*Article* **Urban–Rural Distinction or Economic Segmentation: A Study on Fear and Inferiority in Poor Children's Peer Relationships**

**Shencheng Wang 1 , Baochen Liu 2,\*, Yongzheng Yang 3,\* , Liangwei Yang 4 and Min Zhen 5**

**Abstract:** Peer relationships play an important role in the growth of children. This study offers insights about feelings of fear and inferiority in children's peer relationships. Based on a national survey, the 2018 Construction for Social Policy Support System for Urban and Rural Poor Families in China, initiated by the Ministry of Civil Affairs, and using multiple regression models and a structural equation model, this study discusses whether and how having a rural household registration or being from a poor (*dibao*) family has an isolation effect on fear and inferiority in children's peer relationships. The research findings indicate that children with a rural household registration or those from a *dibao* family are at a disadvantage in peer interactions. Moreover, rural resident identity has an indirect effect on children's fear of peers and inferiority, mainly through psychological resilience, anxiety and depression, and mobile phone dependence. Being from a *dibao* family directly influences children's fear and inferiority in their peer relationships; it also indirectly influences fear of peers and inferiority through psychological resilience. This study suggests that more attention should be paid to fear of peers and inferiority in rural children or children from a *dibao* family.

**Keywords:** children; fear of peers and inferiority; urban–rural distinction; economic segmentation; China

#### **1. Background**

Previous studies have shown that peer relationships have a unique and irreplaceable role in the social and emotional development of children. These relationships impact the healthy development and social adaptation of children's social ability, cognition, emotion, self-conception, and personality [1,2]. Peer relationships and family environment are the two core systems of children's personality formation and socialization [3].

Peer relationships can be positive or negative. Early research primarily examined peer relationships from two perspectives: peer acceptance and friendship. Peer acceptance is a one-way structure of common opinions, reflecting the attitudes group members have toward individuals, such as likes or dislikes, acceptance, or exclusion. Friendship is an individual-oriented two-way structure, reflecting the emotional connection of individuals. With the development of research, scholars have gradually paid attention to difficulties in children's peer relationships [4], such as peer rejection [5] and peer victimization [6]. However, aside from peer exclusion and peer victimization, fear of peers and sense of inferiority are the individual subjective feelings of fear and inferiority in peer interactions, which are associated with social self-perception [7]. From a field perspective, peer exclusion and peer aggression are mainly concentrated in the middle and end of peer communication processes, while fear of peers and inferiority are mainly concentrated in the front end. Fear of peers and inferiority may be the major factors behind children's resistance to

**Citation:** Wang, S.; Liu, B.; Yang, Y.; Yang, L.; Zhen, M. Urban–Rural Distinction or Economic Segmentation: A Study on Fear and Inferiority in Poor Children's Peer Relationships. *Healthcare* **2022**, *10*, 2057. https://doi.org/10.3390/ healthcare10102057

Academic Editors: Yasuhiro Kotera and Elaina Taylor

Received: 17 August 2022 Accepted: 14 October 2022 Published: 17 October 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

social participation and social integration. They might be detrimental to the production of prosocial behavior and could lead to aggressive behavior against others [8]. It is necessary to conduct an in-depth study on the antecedents of fear of peers and inferiority, which will increase the understanding of why some children fall into an adverse situation in peer relationships; such a study will also identify the effective measures needed to help children build and maintain good peer relationships.

Therefore, this study focused on fear of peers and inferiority in Chinese children. In reality, the reasons for children's fear of peers and inferiority may be multifaceted. However, in China, it is important to pay particular attention to two unique social backgrounds that are very important for children's growth. First, there is an urban–rural separation effect in children's development in China [9]. The differences in the geographic regions and the human environments between urban and rural China lead to a gap between urban and rural children's environmental adaptation and interpersonal communication skills [10]. Second, the rapid development of China's economy has produced serious economic divisions between people. Some vulnerable groups have fallen into poverty and have also suffered from social exclusion in terms of political participation and interpersonal communication [10]. Children from poor families, with low social skills and a lack of communication experience, are prone to psychological problems, such as feelings of inferiority [11]. In the study discussed in this paper, we aimed to determine whether a rural household registration or being from a poor family (*dibao* family) has an isolation effect on fear and inferiority in children's peer relationships and to investigate the specific mechanisms underlying this.

#### **2. Research Questions and Analytic Frameworks**

Although fear of peers and inferiority in children's peer interactions are influenced by socio-economic status (SES), some empirical studies have suggested that the effect of SES on children's peer relationships is very weak [12]. These controversies suggest that the effects of SES on children's fear of peers and inferiority may be influenced by mediating mechanisms. Therefore, the present study aimed to examine the association between SES and fear of peers and inferiority among children in China. Moreover, it explored the intermediary mechanisms of the SES stratification constituted by urban–rural distinction and economic segregation that affects fear of peers and inferiority from the perspective of social stratification.

#### *2.1. Socio-Economic Stratification and Peer Fear and Inferiority*

In China, urban–rural distinction and economic segmentation constitute two important aspects of socio-economic stratification. Urban–rural distinction has become an undeniable fact in China. Due to the long-term existence of the country's household registration system, there is a clear distinction between urban and rural areas. Moreover, this system has a comprehensive effect on urban–rural distinction [13], and a disadvantage in peer interactions has been confirmed, thus becoming a typical problem of children's development [9]. Studies have indicated that, due to urban–rural geographical and cultural differences, a certain degree of difference also exists among college students, in terms of environmental adaptation and interpersonal communication [14]. In comparison to rural students, urban students have better interpersonal communication skills [15]. Regarding group cooperation, rural children get along with others significantly better than children from villages and towns [16]. Therefore, this study proposes:

#### **Hypothesis 1.** *Urban–rural distinction has a negative effect on children's fear of peers and inferiority.*

In addition to urban–rural distinction, acute economic segmentation arises from China's rapid economic development. Long-term emphasis on economic efficiency and neglect of social justice have led to a significant gap between rich and poor, as well as a wide social class divide. Economically, some vulnerable groups of society not only fall into poverty, but also suffer all-around social exclusion with regard to political participation and interpersonal communication [13]. Among the associated disadvantages, social exclusion resulting from interpersonal communication is particularly harmful to the growth of poor children and students. Family poverty not only causes and aggravates students' psychological burden, it also negatively impacts their communication needs leading to a low level of social skills and a relative lack of contact experience. They have a high probability of confronting many psychological problems, such as an inferiority complex, impacting their interpersonal communication skills [11]. Students with family economic difficulties are a high-risk group for psychological poverty [17], and there is a gap between poor and non-poor undergraduates [18]. Therefore, this study proposes:

#### **Hypothesis 2.** *Economic segmentation has a negative effect on children's fear of peers and inferiority.*

#### *2.2. Psychological Resilience*

Resilience research began in the 1970s. Some scholars believe that resilience refers to an individual's ability to cope with changes and stressful events in a healthy way [19], while others emphasize that resilience is a process of reintegration. When children encounter serious sources of pressure, they can return to normal with the support of protective factors [20]. Studies have indicated that resilience helps diminish children's depressive symptoms and enables them to initiate peer relationships and cultivate more of them. Children with resilience are more popular among their peers. Consequently, they enjoy better interpersonal relations and social support networks [21] and have relatively more stable and effective social support resources [22].

However, other studies have suggested that SES indirectly reflects the abundance of resources that individuals can mobilize and utilize [23,24]. Individuals with lower SES may incur more health costs in maintaining psychological resilience and they may exhibit poorer mental health [25]. For example, children from rural areas typically have a lower SES, which in turn reduces their level of psychological resilience [26]; this may increase their fear and feelings of inferiority in their peer interactions. Therefore, this study proposes:

**Hypothesis 3.** *Psychological resilience partially mediates the relationship between urban–rural distinction and children's fear of peers and inferiority.*

**Hypothesis 4.** *Psychological resilience partially mediates the relationship between economic segmentation and children's fear of peers and inferiority.*

#### *2.3. Anxiety and Depression*

Anxiety and depression are the commonly diagnosed psychological disorders among children. Anxiety is a group of mental disorders characterized by anxiety and fear, often accompanied by severe depression or other personality disorders. There is a statistically significant correlation between anxiety and depression [27]. Studies have shown that adolescent anxiety and depression has a significant negative correlation with peer relationships. The higher the degree of anxiety and depression is, the worse the child's peer relationships [28]. Children with a higher level of anxiety and depression have poorer social functioning, less classmate support, and less social acceptance in social communication [29]. High anxiety and social insecurity will increase the risk of children's low-quality friendships and peer abuse, and a low level of social support and peer relationships will further deepen children's psychological distress, such as anxiety and depression [30].

Further research has shown that anxiety and depression are closely related to SES. Individuals with lower SES showed stronger anxious depression than individuals with higher economic and social status [31]. Therefore, this study proposes:

**Hypothesis 5.** *Anxious depression partially mediates the relationship between urban–rural distinction and children's fear of peers and inferiority.*

**Hypothesis 6.** *Anxious depression partially mediates the relationship between economic segmentation and children's fear of peers and inferiority.*

#### *2.4. Mobile Phone Dependence*

Attention overload theory considers that individual psychological resources are limited, and the maintenance of target information depends on the number of available psychological resources. The failure of sustained attention comes from limited psychological resources [32]. When individuals with high dependence on mobile phones input a large number of cognitive resources into those devices, they reduce the resources that should have been allocated to other personal activities. Consequently, excessive dependence on mobile phones will lead to children's cognitive failure in social communication as well as many adverse psychological characteristics, such as stress susceptibility and low selfevaluation [33]. Studies have found that, in a group of young people with mobile phone addiction, the negative factors impacting peer relationship quality are more significant than the positive factors. Furthermore, the higher the degree of mobile phone addiction, the more negative the impact is on the quality of peer relationships [34]. Social phobia is significantly associated with the risk of smartphone addiction in young people. Individuals with psychosocial problems, such as social phobia and loneliness, prefer mobile devices rather than face-to-face communication because online communication can reduce anxiety [35].

Research on mobile phone dependence has shown that it is closely related to economic and social status. Students from *dibao* families have higher levels of cell phone addiction than students from non-*dibao* families [36–38]. Therefore, this study proposes:

**Hypothesis 7.** *Mobile phone dependence partially mediates the relationship between urban–rural distinction and children's fear of peers and inferiority.*

**Hypothesis 8.** *Mobile phone dependence partially mediates the relationship between economic segmentation and children's fear of peers and inferiority.*

#### **3. Methods**

#### *3.1. Participants*

The data used in this study were collected by the Peking University Chinese Social Sciences Survey Center in 2018, extracted from a survey project called Chinese Social Policy Support System for Vulnerable Families (CSPSS). The Ministry of Civil Affairs of the People's Republic of China appointed and funded the Institute of Social Science Survey (ISSS) at Peking University to deliver the related project and organize a research team to write the report. It is a national large-scale sample survey project supported by the Chinese Ministry of Civil Affairs, aiming to be representative of the vulnerable Chinese families targeted by the government's social assistance program. Using stratified sampling methods, the project adopted the computer-assisted personal interviewing (CAPI) method to investigate more than 1800 villages in 29 provinces from July 2018 to September 2018. The project has compiled three questionnaire databases: disability, the elderly, and children. Among them, parents and their children were interviewed for the children questionnaire, which included detailed information of the demographic, socio-economic, health, learning, and psychological and social interactions of the respondent parents and their children (aged 8–16 years). The respondent parents and children had to complete separate questionnaires without communicating their opinions with each other. The children were required to answer the questionnaires about children's psychological health and school performance. If a child needed help during the procedure, an interviewer read and explained the questions. If the parents of the children (such as left-behind children in a rural area) were not at home when the interviewers were visiting, the questionnaires for parents could be also completed through a telephone survey. The database has 3342 samples, including 991 samples of urban poor families (*dibao* families), with 1032 urban non-*dibao* families; and 543 samples

of rural *dibao* families, with 776 rural non-*dibao* samples. After deleting the missing and abnormal values in the database, 3334 observations were finally obtained.

#### *3.2. Measurements*

#### 3.2.1. Dependent Variable

To evaluate the children's fear of peers and inferiority, we used the 10-item Fear of peers and Inferiority Scale (PFIS). The participants answered items (e.g., You feel afraid if you do something you have never done before in front of other students) on a 4-point rating scale ranging from 1 = completely disagree to 4 = completely agree. A mean score was computed to yield the composite score, and higher scores indicated higher fear of peers and inferiority. A cumulative score was created by adding the responses of all 10 indicators (ranging from 10 to 40). The higher the total score of the fear of peers and inferiority subscale, the higher the level of fear and inferiority in peer interactions, and the more negative the self-perception. In our study, the Cronbach's alpha coefficient for the PFIS was 0.8357, demonstrating good internal consistency.

#### 3.2.2. Independent Variables

To evaluate the existence of economic segmentation and urban–rural distinction, we used two dummy variables: *dibao* family (0 = no; 1 = yes) and urban family (0 = rural family; 1 = urban family). It should be noted that, in China, families receiving *dibao* are often at the bottom of the economic status hierarchy, which can be considered to be the poorest group.

#### 3.2.3. Mediating Variables

In this study, psychological resilience, anxiety and depression, and mobile phone addiction are the mediator variables.

We used the Child and Youth Resilience Measure Scale (CYRM-R) to measure children's psychological resilience. This scale was developed by Professor Michael Ungar et al. by integrating the results of 35 researchers from 11 countries and 14 regions on psychological resilience in 2009 [39]. The scale consists of 28 items, including three dimensions: individual level, relative level, and social and cultural level. They are evaluated on a fivepoint Likert scale, with a total score ranging from 28 to 140 points. A higher score indicates a better level of psychological resilience. In our study, the Cronbach's alpha coefficient for the CYRM-R (psychological resilience) was 0.9045, indicating good internal consistency.

We used the Revised Child Anxiety and Depression Scale (RCADS 25) to measure the respondents' depression tendencies. RCADS 25, which includes two dimensions (depression and anxiety), is a revised children's anxiety and depression scale tailored for children and adolescents ranging in age from 8 to 18. The RCADS 25 uses a four-point Likert scale, with 1 representing "never" and 4 representing "always" [40]. A cumulative score (ranging from 24 to 91) was obtained by adding the responses of all 25 indicators. A higher score indicates a higher degree of anxiety and depression. In our study, the Cronbach's alpha coefficient for the RCADS 25 was 0.8583, demonstrating good internal consistency.

To assess the tendency of mobile phone addiction, we used the Chinese version of the self-report 17-item Mobile Phone Addiction Index (MPAI), which was based on the English version of the MPAI. MPAI consists of four dimensions of mobile phone addiction: inability to control cravings, feeling anxious and lost, withdrawal/escape, and productivity loss. The participants answer items (e.g., You feel anxious if you have not checked for messages or switched on your mobile phone for some time) on a 5-point rating scale ranging from "1 = not at all" to "5 = always" [41]. A cumulative score (ranging from 14 to 83) was obtained by adding the responses of all 17 indicators. A higher score indicated a stronger tendency toward mobile phone addiction. In our study, the Cronbach's alpha coefficient for the MPAI was 0.8528, demonstrating good internal consistency.

#### 3.2.4. Covariates

Based on the existing studies on the factors influencing peer relationships [42], the present study included three sets of covariates: school characteristics, family characteristics, and personal characteristics. School characteristics mainly included three variables: key school (*zhongdianxuexiao*), public school, and boarding school (*jisuxuexiao*); three of them are dummy variables (0 = no; 1 = yes). Family characteristics mainly included six variables: whether the parents are alive (1 = both; 0 = either or neither), whether the parents are divorced (0 = no; 1 = yes), if the parents quarrel (0 = never or rarely; 1 = occasionally or often), family gatherings (0 = never; 1 = several times a year; 2 = once a month; 3 = two or three times a month; 4 = several times a week: 5 = every day), parent-child communication (0 = never or occasionally; 1 = always or often), and parents' beating and scolding (0 = never or occasionally; 1 = always or often). Personal characteristics mainly included five variables: gender (0 = female; 1 = male), only child (0 = no; 1 = yes), health status (0 = bad; 1 = moderate or good), physical disability (0 = no; 1 = yes), and student leader (0 = no; 1 = yes).

#### *3.3. Analytical Strategies*

Stata 14.0 was used as the data analysis tool for this study. First, we used the t-test to check the differences in the characteristics of two groups of participants (urban vs. rural and *dibao* vs. non-*dibao*). Then, a multiple regression model was used to examine the impact of economic segmentation and urban–rural distinction on the respondents' fear of peers and inferiority. Finally, we used the structural equation model method of maximum likelihood with default values for model estimation.

#### **4. Results**

#### *4.1. Descriptive Analysis*

Table 1 shows the descriptive analysis results of the core dependent variables. The average score of fear of peers and inferiority of all children was 19.942. The average score was higher for rural children (20.746) than urban children (19.415). The average score was higher for children from *dibao* families (20.381) than children from non-*dibao* families (19.570).

#### *4.2. Analysis of the Multiple Regression Model*

To enhance the robustness of the statistical results of the independent variables, the independent variables and three sets of control variables were gradually put into a series of multiple regression models, as shown in Table 2. Model 1 reflects the regression results when only the independent variables are included. Model 2 reflects the regression results when the independent variables and school level control variables are included. Model 3 shows the regression results when the independent variables and the school and personal level control variables are included. Model 4 shows the regression results when the independent variables and the school, personal, and family level control variables are included. With the gradual inclusion of the school, personal, and family characteristic variables, the R2 of the model gradually increased, indicating that the fitting degree of the model was increasingly higher. Moreover, in Model 4, the variance inflation factor (VIF) results were all lower than in Model 2 (specific results are not listed), indicating that there was no multicollinearity issue among the explanatory variables.

*Healthcare* **2022**, *10*, 2057

Notes: *t*-tests were used for continuous variables, and proportion tests were used for variables in proportions.

105

**Table 2.** Analysis results of the multiple regression models.

Robustness standard errors are reported in parentheses. \*\*\* *p* < 0.01, \*\* *p* < 0.05, \* *p* < 0.1.

In Model 1, both the independent variables—of whether the child is from a *dibao* family and whether the child holds an urban household registration—passed the significance test at the 1% level. The data show that the score of fear of peers and inferiority of urban children was 1.399 points lower than that of rural children. The score of fear of peers and inferiority of children from *dibao* families was 0.916 points higher than that of children from non-*dibao* families. The results demonstrate that peer interactions were impacted by urban– rural distinction and from barriers arising from basic living allowances. In comparison to urban children and those with better economic conditions from non-*dibao* families, rural children and children from *dibao* families faced more communication barriers and had stronger fear of peers and inferiority in peer interactions.

In Model 2, both independent variables again passed the significance test at the 1% level. The children's fear of peers and inferiority was still closely related to household registration and family economic conditions. Moreover, among the school characteristic variables, a public school or not and a boarding school or not were significantly associated with fear of peers and inferiority. The data show that the score of fear of peers and inferiority of children in public schools was 0.729 points higher than that of children in private schools. The score of fear of peers and inferiority of children in boarding schools was 1.074 points

higher than that of children in the control group. The control variable of a key school or not was found to have no significant correlation with children's fear of peers and inferiority.

Like Model 1 and Model 2, in Model 3, both independent variables passed the significance test at the 1% level. The results demonstrate that children's fear of peers and inferiority in peer interactions were still closely related to household registration and family economic conditions. Consistent with Model 2, the control variables of a public school or not and a boarding school or not passed the significance test. Moreover, the family characteristic variables of parents' quarrels, family gatherings, parent-child communication, and parents' beating and scolding all passed the significance test.

In Model 4, both independent variables were significantly associated with fear of peers and inferiority, showing the same result as the other three models. Consistent with Model 2 and Model 3, the control variables of a public school or not, a boarding school or not, gender, parents' quarrels, family gatherings, parent-child communication, and parents' beating and scolding all showed the same significance. Personal characteristics, such as gender, only child or not, and a student leader or not, were significantly associated with fear of peers and inferiority.

Based on the descriptive analysis and multiple regression results, Hypothesis 1 and Hypothesis 2 were supported. Specifically, the score of fear of peers and inferiority was significantly higher for rural children than for urban children. The score of fear of peers and inferiority was significantly higher for children from *dibao* families than for children from non-*dibao* families. The results demonstrate that urban–rural distinction and economic segmentation impacted the children's peer interactions.

#### *4.3. Results of the Structural Equation Model*

The multiple regression models demonstrated that urban–rural distinction and acute economic segmentation had an impact on the children's peer interactions. Children with a rural household registration or those from *dibao* families suffered more from fear of peers and inferiority. However, the models cannot explain how the two factors led to a higher level of children's fear and inferiority in peer interactions. To identify the mechanisms, this study used the structural equation model method of maximum likelihood with default values for model estimation based on the literature review and the research hypotheses. In comparison to the multiple regression analyses based on OLS (ordinary least squares), the structural equation model enabled us to conduct a path analysis more efficiently. Table 3 shows the model estimation results based on unstandardized regression coefficients.

The three mediator variables all had a significant direct effect on the score of fear of peers and inferiority of children's peer interaction. Specifically, the score of fear of peers and inferiority decreased by 0.070 points for each point increase in children's psychological resilience. The score of fear of peers and inferiority increased by 0.284 points for each point increase in children's anxiety and depression. The score of fear of peers and inferiority increased by 0.048 points for each point increase in children's mobile phone dependence.

This study found that the independent variable of whether the child is from a *dibao* family had a significant direct effect on the score of fear of peers and inferiority of children's peer interaction; it also affected fear of peers and inferiority through the mediating mechanism of psychological resilience. The psychological resilience score was 2.180 points lower for children from a *dibao* family than for children from non-*dibao* families. However, whether the child was from a *dibao* family did not have a significant effect on the degree of anxiety and depression or on mobile phone dependence. Therefore, the influencing mechanism of a *dibao* family on children's fear and inferiority in peer interactions was the synthesis of the direct effect brought about by basic living allowances and the indirect effect brought about by the mediating variable of psychological resilience. Thus, Hypothesis 4 was supported, but Hypothesis 6 and Hypothesis 8 were not.

**Table 3.** Estimation results of the structural equation model.

Standard errors are reported in parentheses. \*\*\* *p* < 0.01, \*\* *p* < 0.05, \* *p* < 0.1.

This study found that the independent variable of whether the child holds an urban household registration did not have a significant direct effect on children's fear of peers and inferiority in peer interactions. However, this variable had significant effects on children's psychological resilience, anxiety and depression, and mobile phone dependence (all passed the significant positive test). Therefore, this variable had an indirect effect on children's fear of peers and inferiority through the three mediating variables. Specifically, the psychological resilience score was 2.040 points higher for urban children than for rural children. Moreover the anxiety and depression score was 1.609 points lower for urban children than for rural children and the mobile phone dependence score was 1.061 lower for urban children than for rural children. These three mediating mechanisms jointly strengthened the urban–rural distinction in children's peer interactions. Thus, Hypothesis 3, Hypothesis 5, and Hypothesis 7 were supported.

Figure 1 shows the model path diagram based on standardized regression coefficients, which allows us to understand the influencing mechanisms of urban and rural areas and basic living allowances on children's fear of peers and inferiority more intuitively. *Healthcare* **2022**, *10*, x 14 of 17

**Figure 1.** Model path diagram based on the standardized regression coefficients. \*\*\* *p*< 0.01, \*\* *p*< 0.05, \* *p*< 0.1. **Figure 1.** Model path diagram based on the standardized regression coefficients. \*\*\* *p* < 0.01, \*\* *p* < 0.05, \* *p* < 0.1.

#### **5. Conclusions and Policy Suggestions 5. Conclusions and Policy Suggestions**

#### *5.1. Conclusions 5.1. Conclusions*

Using data from the CSPSS national survey, this study found that urban–rural distinction and economic segmentation have an impact on children's fear of peers and inferiority in China. First, rural children suffer much more from fear of peers and inferiority than do urban children. Hypothesis 1 was supported. In China, compared to urban children, rural children have a higher probability of becoming left behind children and they are more likely to have the characteristics of imbalance, sensitive personality, psychological isolation, inferiority and discord. Second, children from *dibao* families are more vulnerable to fear of peers and inferiority than those from families without basic living allowances. Hypothesis 2 was also supported. Because of welfare stigma, children from Using data from the CSPSS national survey, this study found that urban–rural distinction and economic segmentation have an impact on children's fear of peers and inferiority in China. First, rural children suffer much more from fear of peers and inferiority than do urban children. Hypothesis 1 was supported. In China, compared to urban children, rural children have a higher probability of becoming left behind children and they are more likely to have the characteristics of imbalance, sensitive personality, psychological isolation, inferiority and discord. Second, children from *dibao* families are more vulnerable to fear of peers and inferiority than those from families without basic living allowances. Hypothesis 2 was also supported. Because of welfare stigma, children from *dibao* families are at a disadvantage in peer interactions.

*dibao* families are at a disadvantage in peer interactions. This study also examined the mechanisms of the relationship between children's fear of peers and inferiority and urban–rural distinction and economic segmentation. The findings show that urban or rural household registration has no direct effect on children's fear of peers and inferiority, but a rural resident identity indirectly makes rural children suffer more from fear of peers and inferiority by affecting their psychological resilience, anxiety and depression, and mobile phone dependence. Hypotheses 3, 5, and 7 were supported. Similar to previous research [23–26,31,36–38], this study also found higher economic and social status have a significant impact on children's psychological resilience anxiety and depression, and mobile phone dependence. Being from *dibao* families has a direct effect on children's fear of peers and inferiority; it also indirectly leads to a higher level of fear of peers and inferiority by affecting their psychological resilience. Thus, Hypothesis 4 was This study also examined the mechanisms of the relationship between children's fear of peers and inferiority and urban–rural distinction and economic segmentation. The findings show that urban or rural household registration has no direct effect on children's fear of peers and inferiority, but a rural resident identity indirectly makes rural children suffer more from fear of peers and inferiority by affecting their psychological resilience, anxiety and depression, and mobile phone dependence. Hypotheses 3, 5, and 7 were supported. Similar to previous research [23–26,31,36–38], this study also found higher economic and social status have a significant impact on children's psychological resilience anxiety and depression, and mobile phone dependence. Being from *dibao* families has a direct effect on children's fear of peers and inferiority; it also indirectly leads to a higher level of fear of peers and inferiority by affecting their psychological resilience. Thus, Hypothesis 4 was supported, but Hypothesis 6 and Hypothesis 8 were not. Compared to previous

supported, but Hypothesis 6 and Hypothesis 8 were not. Compared to previous research [31,36–38], this study further found that urban–rural distinction has a significant impact

only on children's anxiety and depression, and mobile phone dependence.

research [31,36–38], this study further found that urban–rural distinction has a significant impact only on children's anxiety and depression, and mobile phone dependence.

Finally, this study found that, aside from urban or rural household registration and being from *dibao* families, children's personal characteristics, family environment, and school environment all affect their fear of peers and inferiority in peer interactions. Specifically, as the children grow older, their fear of peers and inferiority become more serious. Girls face more serious fear of peers and inferiority than boys.  Children's health status is positively correlated with fear of peers and inferiority. Student leaders can help children diminish fear of peers and inferiority. Children from divorced families have more severe fear of peers and inferiority. Parental relationship, family relationship, and parent-child relationship are all negatively correlated with children's fear of peers and inferiority. Children in public schools have a higher level of fear of peers and inferiority than those in private schools. Children in boarding schools have a higher level of fear of peers and inferiority than those in day schools. Children's relationship with their teachers has a significantly negative correlation with fear of peers and inferiority.

#### *5.2. Policy Suggestions*

Positive peer interactions and developing and maintaining good peer relationships are conducive to children's healthy growth. The government, family, and school should pay active attention to the problem of children's fear of peers and inferiority, warranting timely interventions and help. They should encourage children to actively participate in peer interactions and create and maintain good peer relationships. Therefore, based on the research findings, this study provides the following suggestions.

First, policy makers should focus on the fear of peers and inferiority of rural children and children from *dibao* families. For rural children, it is necessary to concentrate on strengthening their psychological resilience, alleviating their anxiety and depression, and diminishing their dependence on mobile phones. For children from *dibao* families, it is essential to enhance their psychological resilience and prevent the *dibao* family from creating feelings of inferiority in their children's social interactions.

Second, policy makers should pay special attention to fear of peers and inferiority in exceptional children (*teshuertong*). Psychological changes of social cognition in older children are worth our attention, and it is necessary for us to solve the problem of fear of peers and inferiority. More support for and attention to girls and children who are not an only child is needed to enhance their peer interactions. Policy makers should work to improve children's health status to avoid the psychological problem of fear of peers and inferiority caused by health problems. Children from divorced families also deserve our attention, and we can help them by actively providing psychological support and encouraging them to engage in peer interactions to offset the negative psychological effects from divorce.

Third, families and schools should play important roles in solving the problem of fear of peers and inferiority. In a family, a harmonious conjugal relationship, supportive family atmosphere, and a close parent-child relationship are conducive to addressing children's problem of fear of peers and inferiority. Parents are advised to have fewer quarrels or avoid them. We suggest that parents should often organize family outings and regularly communicate with their children. For schools, children living on campus are the center of attention, and each school should support them in engaging in peer interactions. It is also necessary to build and maintain good relationships between teachers and students, and teachers should guide children and become role models. Teachers are advised to encourage children to actively participate in peer interactions. Children should be motivated to play an active role in class activities and to campaign for student leaders. In doing so, they can improve their ability to avoid fear of peers and inferiority.

**Author Contributions:** Conceptualization, S.W. and B.L.; methodology, S.W.; software, Y.Y.; validation, Y.Y., L.Y. and S.W.; formal analysis, B.L.; investigation, M.Z.; resources, B.L.; data curation, L.Y.; writing—original draft preparation, B.L.; writing—review and editing, L.Y.; visualization, M.Z.; supervision, L.Y.; project administration, Y.Y. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** The study did not require ethical approval.

**Informed Consent Statement:** Informed consent was obtained from all the subjects involved in the study.

**Data Availability Statement:** The data that support the findings of this study are available from the corresponding author upon reasonable request.

**Acknowledgments:** The authors thank Keqing Han, a professor in the National Institute of Social Development, Chinese Academy of Social Sciences/School of Sociology and Ethnology, University of Chinese Academy of Social Science.

**Conflicts of Interest:** The authors declare no potential conflict of interest.

#### **References**

**Yasushi Okamura 1,2,\* , Yuki Murahashi 1 , Yuna Umeda 1 , Toshihiro Misumi 3 , Takeshi Asami 2 , Masanari Itokawa 4 , Hirohiko Harima 1 , Masafumi Mizuno 1 , Hisato Matsunaga 5 and Akitoyo Hishimoto 2**

**Abstract:** (1) Background: Even though the comorbidity of obsessive-compulsive disorder (OCD) and a psychotic disorder (PD), such as schizophrenia, is being increasingly recognized, the impact of this comorbidity on the clinical presentation, including insight into obsessive-compulsive symptoms and the functioning of OCD, remains unclear. (2) Methods: To investigate clinical differences between OCD patients with and without PD, 86 Japanese outpatients who met the DSM-IV-TR criteria for OCD were recruited and divided into two groups: 28 OCD patients with PD, and 58 OCD patients without PD. The two groups were cross-sectionally compared in terms of their sociodemographic profiles and clinical characteristics, including the DSM-IV-TR insight specifier and the Global Assessment of Functioning (GAF). (3) Results: The results showed that OCD patients with PD scored lower on both the insight and GAF assessments. (4) Conclusions: The present study suggests that comorbid PD in OCD is a clinical entity.

**Keywords:** obsessive-compulsive disorder; psychotic disorder; schizophrenia; comorbidity; insight; functioning

## **1. Introduction**

*1.1. Background*

The relationships between obsessive-compulsive disorder (OCD) and various psychotic disorders (PDs), such as schizophrenia, have long been noted [1–6]. OCD, schizophrenia, and their comorbidity interact with each other in a manner that may affect prognosis and treatment [7–10]. The comorbidity of OCD and schizophrenia is currently being gradually recognized [11], and a common biological basis may underlie the higher-than-expected comorbidity rate [12,13].

Most of previous studies have focused on patients with schizophrenia, with or without obsessive-compulsive symptoms or OCD [14], but not vice versa. It is clear from the assessments by a number of investigators over the last two decades that a subgroup of patients with schizophrenia holds co-occurring obsessions and compulsions, while early studies on psychotic symptoms in patients with primary OCD did not use standardized diagnostic criteria [15]. Prior to the DSM-III-R [16], the diagnosis of OCD was ruled out by the presence of schizophrenia, and obsessive-compulsive symptoms in patients with schizophrenia were interpreted as symptoms of schizophrenia, as is still the case in ICD-10 [13,17]. Therefore, research on the comorbidity and relationship between the

**Citation:** Okamura, Y.; Murahashi, Y.; Umeda, Y.; Misumi, T.; Asami, T.; Itokawa, M.; Harima, H.; Mizuno, M.; Matsunaga, H.; Hishimoto, A. Obsessive-Compulsive Disorder with Psychotic Features: Is It a Clinical Entity? *Healthcare* **2022**, *10*, 1910. https://doi.org/10.3390/ healthcare10101910

Academic Editor: Brandon Gaudiano

Received: 8 August 2022 Accepted: 24 September 2022 Published: 29 September 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

two disorders has mainly emphasized broad variations in the psychopathological aspects of schizophrenia. DSM-5 [18] noted that the prevalence of OCD was higher in patients with schizophrenia than in that in a general population. Achim et al. (2011) showed that 12% of patients with schizophrenia had OCD. While obsessive-compulsive symptoms in schizophrenia have been proposed as a defense against psychotic deterioration [19] and, thus, are a predictor of a positive prognosis [20,21], many studies reported that the comorbidity of OCD among patients with schizophrenia had a negative impact on their prognosis [8,22–24]. Claims have been made [25–29] that the comorbidity of schizophrenia and OCD is a subtype of schizophrenia, with specific clinical features, but not without disagreement [30].

Less attention has been paid to OCD patients who are with or without PD. Comorbid PDs are frequently indicated as exclusion criteria in the majority of clinical research on OCD. Hence, limited information is currently available on the clinical characteristics of OCD patients with schizophrenia [13,31]. Numerous studies on psychotic traits comorbid with OCD have focused on schizotypal personality traits [32–35]. Epidemiological studies showed that 1–12.5% of patients with previously diagnosed OCD developed PD [36], and about one out of ten (12%) of patients with OCD met the diagnostic criteria for schizophrenia [25]. Recent meta-analyses found that individuals with OCD are more likely to have psychosis than the general population [37], and recent large-scale studies found that OCD increased the risk of developing schizophrenia after the onset of OCD [38–41], which is in contrast to the findings of previous studies showing that OCD was not associated with an increased risk of schizophrenia [42,43]. OCD with schizophrenia was more common in men [7], was associated with a lower score on the Global Assessment of Functioning (GAF) [9], had a more deteriorative course [7], was more resistant to conventional OCD treatments [44], and was susceptible to the exacerbation of psychotic symptoms when an anti-OCD agent was administered [10].

As used in Matsunaga et al.'s (2002) study, the GAF is internationally well known and widely used for scoring the severity of illness in psychiatry [45], and is recommended for routine clinical use [46]. The GAF summarizes the clinician's view of the patient's current degree of impairment in terms of psychosocial and occupational or educational function. Despite this, the GAF has been significantly less used in OCD studies.

Regarding insight into the obsessive-compulsive symptoms of pivotal clinical importance [42], Matsunaga et al. (2002) reported that a large percentage of patients with OCD had poor insight [9], and this may affect treatment and prognosis [47]. However, many studies discussing insight in patients with OCD excluded a psychotic comorbidity [35,48–51]. Studies on insight in patients with OCD with PD, especially schizophrenia, are rare [9,52]. It is still debatable whether comorbid PD is associated with a better [13] or worse [7,9,30] outcome of OCD.

A specifier of OCD with poor insight was first introduced in DSM-IV-TR [53]. The DSM-5 provides 3 insight specifiers: (1) good to fair, (2) poor, and (3) absent/delusional beliefs. Similarly, the ICD-11 has recently employed simpler dichotomous insight specifiers: (1) good to fair insight or (2) poor to absent insight [47]. As far as we know, there is one previous study on clinical characteristics and insight in patients with OCD using dichotomous insight specifiers [49]; this study, however, evaluated only OCD patients without PDs.

#### *1.2. Objectives*

The present study compared clinical characteristics between OCD patients with and without PD to identify what would differentiate the two groups, with particular focus on insight into OCD and the Global Assessment of Functioning. Our hypotheses were that OCD patients with PD would show poorer insight and lower GAF compared with OCD patients without PD.

#### **2. Methods**

#### *2.1. Participants*

Between April 2015 and April 2022, 86 outpatients at the Department of Psychiatry at Tokyo Metropolitan Matsuzawa Hospital were enrolled after submitting their written informed consent to participate in this study. Our hospital, the largest psychiatric center in Tokyo, receives approximately 7600 new patients annually, including 45 new OCD patients. After conducting surveys of outpatient medical records, all patients had been diagnosed with OCD (based on the DSM-IV-TR criteria) independently by an experienced psychiatrist (Y.O.) with more than five years of experience in the treatment of OCD, who was different from the attending psychiatrists. Inclusion criteria were patients with OCD based on the DSM-IV-TR criteria. No specific exclusion criteria were established. All patients were assessed using the Mini International Neuropsychiatric Interview, Japanese version 5.0.0 2003 (MINI), administered by one of the authors (Y.O.) or the attending psychiatrist. The MINI is a reliable and valid structured interview that may be administered by clinicians or trained non-clinicians to screen for 17 of the most common mental disorders listed in the ICD-10 and DSM-IV-TR [54–58]. The interview confirmed the diagnosis of OCD in all patients for the previous month, except for six who clearly had a history of OCD symptoms and irrational feelings about their obsessive-compulsive symptoms, but who were free from OCD symptoms in the month prior to the interview. Comorbidities not covered by the MINI were diagnosed according to the ICD-10. We also ensured that in OCD patients with PD, psychotic symptoms did not consist only of the delusional nature of insight into their obsessive-compulsive symptoms, but included other symptoms related to PD, including delusions other than those only related to poor insight, hallucinations, thought disorders, and negative symptoms. A total of 86 patients with OCD were divided into 2 groups: 28 patients with comorbid PD (26 with schizophrenia, one with schizotypal disorder, and one with schizoaffective disorder, depressive type, according to ICD-10) and 58 patients without PD.

#### *2.2. Ethical Considerations*

All of the procedures in the present study complied with the ethical standards of the relevant national and institutional committees on human experimentation and were conducted according to the guidelines of Declaration of Helsinki. The present study was approved by the Ethics Committee of Tokyo Metropolitan Matsuzawa Hospital. Detailed explanations of the study procedures were provided to each participant prior to their informed consent.

#### *2.3. Clinical Evaluation*

A detailed interview was conducted by one of the authors (Y.O.) covering the information on the patients' demographic profiles, clinical features, social background factors, and family and medical histories, as well as the clinical course and characteristics of their OCD. Insight levels were dichotomously assessed using the DSM-IV-TR insight specifier, which defines poor or absent/delusional insight as an individual's lack of awareness that his or her obsessions and compulsions are irrational during most episodes of OCD [53]. Patients other than those with poor to absent/delusional insight were assigned to the group characterized as having good to fair insight. If a patient had multiple obsessive-compulsive symptoms and no insight into at least one of these symptoms, the patient was defined as having poor to absent/delusional insight. Then, 20 out of 86 participants were randomly selected from the patients attending in January and February 2022 to examine the inter-rater reliability of the assessment of insight based on a joint interview by two of the authors (Y.O. and Y.M.), and the kappa coefficient [59] was 0.88.

Global severity and the prevalence of obsessive and compulsive symptoms was evaluated using the Yale–Brown Obsessive Compulsive Scale (Y-BOCS) [60]; general functioning was assessed using the Global Assessment of Functioning (GAF) [16,61,62]; disease severity was evaluated using the Clinical Global Impressions and Severity of Illness (CGI-S) [63]; and the severity of depression was rated using the Japanese version of the GRID-Hamilton Rating Scale for Depression (GRID-HAMD) [64,65], a structured interview incorporating the Hamilton Rating Scale for Depression (HAMD) [66], the international gold standard for assessing the severity of depression with high inter-rater reliability.

#### *2.4. Statistical Analysis*

Continuous variables were summarized with means (standard deviation, SD) regarding OCD with and without PD, and compared using a *t*-test between groups. Categorical variables were presented as frequencies and percentages by groups, and compared using the chi-square test or Fisher's exact test. The significance level was set at *p* < 0.05. A multivariate logistic regression analysis was used to extract the most influential clinical variables distinguishing OCD, with and without a psychotic comorbidity. The independent variables used were all seven variables that were significant in the bivariate analysis the five clinical factors reported in previous studies as significant for distinguishing the two groups: gender, marital status, age at OCD onset, GAF, and CGI-S, plus the two new items significantly differing between the two groups in the present study, namely, insight and an involuntary initial visit to a healthcare provider for a consultation regarding obsessive-compulsive symptoms. Statistical analyses were performed using IBM SPSS Statistics (Version 23; IBM Corporation, Armonk, NY, USA, 1989, 2015) (SPSS Inc., Chicago, IL, USA).

#### **3. Results**

#### *3.1. Sociodemographic and Clinical Characteristics*

No significant differences were observed in age, housemates, education, employment, or a medical or family history of a psychiatric disease, or comorbidity of psychiatric disorders other than PD between the OCD cases with and without PD (Table 1). The gender ratio was different between the two groups: men were overrepresented in OCD patients with PD. None of the OCD patients were married among OCD patients with PD, while one quartier of the OCD patients without PD were married.

**Table 1.** Comparison between OCD with psychotic disorder (*n* = 28) and OCD without psychotic disorder (*n* = 58): sociodemographic profiles and clinical characteristics.

**Table 1.** *Cont.*

The *t*-test or chi-square test were used to compare the groups, and Fisher's exact test was used if there were cells with expected frequencies of five or less.

#### *3.2. OCD-Related Aspects*

A total of 41 out of the 86 patients examined (47.7%) had poor to absent/delusional insight. Patients in the OCD with PD group were significantly more likely than those without PD to have poor to absent/delusional insight (23/28 vs. 18/58, *p* < 0.001) (Table 2).

The mean age of onset of OCD was lower in OCD patients with PD. The mean (SD) duration of untreated OCD was not different between the two groups. OCD patients with PD were more likely than those without PD to initially make an involuntary visit to a healthcare provider for a consultation regarding obsessive-compulsive symptoms (Table 2).

**Table 2.** Comparison between OCD with psychotic disorder (*n* = 28) and OCD without psychotic disorder (*n* = 58): clinical features and measures.

GAF = Global Assessment of Functioning; CGI-S = Clinical Global Impressions of Severity scale; GRID-HAMD = GRID-Hamilton Rating Scale for Depression; Y-BOCS = Yale–Brown Obsessive-Compulsive Scale. The *t*-test or chi-square test was used to compare the groups, and Fisher's exact test was used if there were cells with expected frequencies of five or less.

OCD patients with and without PD were not different in terms of the mean Y-BOCS scores and the types of OCD symptoms, as well as the mean (SD) GRID-HAMD score (Table 2).

The GAF score was significantly lower, and the CGI-S was significantly higher in the OCD with PD group than in the OCD without PD group (Table 2).

#### *3.3. Temporal Course of OCD and Schizophrenia*

Among the 26 OCD patients with schizophrenia, the onset of OCD preceded schizophrenia in a majority of cases (22 patients); the onset of the disorders was simultaneous in two patients, and the onset of schizophrenia preceded OCD in two patients. In the 22 patients in whom the onset of OCD preceded schizophrenia, the mean (SD) age of OCD onset was 15.0 (5.5) years. The mean (SD) delay of schizophrenia onset after OCD was 9.7 (7.5) years, and the mean (SD) onset age of schizophrenia was 24.7 (10.4) years.

#### *3.4. Multivariate Analysis*

**Table 2.** *Cont.*

The multivariate logistic regression analysis was performed to identify the clinical variables that best distinguish OCD with PD from OCD without PD (Table 3). Two items significantly predicted group membership: poor to absent/delusional insight (odds ratio: 0.065; *p* < 0.001) and lower GAF (odds ratio: 0.927; *p* = 0.012).

**Table 3.** Multivariate logistic regression analysis of factors of OCD with psychotic disorder (*n* = 28) and OCD without psychotic disorder (*n* = 58): sociodemographic profiles, clinical features, and measures.

CI = confidence interval.

#### **4. Discussion**

The main results of this study were that OCD patients with PD scored lower in insight and GAF evaluations compared with OCD patients without PD.

#### *4.1. Insight*

In the present study, 41 patients (47.7%) were considered to have poor to absent/delusional insight, which is consistent with previous findings. Matsunaga et al. (2002) reported that a large percentage of patients with OCD had poor insight. Although a lack of insight is generally assumed to be rare in patients with OCD [7], recent studies demonstrated that the frequency of poor insight was 15–31% in patients with OCD without PD [48–51] and 9–36% in patients with OCD with PD [9,52]. The present results showed a slightly higher prevalence of OCD patients with poor insight, which may be attributed to the higher rate of psychotic comorbidity (32.6%) than in previous studies (20% [9] and 1.7% [52]). The prevalence rate of poor insight in patients with OCD may be influenced by the degree of treatment for OCD at the time of interview, since previous studies have reported that insight can be improved after treatment for OCD [9].

The results of the present study are consistent with previous findings showing that OCD with schizophrenia was correlated more strongly with poor insight than OCD without schizophrenia [9,30,67]. As for the mechanism of poor insight in OCD with schizophrenia, it is possible that the schizophrenic thought disorders may contribute to the poor insight into OCD. Further study considering the degree and effect of thought disorders due to schizophrenia on insight into OCD are required.

The assessment of insight or comorbid schizophrenia in OCD is important because it is relevant to treatment planning. Some previous studies reported that OCD with poor insight was closely associated with a poorer response to medication [50], and some reported that OCD patients with schizophrenia were often resistant to typical OCD treatments [44]. As for pharmacological treatment, for example, in the American Psychiatric Association practice guideline for the treatment of patients with OCD, the pharmacological treatment of OCD with poor insight or with comorbid schizophrenia has not been established, and psychiatrists must rely on clinical judgment in formulating a treatment plan, since no large, controlled trials have yet been conducted [68]. Some reports stated that the use of an augmenting atypical antipsychotic was effective in patients with poor insight and an early age of OCD onset [69], and olanzapine monotherapy has been beneficial for patients with co-occurring schizophrenia in two case series, while second-generation antipsychotics were reported to exacerbate obsessive-compulsive symptoms [68]. Therefore, since there is no consensus on pharmacological treatment of OCD patients with poor insight or with the comorbidity of schizophrenia, those groups of patients may be resistant to conventional OCD treatment, and further research is needed to improve pharmacological therapeutic strategies.

#### *4.2. Sociodemographic Profiles and Clinical Characteristics*

In the present study, the OCD group with PD was significantly more likely than the OCD group without PD to exhibit the following clinical characteristics: unmarried, male, with poor prognostic factors, including a lower GAF and a higher CGI-S score in the univariate analysis, which is consistent with previous findings [7,9,30]. Among these factors, the multivariate logistic regression analysis revealed that the GAF score was a significant predictor of the OCD group with PD, suggesting the negative clinical impact of the comorbidity of PD and OCD. Since GAF measures the degree of mental illness by rating psychological, social, and occupational functioning [45], further research is needed to evaluate this issue using more specific rating scales that evaluate each function separately.

In the present study, the mean untreated duration of OCD was 7.1 years, which closely corresponded to the 7 years reported by previous studies [70]; however, the period may be as long as 17 years [71]. The prevalence of OCD in the general population is reportedly as high as 1.1–1.8% [18] or 2.5% [25]. Many patients with OCD hesitate to seek medical care and exhibit a low rate of hospital visits. Comorbidities may complicate the disease and make it enduring, and a chronic course is one of the poorest prognostic factors [72]. Therefore, early interventions, such as sharing knowledge about OCD and the importance of early consultation as part of medical care, with the general public and family physicians

and enabling early access to treatment by OCD experts, is important for the prevention of chronicity and severity in OCD.

#### *4.3. Temporal Course of OCD and Schizophrenia*

There are four possibilities regarding the pathogenesis of the comorbidity of OCD and schizophrenia. First, the two disorders may coexist by chance, without affecting each other. Second, OCD may develop first as a prodromal symptom of schizophrenia, or schizophrenia with OCD may represent a subtype of schizophrenia [28]. Previous studies on OCD in individuals at ultra-high risk of psychosis reported various conclusions [73,74]. Third, coexistent OCD and schizophrenia may have a mutually exacerbating or amplifying effect [29,75], and persistent OCD may predispose a patient to an increased risk of developing schizophrenia [40,41,73]. OCD may also become schizophrenia [76] or another form of psychosis [42]. Finally, patients with the comorbidity of OCD and schizophrenia may have common risk factors or a neurobiological basis [12,77,78]. In the present study, the onset of OCD preceded that of schizophrenia in most of the cases with PD, which is in line with previous findings [39,79,80]. In comorbidity cases, average ages at the onsets of OCD and schizophrenia were 15.0 years (slightly lower than the DSM-5 figure of 19.5 years, which was similar to those reported in previous studies [7,13]) and 24.7 years, respectively. Among the above four possibilities, the second, third, and fourth possibilities are the most likely, and the coexistence of the two disorders suggests more than a chance occurrence, because OCD with PD may be distinct from OCD without PD, based on poor to absent/delusional insight and the lower GAF score found in the present study. In addition, previous reports may configure such OCD with PD groups characterized by male predominance, younger age at OCD onset, and poor prognosis. To explore these possibilities, increasing the sample size and conducting cluster analysis or latent class analysis in a heterogeneous group of OCD patients with various comorbidities may also be useful in elucidating the pathophysiology of OCD. Such studies would provide a more detailed picture of the relationship between the two disorders, or of the cases of comorbidity of OCD and schizophrenia, especially in patients characterized by poor insight, low functioning, male predominance, younger age at OCD onset, and poor prognosis.

#### *4.4. Strengths and Limitations*

The present study has three strengths. First, it is one of the few studies to focus on the clinical characteristics of OCD with and without PD, in contrast to the large number of previous studies on schizophrenia with and without OCD. Recognizing the difference between OCD patients with and without PD may improve current treatments. For example, clinicians may provide adequate psychoeducation to patients with a comorbidity of OCD and psychosis in order to improve their insight, or consider a sufficient number of treatment options, such as the addition of antipsychotics if patients are resistant to conventional OCD treatment, or introduce the use of measures to prevent the development of schizophrenia.

Second, the present study contains rather common and practical information on clinical judgement in daily psychiatric settings. Psychiatrists need to make treatment plans for patients with OCD with various comorbidities, including PD, and to seek multidimensional information about the patients based on the results of the GAF; with these processes, we believe, better treatment of the patients with OCD can be achieved.

Third, the present study was conducted at a general psychiatric center in Japan, with no outpatient clinic specializing in OCD treatment. In Japan, there are not sufficient OCD specialists, and many psychiatric institutions do not have outpatient clinics specializing in OCD. Patients with OCD hesitate to disclose their obsessive-compulsive symptoms, resulting in a long period of time before they receive specialized treatment. Furthermore, clinicians may overlook obsessive-compulsive symptoms because OCD patients with poor insight may present to general psychiatric outpatient clinics for other prominent psychiatric symptoms, such as depression and psychomotor agitation. While this study was conducted in a more general psychiatric institution with no outpatient clinic specializing in OCD, it is

important to note that our hospital is a medical institution that treats many patients with schizophrenia, particularly the most severe forms of the disorder.

The present study is not without limitations. It contained a selection bias. The study center is the largest general psychiatric center in Tokyo, but has no specialized OCD treatment clinic. We included one patient with schizotypal disorder and one with schizoaffective disorder under rubric of PD. This may have biased the results. However, we obtained virtually the same results (Supplementary Tables S1-1, S1-2, and S1-3) when we repeated the analysis using 26 patients with schizophrenia and 58 OCD patients without PD (thus excluding the above 2 patients). Our OCD patients with PD included four patients with OCD onset that did not precede the onset of PD. This may have biased the results. However, we obtained virtually the same results (Supplementary Tables S2-1, S2-2, and S2-3) when we repeated the analysis using 24 patients whose OCD onset preceded that of PD and 58 OCD patients without PD (thus excluding the above 4 patients). Furthermore, the present study was exploratory; hence, the results of the multivariate logistic regression were not conclusive. Moreover, this study did not use a more detailed OCD insight scale. Notwithstanding these limitations, we believe this study provides clinically essential results, with practical applications.

#### **5. Conclusions**

The present study demonstrated that patients with a comorbidity of OCD and psychotic disorders were more likely to have poor insight and a lower GAF score than patients with OCD without psychotic disorders, and suggested that a psychotic disorder is one of the important clinical factors in assessing patients with OCD. The present results indicate that patients with this comorbidity may have a clinically different phenotype from that of patients with OCD without psychotic disorders. Future studies that enroll a larger cohort and employ more quantitative and qualitative assessment scales or multicenter research, including other institutions specializing in OCD clinics, are needed to generalize the results.

**Supplementary Materials:** The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/healthcare10101910/s1, Table S1-1: Comparison between OCD with schizophrenia (*n* = 26) and OCD without psychotic disorder (*n* = 58): sociodemographic profiles and clinical characteristics; Table S1-2: Comparison between OCD with schizophrenia (*n* = 26) and OCD without psychotic disorder (*n* = 58): clinical features and measures; Table S1-3: Multivariate logistic regression analysis of factors of OCD with schizophrenia (*n* = 26) and OCD without psychotic disorder (*n* = 58): sociodemographic profiles, clinical features, and measures; Table S2-1: Comparison between OCD with the onset of OCD preceding the onset of psychotic disorder (*n* = 24) and OCD without psychotic disorder (*n* = 58): sociodemographic profiles and clinical characteristics; Table S2-2: Comparison between OCD with the onset of OCD preceding the onset of psychotic disorder (*n* = 24) and OCD without psychotic disorder (*n* = 58): clinical features and measures; Table S2-3: Multivariate logistic regression analysis of factors of OCD with the onset of OCD precede the onset of psychotic disorder (*n* = 24) and OCD without psychotic disorder (*n* = 58): sociodemographic profiles, clinical features, and measures.

**Author Contributions:** All authors discussed the research idea and were involved in the data collection and analysis; Y.O. wrote the first draft of the manuscript; Y.M., Y.U., T.M., T.A., M.I., H.H., M.M., H.M. and A.H. reviewed the manuscript and added comments. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the Tokyo Metropolitan Government, grant numbers H27080303, H29080301, R01080303, R03080302 and R04080302.

**Institutional Review Board Statement:** The study was conducted according to the guidelines of the Declaration of Helsinki and was approved by the Ethics Committee of the Tokyo Metropolitan Matsuzawa Hospital, IRB code numbers 2015-1, 2016-1, 2017-2, 2018-22, and 2021-19.

**Informed Consent Statement:** Written informed consent was obtained from all subjects involved in the study.

**Data Availability Statement:** All data were generated at the Tokyo Metropolitan Matsuzawa Hospital, Japan. The derived data supporting the findings of this study are available from the corresponding author on request.

**Acknowledgments:** The authors would like to express their deepest gratitude to Toshinori Kitamura, Director of the Kitamura Institute of Mental Health Tokyo, who provided significant guidance in this research.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


**9. Acknowledgment**

The author of this chapter thanks Professors Pedro Núñez and Cristina González-Silgo at Universidad de La Laguna (Spain), and Professor John E. Greedan at McMaster University (Canada) for such important contributions to the field of the perovskites which came strongly in useful for the development of his knowledge of it as well as for having been remarkable mentors during his years of research.


Simulating 100000 AMP data
clear
A = xlsread('200sample', 'W1:AL16
                                       );#A is the state transition probability matrix TR
B = zeros(1,100000);
B(1) = 16;
i = 16;
s = zeros(1,16);
n = 2;
for n = 2:100000
r = rand(1);
i = B(n-1);
s(1) = A(i,1);
for j = 2:16
s(j) = s(j-1)+A(i,j);
if r >= 0&&r <= s(1)
B(n) = 1;
elseif r >= s(j-1)&&r <= s(j)
B(n) = j;
end
end
end
B
for i = 1:100000
r = rand(1);
B(i) = 1310+B(i)*5-5*r;
end
```
#### **References**

B'

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**4. Results**

#### *4.1. Preprocessing Data*

As a result of the experiments, the fatigue testing number of cycles to failure (*Nf*) was obtained. According to the experimental plan, specimens of 304 and 316L steels were burnished with 16 combinations. Low and high levels of the factors were coded with −1 and 1. Levels of two- and three-factor interactions were calculated as a multiplication of main factor levels.

The specimens of both steel batches were tested successively at each combination (replication r = 4), resulting in a total of 16 × 4 = 64 specimens (32 specimens of each kind of steel). The descriptive statistics of the fatigue data are shown in Table 4. Considering that unlike AISI 316L, specimens of AISI 304 were notched, the fatigue life results were as expected. The 316L specimens' fatigue life lay predominantly in the 106 range, while the fatigue life of 304 specimens lay predominantly in the 105 range.

**Table 4.** Results from the fatigue tests (descriptive statistics).

The fatigue life, even at constant stress amplitude, showed stochastic behavior. The materials' fatigue resistance due to the randomness of microdefect distribution, loading condition variations, and specimen preparation were the main sources of uncertainty. To model fatigue life, Normal and LogNormal distributions are commonly used.

Of particular interest in this study was the increase of the fatigue life due to burnishing operation with different combinations of regime parameters. To identify the characteristics of fatigue life gain, additional experiments with non-burnished specimens were carried out at the same loading conditions. The mean result for 304 steel was 2 × 104 cycles (tested four specimens). For 316L steel, the mean result was 14 × 104 cycles (tested three specimens). Based on these results, value *logCycles* representing gain of the fatigue life due to burnishing were formed. Cycles to failure of burnished specimens are divided into base cycles of non-burnished specimens and ones, converted to logarithmic scale, using the decibel rule to get more physical meaning, (Equation (2))

$$\log \text{Cycles} = 20 \cdot \log \left( \frac{\text{cycles to failure of burnished specimen}}{\text{cycles to failure of base specimen}} \right) \tag{2}$$

Descriptive statistics of data converted to log scale are shown in Table 4. These data are considered as primary data for the statistical analysis.

To ensure comparability of the data for different materials, the logCycles were scaled using a robust scaler from the Python library "SciKit Learn" [43]. This type of scaler uses the first and third percentile values and is more robust to outliers Equation (3). This kind of scaling can be applied to additional data (if replication of the experiment is made). The histograms of scaled data are shown in Figure 5.

$$y\_{scaled} = \frac{y\_i - q\_1(0.25)}{q\_3(0.75) - q\_1(0.25)}\tag{3}$$

**Figure 5.** Scaled data histogram.

Most of the data were in the unit range (−1; +1). The whole range of data was (−1.5; +1.5). As shown in Table 5, for the particular materials included in this research, mean and *q*1(*0.25*) and *q*3(*0.75*) quantiles were quite similar and scaling just centered the data and converted standard deviation to 1.

**Table 5.** Results from the fatigue tests, converted to log scale (descriptive statistics).

#### *4.2. Effects and T-Test*

The main effect of a given factor is the mean difference in the level of response as the input moves from the low to the high level [44]. Combined two- and three-factor effects (interactions) are calculated by multiplication of the main factor levels. For example, two-factor interaction is positive when the inputs move in the same directions and negative when the inputs move in opposite directions. To visualize these effects, linear regression plots are presented on Figures 6–8. Each kind of steel is treated separately for comparison.

In previous research [36], only the results of fatigue testing of AISI 304 steel were analyzed. It was found that the main factors A and D, and the interactions AC and AD, had the greatest impact. The new data from the 316L steel fatigue testing showed similar behavior, according to the main factors. In contrast, interaction AD was very strong, but the slope was different, comparing steel types (positive for 316L and negative for 304), as shown in Figure 7. From the three-factor interactions, ACD seems to be important (Figure 8).

**Figure 6.** Regression plots representing the main effects.

**Figure 7.** Regression plots representing two-factor interactions.

**Figure 8.** Regression plots representing three-factor interactions.

Since steels were burnished within the same experimental plan, and the fatigue testing procedure was the same, similar effects should be expected, so the new effects calculation was made considering the whole dataset. The main effects and interactions are given in descending order of their absolute values in Table 6. A Pareto chart (see Figure 9) shows that the first seven factors from the table should be considered significant (D, A, ACD, AD, AC, BCD, BD), because they covered about 80% of the total effect.

**Table 6.** Main effects, two- and three-factor interactions and *p* values.

**Figure 9.** Pareto plot factors (regime parameters) and interactions.

The obtained results were confirmed by *t*-test. This test checks the null hypothesis if the mean values of the two groups of samples are identical. The *p*-values, calculated from the *t*-test, are given in the last column of Table 2. All of them were greater than 5% (*p* > 0.05), which means that the null hypothesis cannot be rejected with 95% level of confidence for all the factors and interactions. If value *p* = 0.1 (90% confidence) is taken as a significance level, the null hypothesis can be rejected for D and A factors and these factors are considered significant for the regression model. The values of these factors confirm the general findings for the burnishing processes: that higher force (A) and low federate (D) guarantee a higher degree of plastic deformation, thus benefiting the fatigue life [28], but give no information about the influence of the regular relief degree of imbrication, connected with factors B and C.

More detailed statistical inference from such noisy data can be obtained, using the Bayesian approach. Bayesian models are called probability models, since as a result distribution rather than the point estimates for the unknown parameters are obtained. According to the Bayesian rule Equation (4), the posterior probability of parameters of interest *θ*, based on the observed data *y*, can be estimated, using our prior knowledge about these parameters (*θ*). The term *P*(*y*|*θ*), called likelihood, is a probabilistic model for the data. The denominator term *P*(*y*) is the marginal probability of the data, called evidence. Since it is just a normalizing constant, it can be omitted and stated that posterior probability is proportional to likelihood times, prior probability.

$$P(\theta|y) = \frac{P(y|\theta) \cdot P(\theta)}{P(y)},\tag{4}$$

where *P*(*θ*|*y*)—posterior; *P*(*θ*)—prior; *P*(*y*|*θ*)—likelihood; *P*(*y*) = *P*(*y*|*θ*)·*P*(*θ*)*dθ*—evidence.

*P*(*θ*|*y*) ∝ *P*(*y*|*θ*)·*P*(*θ*)

For the continuous random variables, *P*(*θ*|*y*) is a probability density function (PDF) of a certain distribution. So, Bayesian modeling requires first setting the appropriate likelihood distribution, which describes how the data can be generated, and second, choosing the prior probability distributions for all the unknown *θ* parameters. Prior distributions can be constructed as non-informative, i.e., diffuse or even improper, which PDF does not integrate to 1. If too informative (strong) prior distributions are used, there is a risk in ignoring the experimental data. Of course, in the presence of enough data, the prior choice is ignored, and likelihood dominates the posterior distribution. The Bayesian probabilistic model can be updated if new data are available just by setting the posterior distributions to prior for the new data.

For some of the simple cases, a closed form solution for the posterior density is given in the literature [37]. Nevertheless, for all probabilistic models, Bayesian inferences can be made just by simulation. To ensure random, non-correlated samples covering the whole distribution, Markov chain Monte Carlo (MCMC) sampling algorithms are used. Nowadays, numerous statistical packages and libraries for "R" and Python are available. Some of the most popular are WinBUGs, JAGS, Stan, and PyMC.

#### *4.3. Regression Model*

4.3.1. Ordinary Least Square Regression (OLS).

Ordinary least square linear regression Equation (5) assumes Gaussian distribution of the noise.

$$y = X\beta + \epsilon,\tag{5}$$

where *y* ∈ R*n*×1—column vector of parameter of interest (regressors); *X* ∈ R*n*×*k*+1 = [{1}, {*x*1}, {*x*2} ... {*xk*}], predictors (or design matrix); *β* ∈ R*k*+1×1—column vector of regression coefficients; ∼ *N* 0, *σ*2 *I* —Gaussian noise.

As the effects and interactions are calculated, a linear regression model can be formed as Equation (6), where the first term is a mean of the dependent variable *y*, and to calculate the other coefficients *i* th effect or interaction value should be divided by 2, since it shows the amount of change of the regressor as predictor *xi* moves 2 steps, from −1 to +1.

$$\mathcal{Y} = \mathbb{X}\mathcal{Y} = \mathbb{y} + \frac{1}{2} \sum\_{i=1}^{k} \sum\_{i} effect\_i \times \mathbf{x}\_i \tag{6}$$

The probabilistic model of linear regression can be expressed as Equation (7). Data *yi* comes from Normal distribution with a mean equal to OLS estimation *y*ˆ and variation *σ*2 = .

$$y\_i \sim \mathcal{N}\left(X\beta, \sigma^2\right),\tag{7}$$

where *i* = 1,2, . . . ,*n* is the number of data points

From a Bayesian perspective, each regression coefficient can be treated as a random variable, coming from a Normal distribution with unknown mean and variance Equation (8).

$$
\beta\_i \sim \text{ N}\left(\mu\_{i\prime} \text{ s}\_i^2\right), \tag{8}
$$

Under a non-informative Jeffrey's prior, this problem has a closed form solution [37]. The resulting parameters of posterior are dominated by experimental data. The marginalized distribution for mean *μ*, with the integrated *s*2 is a non-centered Student-t distribution Equation (9).

$$
\mu\_i \mid y \sim t\_{n-k-1} \left( m\_{i\prime} \; S\_i^2 \right) \tag{9}
$$

The location parameter mi is equal to the least squares estimation of regression coefficients, the scale parameter *S*2 *i* is equal to the standard error, and the degrees of freedom are equal to the degrees of freedom of the regression model. From this distribution, credible intervals CI and/or high-density intervals (HDI) with a certain probability can be formed.

Results from the OLS regression, including the first seven factors from the Pareto plot, are given in Table 7. To perform this regression, the Python library Statsmodels was used [45].

**Table 7.** Ordinary least square (OLS) regression results.

Looking at the 95% HDI, again the conclusion is that there was no significant factor with a significance level α = 5%.


*<IP_ADDRESS>. Oxygen donor ligands*

Organic acids such as malate, aconitate, malonate, oxalate, tartrate and citrate are involved in metal uptake restriction and dexotification in plants. These carboxylic acid anions form complexes with divalent and trivalent metal ions with high stability. They are involved in the restriction of metal entry into the cell, metal exclusion in the root cells, accumulation and transport within the plants. In wheat (*T. aestivum*), citrate and malate formed complexes with Cu in order to immobilize this metal in the rhizosphere thus preventing its entry into the cell (Yong and Ma 2002). Citrate was also involved in the hyperaccumulation of Ni in 17 New Caledonian plants and the amount of citrate produced was highly correlated with the accu‐ mulation of Ni (Lee *et al.,* 1977). The accumulation of Zn in some plants is facilitated by the transport of malate-Zn complexes. Upon the Zn ions uptake into the cytoplasm, they are bound to malate, which serves as a carrier to transport the Zn ions to the vacuole. Once there, the Zn ions are complexed by a terminal acceptor and released from malate. The malate is then able to return to the cytoplasm and transport additional Zn ions to the vacuole (Yong and Ma 2002). Still and Williams (1980) reported that the transport of free Ni ions to root cells via membrane is restricted. However, when Ni is bound to organic compounds such as citric and malic acids, it can be transported across the plasma membrane (Yong and Ma 2002). In *Zea mays*, the production of organic acid is influenced by external aluminium ion concentration (Pintro *et al.,* 1997). Also, in manganese tolerant *T. aestivum* cultivars, the production of malic, citric or aconitic acid was not induced when exposed to this metal but for the manganese sensitive cultivars, the organic acids concentration slightly increased (Burke *et al.,* 1990).


**1.6.1 Historical background**

India has been universally accepted as the original home of these two pulse crops. While green gram was spread to many countries, especially in tropical and subtropical Asia, black gram has remained more or less confined to South Asia. Currently, green gram is being grown in USA.