The concept of FQOL has been used to assess family adjustment outcomes for children with autism and is increasingly attracting the attention of researchers worldwide (6, 7). Several studies have shown that FQOL for children with autism is lower than for families of children with other disabilities (8, 9), making the study of FQOL for children with autism particularly important for social welfare.

Previous research has focused on exploring children with autism's overall FQOL and its possible predictors. These predictors focus on the child with ASD's: (1) individual level (6, 7, 10), (2) family level (6, 7, 11–14), and (3) social support level (15, 16).

The severity of symptoms in children with autism negatively predicts their FQOL (6, 7, 10). In addition to social support (15, 16), family cohesion (7), parental stress (11), and parental involvement (12) are associated with FQOL, indicating it is the result of multiple factors.

Although there is still a lack of representative large-scale epidemiological surveys on children with autism in China, the number of children being diagnosed with autism is increasing. Meanwhile, Chinese families experience high stress levels and low FQOL (17). These families experience high levels of parenting stress, financial burden, and limited family support (18). Hence, further investigating FQOL among children with autism in China is worthwhile.

Previous findings suggested that parental stress is greater for parents of children with autism than for those of typically developing children and children with other disability types (19–21). In the existing studies, parental stress, as an independent variable, affects the lives and growth of many children with autism and their parents. The relationship between parental stress and FQOL has received much attention, and some studies have demonstrated parental stress' lasting impact on children with autism's FQOL (22).

The current research on parental stress related to ASD and FQOL comprises three main aspects. The first aspect concerns their current state; parents of children with autism tend to have higher levels of parental stress and lower levels of FQOL [e.g., (8, 23, 24)]. The second aspect concerns the outcome assessments of parental stress, with some studies involving FQOL as an important parental stress outcome in assessing autistic children's families' overall satisfaction [e.g., (9)].

The third aspect regards their causal analysis. For instance, Likhitweerawong et al. (25) identified that, among 61 and 63 Thai caregivers of children with and without ASD, respectively, higher parental stress correlated moderately with lower authoritative, higher authoritarian, and higher permissive parenting styles, while a negative correlation was found between authoritarian and permissive parenting styles and children with ASD's quality of life. Pozo et al. (7) found that among 118 Spanish parents (59 mothers and 59 fathers) with a child with ASD, behavior problems negatively affected FQOL indirectly (through sense of coherence). The severity of the disorder and social support levels played significant roles in FQOL models for both fathers and mothers, whereas coping played differentiated roles in their FQOL. Through a meta-analysis of 29 studies (N = 4,864), Wang et al. (26) found that among caregivers for autism, social support partially mediated the relationship between coping (positive and negative) and family quality of life.

During the COVID-19 pandemic, people have stayed home and socially isolated themselves to avoid contracting the virus (27). Existing studies have demonstrated that while isolation somewhat reduces the risk of virus transmission, it also brings anxiety and psychological stress (28–30). In particular, parents affected by the pandemic who are raising infants or children with disabilities receive lower levels of social support and are at greater risk of psychological distress (3, 31–33).

The relationship between parental stress and FQOL is of great academic interest. Studies exploring the relationship between the two could help to reduce stress and improve FQOL for children with autism and their families during COVID-19. Some studies have analyzed parental stress as an influential factor in family relationships, regulation, and social support in the COVID-19 epidemic context (34–36). However, to the authors' best knowledge, no studies have focused on the relationship between pandemic stress and FQOL of children with autism. Thus, identifying and discussing the role of COVID-19-pandemic-related stress in parents of children with autism's FQOL is worthwhile.

Research on parental involvement originated with Englund et al.s' (37) study, which noted a positive relationship between parental involvement and children's school performance. Existing studies summarize the basic content and common forms of parental involvement, which mainly include the child's education plan, intervention plan, and educational career planning (38–40), as well as participation after communication with the intervention team and participation with the child in implementing the program (41, 42).

Parents need to spend more time and energy caring for children with autism, so it is essential to study parental involvement and related factors, which are important parts of developmental and therapeutic strategies for children with autism and particularly critical in the child's early development, education, and therapeutic interventions (43, 44). Parental involvement with children with autism covers a wide range of areas, including participating in the child's development, learning, and treatment and actively interacting with teachers and physicians (45, 46). Increasingly, parents of children with autism are becoming involved in their child's activities and interventions, participating in homework tutoring, parent training, and the design and implementation of intervention processes (29, 47–49). In this process, it is possible to gain a more comprehensive understanding of the effectiveness of engagement behaviors and thus better design and implement them when considering family outcomes, using FQOL as an indicator (50, 51).

It has been confirmed that parental involvement in the care and education of children with autism can have a positive impact on the child's behavioral styles, character personality, future development, and family relationships and interactions (52–54). Some studies have focused on the impact of parental psychological stress on parental involvement in children with autism, showing that increased parenting stress and decreased supportive behaviors and child care lead to decreased parental involvement (55, 56).

Some existing studies have confirmed the relationship between parental stress and involvement (57, 58), while others have demonstrated that parental involvement can influence FQOL (12, 59). In China, studies have found that parents of children with autism have higher parental psychological stress and are less actively involved in parenting than parents of normal children and children with other disabilities (60, 61). Thus, it is valuable to explore whether parental involvement mediates the relationship between pandemic stress and FQOL.

The purpose of this study was to enrich the research on the relationships among pandemic stress, parental involvement, and FQOL for children with autism. Two research questions were proposed: (1) What are the current status of pandemic stress, parental involvement, and FQOL for children with autism in China? (2) What are the relationships among pandemic stress, parental involvement, and FQOL? Based on previous studies, two hypotheses were made. The first was that pandemic stress would directly predict FQOL. The second was that pandemic stress would indirectly predict FQOL, mediated by parental involvement.

A review of the current literature and research hypotheses suggested that pandemic stress would predict FQOL through direct and indirect pathways, with parental involvement mediating the latter. This study's proposed hypothetical model is shown in Figure 1.

As the study did not have direct access to a list of children with autism in China, it used schools as a hub to introduce the online questionnaire to principals of special public schools serving children under the age of 22 with autism, in 31 provinces, autonomous regions, and municipalities. The principals then introduced and distributed the questionnaire to their students' parents, encouraging them to participate in this research.

All participants in the study completed the questionnaire online, which usually took about 20 min. All participants uploaded an informed consent form stating that participation was voluntary and that all information collected through the questionnaire would be kept strictly confidential and used for academic research only. All demographic information was anonymized. Upon completing the questionnaire, participants were randomly given an online bonus package, with a one-third chance of winning, to show the researchers' appreciation for their participation. It is worth noting that the data was collected when children were able to attend classes a bit in person/hybrid learning.

Eight hundred and one families of children with autism completed the survey. Since the present research target children with autism, and those with autism usually lag behind the normal population across diverse developmental domains, we selected families with children aged ≤22 years as our sample, resulting in a final sample of 761 families. Removing outliers left 709 participants, 16% male and 84% female. Parents were mostly 31–50 years old. Their education was mostly at the bachelor's degree level or above. Most of the children with autism are 8–17 years old, mostly primary school students. About 40 % of the family reported a monthly income of <5,000 yuan (equivalent to 710 US dollars), below the poverty threshold (the level deemed necessary to achieve an adequate standard of living in China). Table 1 shows the demographic information of the children and their parents.

A demographic sheet and three inventories were adopted in this study. The demographic sheet included questions to gather respondents' personal information (i.e., gender, age, employment status, educational level, family structure, monthly household income, number of children) and their children with disabilities (i.e., age, educational level). The three inventories were as follows.

Data cleaning was carried out before data analysis. No variables had missing data. The outliers were processed by IBM SPSS 27.0, and 52 samples with standard scores less than or greater than 3 were removed, leaving a final sample of 709. An examination of correlations revealed that no independent variables were highly correlated (r > 0.80). The multi-collinearity statistics including Tolerance and VIF (variance inflation factor) were within acceptable limits.

SPSS 27.0 was used to test the three scales' reliability. SEM was used to conduct CFA on the modified Family Quality of Life Scale and Parental Involvement Scale. EFA was conducted for the Pandemic Stress Scale.

SPSS 27.0 was used to describe each FQOL subscale to answer the first research question. Then, one-sample t-tests were conducted to assess the mean difference between participants' perceptions of these variables and the hypothesized midpoint score (i.e., critical value = 3).

Structural equation modeling (SEM) was applied to test the hypothetical model to answer the second question (see Figure 1). SEM is a series of multivariate statistical models used to estimate the effects and relationships between multiple variables representing a hypothetical, theoretical model (68). In the present research, the three variables were the sum of the items from each scale. Due to the risk perception and concern and physical and mental reaction subscales' low loading coefficients for pandemic stress and the non-significant direct effect between pandemic stress and FQOL in the hypothetical model, a new model was reconstructed, within which the three factors of pandemic stress were used as observed independent variables (see Figure 4).

The first research question addressed the current status of pandemic stress, parental involvement, and FQOL among families of children with autism in China. As shown in Table 2, the FQOL for children with autism in China is significantly higher than the expected average (score 3). Emotional happiness was the lowest [M = 3.12, SD = 0.81, t₍₇₀₈₎ =3.92, p < 0.001], followed by disability-related support [M = 3.26, SD = 0.83, t₍₇₀₈₎ = 8.33, p < 0.001]; the highest was family interaction [M = 3.91, SD = 0.77, t₍₇₀₈₎ = 31.35, p < 0.001], followed by family care and support [M = 3.80, SD = 0.70, t₍₇₀₈₎ = 30.55, p < 0.001].

Parents' involvement with their children with autism was above our expected average (score 3). Interest development was highest [M = 4.03, SD = 0.63, t₍₇₀₈₎ = 43.67, p < 0.001], followed by help with homework (M = 3.89, SD = 0.68, t₍₇₀₈₎ = 34.88, p < 0.001).

Of the three dimensions of pandemic stress, risk perception and concern [M = 2.51, SD = 0.90, t₍₇₀₈₎ = −14.60, p < 0.001] and physical and mental reaction [M = 2.83, SD = 0.83, t₍₇₀₈₎ = −5.45, p < 0.001] were lower than the expected mean, while pragmatic hopefulness was higher [M = 3.91, SD = 0.66, t₍₇₀₈₎ = 37.02, p < 0.001].

The second research question concerned the relationship between pandemic stress, parental involvement, and FQOL. The final SEM (see Figure 4) was determined and the model fit index indicated it was feasible, where X²/df = 13.40, RMSEA = 0.13, GFI = 0.86, AGFI = 0.80, CFI = 0.78, IFI = 0.78, and TLI = 0.72.

The modification indices function was used to see if Amos could propose further improvements to the model. After the modification, the SEM has a better model fit index, X²/df = 5.323, RMSEA = 0.08, GFI = 0.95, AGFI = 0.91, CFI = 0.94, IFI = 0.94, TLI = 0.90. In addition, by conducting exploratory model exploration with Amos, the output suggested deleting the direct covariate path between pragmatic hopefulness and FQOL; the current model was the preferred SEM for revealing these data and describing the correlation effects between pandemic stress, parental involvement, and FQOL.

The range of standardized loadings for each latent variable and the observed scales and standardized path coefficient is shown in Figure 4. FQOL ranged from 0.62 to 0.79 and parental involvement ranged from 0.49 to 0.91, with all loading indices >0.40 and statistically significant (p < 0.001), indicating that the dimensions of the factors adequately measured and explained the latent variables.

The direct effect of pragmatic hopefulness on FQOL was not significant and had a positive effect on FQOL through the mediation of parental involvement as shown in Table 3, a full mediation effect with an effect size of 0.20^*0.57 = 0.114. Risk perception and concern had a direct positive effect on FQOL with a size of 0.11 and a negative effect on FQOL through the mediation of parental involvement with a size of −0.17^*0.57 = −0.097. The total effect of risk perception and concern on FQOL is positive, size 0.11–0.17^*0.57 = 0.013; physical and mental reaction had a direct negative effect on FQOL, size −0.55, a positive effect on FQOL mediated through parental involvement, size 0.45^*0.57 = 0.257, a negative total effect on FQOL with a size of −0.55 + 0.45^*0.57 = −0.293.

To summarize, the model results largely supported the two hypotheses. Consistent with the first hypothesis, there was a significant direct correlation between pandemic stress and FQOL. The direct predictive effect of pandemic stress on FQOL was supported by two dimensions, physical and mental reaction and risk perception and concern, where physical and mental reaction was negatively related to FQOL and risk perception and concern was positively related to FQOL. Consistent with the second hypothesis, there was a significant indirect correlation between pandemic stress and FQOL, mediated by parental involvement. The three dimensions of physical and mental reaction, risk perception and concern, and pragmatic hopefulness supported the indirect predictive role of pandemic stress on FQOL, where physical and mental reaction was positively related to FQOL, risk perception and concern was negatively related to FQOL, and pragmatic hopefulness was positively related to FQOL.

Families of children with ASD had relatively higher satisfaction with family interaction and relatively lower satisfaction with their emotional wellbeing, which is consistent with previous research (69). On the one hand, this may be due to the fact that many people in China consider ASD as a stigma (70), and social labeling and self-labeling reduce their self-identity and emotional level needs. On the other hand, studies have showed that family quality of life for children with ASD decreases under the psychological stress [e.g., (5)]. Family quality of life for children with ASD was significantly influenced by the pandemic. For parents of children with ASD, their interaction with the surrounding environment was reduced, and consequently social inclusion was hindered as well as emotional needs were unmet.

During the COVID-19, parents of children with special needs spent more time and energy caring for their children because of the limitations of pandemic prevention regulations such as isolation (34–36). In China, parents of children with ASD are often involved in all aspects of their children's learning and life due to their children's medical condition. Results showed that parents were sufficiently involved in all four areas, with the highest involvement being in “interest development-extracurricular activities”, which is consistent with previous studies (67, 71). Meanwhile, the lowest level of involvement was “monitoring”, which is consistent with several studies on parental involvement in cerebral palsy, surgical hospitalization, and mobile children (72–74).

Previous studies have confirmed the positive predictive effect of parental involvement behaviors on FQOL (12, 50, 58), and promoting parental involvement in the learning, living, and rehabilitation interventions of children with ASD is beneficial not only for the development of children with ASD, but also for their family life situation.

For physical and mental reaction, the SEM results show a direct negative effect of physical and mental reaction on family quality of life and a positive effect on family quality of life mediated by parental involvement, with a negative overall effect of physical and mental reaction on family quality of life. Higher physical and mental reaction means parents of children with ASD experience more physical and mental suffering in pandemic, such as insomnia, and have more need for counseling caused by high level anxiety. Family quality of life is a multidimensional concept that involves people's emotional wellbeing, and the physical and mental reaction to the pandemic reduce people's emotional wellbeing, which in turn reduces the quality of family life.

Risk perception and concern had a direct positive effect on family quality of life and a negative effect on family quality of life mediated through parental involvement, with a small positive total effect on family quality of life. This is also inconsistent with previous results regarding the negative effect of stress on family quality of life (7, 8, 24, 25). Considering the pandemic, the more severe the perception of the pandemic, the stronger the desire to reduce the impact of the pandemic on children with ASD in various ways, and the increased family care, material wellbeing and disability-related support, which would improve their quality of life; at the same time, risk perception and concern of the pandemic may discourage parents from participating in their children's lives and thus reduce their participation behavior, but overall, risk perception and concern during the pandemic enhance family quality of life to some extent.

Although pragmatic hopefulness has no direct effect on FQOL, it has positive indirect effect on FQOL through parental involvement. The higher level of pragmatic hopefulness results in higher parental involvement, and the higher level of parental involvement results in higher level of FQOL. This means the increase of pragmatic hopefulness can improve FQOL for children with ASD. The continued spread of pandemic and the associated home isolation requires pragmatic hope so that families of children with autism could mobilize their own resources for a more active life. Providing social support to families of children with autism to help them develop an objective and positive intellectual orientation to the outbreak is critical (56), and the public health sector should provide families of children with autism with timely and correct knowledge and guidance about the impact of the outbreak on their personal health as well as on their child's growth and development (4, 21).

It is worth exploring that as a dimension of pandemic stress, physical and mental reaction elevate parental involvement, which is contrary to findings of previous research (55, 56). This may be related to the context of the pandemic. Parents reacted strongly both physically and mentally during the pandemic and were more concerned about their children, minimizing the impact on their children by over-caring for them. At the same time, the policy of home isolation in pandemic situations requires greater parental control of children in the home, and school rules for online teaching make parents more participating in their children' schooling actively or passively.