Article Critique – Binary logistic Regression

Article critique: Binary logistic Regression

ORIGINAL RESEARCH
published: 12 June 2018

doi: 10.3389/fpsyt.2018.00258

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Edited by:

Meichun Mohler-Kuo,

University of Applied Sciences and

Arts of Western Switzerland,

Switzerland

Reviewed by:

Eric Noorthoorn,

GGNet Mental Health Centre,

Netherlands

Raoul Borbé,

Universität Ulm, Germany

*Correspondence:

Florian Hotzy

florian.hotzy@puk.zh.ch

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

Citation:

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
Regression

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

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Hotzy et al. Machine Learning and Coercion

INTRODUCTION

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
coercion.

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.

METHODS

Setting
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
SVMs.

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.

RESULTS

Comparison Between Groups of Patients
With/Without Coercion During Involuntary
Hospitalization
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)
= 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
[χ2

(6)
= 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.

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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

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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).

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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

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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.

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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. This article does
not contain any studies with animals performed by any of
the authors.

AUTHOR CONTRIBUTIONS

FH, SO, and MJ: conception and design, data collection,
analysis and interpretation of data; FH: drafting the article;
FH, AS, AT, PH, ES, SO, and MJ: revising the article
critically for important intellectual content; FH, SO, MJ,
AS, AT, PH, and ES: final approval of the version to be
published.

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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

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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

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• 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