines the relevance of the included variables for clinical use and future research. Although the parameter were not able to explain all variance some of them can be defined as substantial “risk factors” for the experience of coercion during psychiatric hospitalization. In the 8 item model the CGI at admission had the highest weight, followed by reason for IC, former IC, and police involvement at admission. In the 18 item model retainment had the highest weight. By knowing risk factors and their weights it might be possible to identify groups of patients at risk by using a risk assessment tool. Patients could be divided into different risk groups. Treatment strategies could be adjusted to the different risk groups and help to prevent the occurrence of situations in which the usage of coercion seems necessary. Harm to others as reason for IC, former IC, and police involvement at admission were high weighted in both approaches. Combined with the finding that most coercive measures were applied due to harm to others this implies that aggression is a challenge for staff. This has also been shown in other studies (26, 30, 37–39) and was one reason to develop specialized PICU’s where staff is trained in aggression management (40). Retainment, the highest weighted predictor in the 18 item model, implies a high-risk situation and should be considered as a reason for the transfer to such PICUs (15). The CGI, which was highly weighted in the 8 item model is not specific but implies that patients at risk may be more likely to meet the criteria for severe mental illness (SMI). Although being less weighted, the psychiatric diagnosis should also be included in the risk assessment. Patients with a psychotic disorder or a personality disorder appeared to have an increased risk to experience coercion in our analysis and in previous literature (16–26). Also male gender should be considered in the risk assessment. Nevertheless, gender needs to be reflected with caution because other studies found female gender to be significantly associated with coercion (22, 29). Frontiers in Psychiatry | 7 June 2018 | Volume 9 | Article 258 Hotzy et al. Machine Learning and Coercion TABLE 5 | Comparison of the 8 and 18 item models. Quadratic SVM Ensemble RUSBoosted Trees Logistic regression SPSS binary logistic regression 8 ITEM MODEL Area under curve 0.74 0.73 0.73 0.75 Balanced accuracy (%) (Specifity + Sensitivity/2) 69 68.5 66,5 68.5 Specificity (%) 78 68 74 76 Sensitivity (%) 60 69 59 61 PPV (%) 68 62 64 67 NPV (%) 72 74 71 72 18 ITEM MODEL Area under curve 0.78 0.78 0.82 0.86 Balanced accuracy (%) (Specifity + Sensitivity/2) 76 71.5 75 78.5 Specificity (%) 83 74 79 84 Sensitivity (%) 69 69 71 73 PPV (%) 75 67 72 78 NPV (%) 78 76 78 80 NPV, negative predictive value; PPV, positive predictive value; SVM, support vector machines. TABLE 6 | Comparison of the 6 and 16 item models. Quadratic SVM Ensemble RUSBoosted Trees Logistic regression SPSS binary logistic regression 6 ITEM MODEL Area under curve 0.72 0.69 0.73 0.75 Balanced accuracy (%) (Specifity + Sensitivity/2) 69 67 67 69 Specificity (%) 77 63 78 79 Sensitivity (%) 61 71 56 59 PPV (%) 67 59 66 68 NPV (%) 72 74 70 71 16 ITEM MODEL Area under curve 0.78 0.78 0.82 0.85 Balanced accuracy (%) (Specifity + Sensitivity/2) 75 71 74 77 Specificity (%) 84 73 77 81 Sensitivity (%) 66 69 71 73 PPV (%) 76 66 70 75 NPV (%) 76 75 77 79 NPV, negative predictive value; PPV, positive predictive value; SVM, support vector machines. In patients at risk the regular use of the Brøset Violence Checklist could be helpful in identifying situations where the risk for aggressive behavior is increased (41) and was shown to result in a decreased rate of aggressive incidents (42). A cooperation between mental health community and hospital teams (43), personal safety plans or treatment planning (25, 43), single rooms and retreat-rooms on the ward may help avoiding interpersonal stress. As mentioned above it was also shown that the segregation of disruptive patients in a psychiatric intensive care unit (PICU) (44) and the ward atmosphere (35) were effective in the reduction of aggressive behavior. A more recovery orientated view might be helpful to build a relationship between patient and the therapeutic team. Also staff training in communication skills, fast building and maintenance of a stable therapeutic relationship could help to reduce situations in which coercion is used (37). As mentioned above, previous studies followed different methodological protocols. To provide comparability between different study sites, statistical models should be used which follow a comparable methodological approach. These models should have a good accuracy and be easy to replicate in different countries. This study could show that ML algorithms (logistic regression, SVM, decision trees) can predict the outcome coercion /no coercion in a group of patients with a good accuracy and explain some of the variance. Furthermore machine learning can be used for weighting of the included predictors. Cross validation provides a better generalizability of the results which is attractive for the usage in different study sites. Previous studies Frontiers in Psychiatry | 8 June 2018 | Volume 9 | Article 258 Hotzy et al. Machine Learning and Coercion FIGURE 1 | Bar graphs showing weighting factors assigned to each variable based on their relevance in distinguishing the outcome coercion from no coercion. Variables which increase the probability of an individual patient to experience coercion were assigned positive weighting factors whilst those that decrease the probability of a patient experiencing coercion were assigned negative weighting factors. *Significant at the 0.05 level. could show that beside risk-factors in patients also procedural factors like closed ward doors (45), architecture and atmosphere of a ward (35, 46) or interpersonal factors like escalating behavior of staff (47, 48) may be a risk for violent behavior in the patients and consecutively the usage of coercion. Future studies should therefore aim to analyze the weights of clinical culture, attitude toward coercion in the therapeutic teams and organizational factors to test if these factors account for the unexplained variance in the prediction models used in this study. LIMITATIONS Some limitations must be mentioned regarding to this study. Although we runned tests for each predictor alone and different combinations of the predictors some of the predictor variables may influence each other. This may have lead to a bias in the prediction potency of the models. Artificial balance was created by decreasing the number of participants with the outcome no coercion. In the group comparison some categories (e.g., diagnostic groups, harm-criteria, CGI-groups) were very small and due to that may have contributed to a significant effect. Previous studies showed comparable findings. On this background we included these small groups in analysis. Further studies should re-evaluate our results with a bigger sample size. The analysis was based on retrospectively collected data, and it was not possible to assess the subjective perspectives of patients and physicians in a standardized form. Due to the retrospective character of the study the psychopathological symptoms could not be assessed in a standardized way. Because of that, important information about the severity of symptoms during the situation in which coercion was used is lacking. Furthermore it was not possible to assess if alternatives were used before coercion had to be used. We were not able to include data on treatment culture and socio-cultural factors in general into our analysis. This would be an interesting topic for future research. CONCLUSION This study was able to show that ML is useful in the prediction of coercion and reach comparable results to binary logistic regression although the trained algorithms are used on new sets of validation data (five-fold cross validation) which allows a better generalizability. ML is a promising approach for further research on risk factors and the occurrence of coercion in psychiatry. Frontiers in Psychiatry | 9 June 2018 | Volume 9 | Article 258 Hotzy et al. Machine Learning and Coercion Weighting of risk factors may be helpful in the risk-assessment of the individual patients. In patients at risk special therapeutic strategies could be helpful to prevent the occurrence of aggressive behavior and consecutively coercion. Future studies should evaluate the potency of these strategies and the usefulness of risk-assessment tools. ETHICS STATEMENT The study was reviewed and approved by the Cantonal Ethics committee of Zurich, Switzerland (Ref.-No. EK: 2016- 00749, decision on 01.09.2016). Commitment documents as well as the medical records of patients involuntarily hospitalized at the University Hospital of Psychiatry Zurich during a 6-month period from January first to June 30, 2016 were analyzed. All procedures were in accordance with the ethical standards of the institutional and/or national research committee and with the 1964 Helsinki declaration and its later amendments or comparable ethical standards. This is a retrospective study. For this type of study formal consent is not required. 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Aversive stimulation by staff and violence by psychiatric patients. Br J Clin Psychol. (1996) 35(Pt 1):11–20. 48. Haugvaldstad MJ, Husum TL. Influence of staff’s emotional reactions on the escalation of patient aggression in mental health care. Int J Law Psychiatry (2016) 49(Pt A):130–7. doi: 10.1016/j.ijlp.2016.09.001 Conflict of Interest Statement: The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. Copyright © 2018 Hotzy, Theodoridou, Hoff, Schneeberger, Seifritz, Olbrich and Jäger. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms. Frontiers in Psychiatry | 11 June 2018 | Volume 9 | Article 258 Machine Learning: An Approach in Identifying Risk Factors for Coercion Compared to Binary Logistic Regression Introduction Methods Setting Study Sample Selection of Predictor Variables Analysis and Machine Learning Logistic Regression Support Vector Machines (SVM) Decision Trees Imbalance Problem Results Comparison Between Groups of Patients With/Without Coercion During Involuntary Hospitalization Two Models to Predict the Outcome Coercion/No Coercion Weighting of Risk Factors to Experience Coercion Discussion Limitations Conclusion Ethics Statement Author Contributions References

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