Informant Discrepancy in Report of Parent-adolescent Conflict as a Predictor of Hopelessness among Depressed Adolescents: A Replication Study

More knowledge is needed about how family factors influence depression features in adolescents. We aimed to replicate a previous small sample study showing that higher discrepancy between adolescents and caregivers in report of conflict predicted more hopelessness in adolescents with major depression. The current sample comprised 417 adolescent and maternal caregiver dyads. The adolescents were aged between 12 and 17 years (55.4% female, 44.6% male). The sample was drawn from the Treatment of Adolescents with Depression Study (TADS). Analyses were conducted using latent difference score modelling, item response theory, and linear regression in a Bayesian framework. Higher adolescent-perceived conflict relative to caregiver-perceived conflict predicted more adolescent hopelessness. This replicated the original findings in a much larger sample. Adolescent gender did not influence the associations. Addressing divergence in adolescent and parent perceptions of conflict may be relevant to ameliorate hopelessness in treatment of adolescents with depression. Hopelessness is a key complication in adolescent depression, and identifying factors associated with hopelessness is relevant for improving treatments. Parents and adolescents often perceive the level of conflict between them differently. This study replicated a previous finding that parents reporting less conflict than the adolescent predicts hopelessness among depressed adolescents. Interventions to align parent and adolescent perceptions of the relationship should be further investigated as brief interventions to reduce hopelessness in adolescent depression. Hopelessness is a key complication in adolescent depression, and identifying factors associated with hopelessness is relevant for improving treatments. Parents and adolescents often perceive the level of conflict between them differently. This study replicated a previous finding that parents reporting less conflict than the adolescent predicts hopelessness among depressed adolescents. Interventions to align parent and adolescent perceptions of the relationship should be further investigated as brief interventions to reduce hopelessness in adolescent depression.

• Parents and adolescents often perceive the level of conflict between them differently.
• This study replicated a previous finding that parents reporting less conflict than the adolescent predicts hopelessness among depressed adolescents.
• Interventions to align parent and adolescent perceptions of the relationship should be further investigated as brief interventions to reduce hopelessness in adolescent depression.
Despite good evidence for the efficacy of psychological treatments for adolescent depression, effect sizes are modest (Cuijpers et al., 2021;Eckshtain et al., 2019). Treatment outcomes in regular care are heterogeneous, but available evidence suggests many adolescents treated for depression do not experience an improvement in their symptoms (Bear et al., 2020). Increased knowledge about the causes and maintaining factors of adolescent depression can contribute to development of more effective treatments.

Hopelessness Is an Important Complication in Adolescent Depression
Depression is a multifaceted phenomenon, comprising a range of emotional, somatic, behavioural, and cognitive features (Clayborne et al., 2019). The focus of the current study is on hopelessness, which can be defined as a state in which a person expects negative events, believes goals cannot be achieved, and feels s(he) is powerless to improve the future (Marchetti, 2018). Hopelessness is an inherent conceptual and empirically demonstrated depression component, and is associated both with depression onset, poor depression treatment outcomes, and is a risk for malignant trajectories following depression (e.g. suicide risk; Alloy et al., 2008;Asarnow et al., 2009;Davies et al., 2020;Wolfe et al., 2019). Some predictors of hopelessness among depressed adolescents have been reported, including poor family relationships, cognitive distortions, traumatic events, and negative self evaluations (Becker-Weidman et al., 2009;Duyan, 2016;Kashani et al., 1994), but the literature is quite limited.
A family factor that may be particularly linked to hopelessness in adolescence, is caregiver-adolescent conflict. Conflicts with caregivers may trigger feelings and cognitions concerning not belonging, not being heard and understood, and not being supported, which in turn may boost a sense of hopelessness (Becker-Weidman et al., 2009;Kim et al., 2015;Kwok & Shek, 2010). However, parents and adolescents often do not agree about how much they disagree. A substantial body of research shows that discrepancy is the norm rather than the exception when different informants report on psychosocial variables, and that this discrepancy may be informative (De Los Reyes et al., 2015;Korelitz & Garber, 2016).

Informant Discrepancies in Report of Conflict
Informant discrepancies in report of parent-adolescent conflict may indicate that the parent-adolescent dyad lacks a shared representation of their relationship, and we would argue that this might be particularly distressing to the adolescent. Conflicts are less likely to be resolvable through problem-solving or negotiation (Missotten et al., 2017) when those in conflict have diverging representations of it. In obligatory relationships, such as that of an adolescent to their parents (Laursen & Collins, 2009), such unresolvable conflict is likely to be perceived as an inescapable source of distress. In this way, discrepancy in report of parentadolescent conflict may be an indicator of a relational state that makes the adolescent expect persistent and unavoidable distress. Such expectations are in themselves an important aspect of hopelessness (Marchetti, 2018).

The Current Study
A previous study indicated that discrepancy in the perception of conflict between adolescents and parents may have a stronger relationship with hopelessness among depressed adolescents than the level of conflict as such (Rognli et al., 2021). Adolescent hopelessness was highest when adolescents reported high caregiver-adolescent conflict while caregivers reported low conflict. However, that study had considerable limitations.The sample size was small (n = 57), and the gender distribution was uneven (87% female, 13% male). We concluded that the study findings needed replication in larger and more gender balanced samples, and this is the aim of the current study. Replication studies are strongly needed in mental health research (Tackett et al., 2019).
In the current paper, we take advantage of the open science paradigm that has followed the replication crisis discourse (Hillary & Medaglia, 2020) and use data from the Treatment of Adolescents with Depression Study (TADS, The TADS Team, 2003) to replicate the findings of Rognli et al., (2021). TADS was a large, four-arm multisite clinical trial of treatments for adolescent depression, conducted in the United States between 1998 and 2004. TADS compared treatment with fluoxetine, pill placebo, cognitive behavioural therapy (CBT), and combined treatment with fluoxetine and CBT. The sample was ethnically and sociodemographically diverse (The TADS Team, 2005). The complete dataset from TADS has been made available for research through the National Institute of Mental Health Data Archive. In line with the original study, we hypothesised that adolescents reporting more severe conflict than their parent would predict hopelessness, above and beyond the absolute level of conflict. The replication was preregistered at https://doi.org/10.17605/OSF.IO/D72WG.

Participants
The sample comprised 231 female (55.4%) and 186 male adolescents (44.6%), and their maternal caregivers (N = 417). Adolescents participating in TADS and their caregivers were eligible for inclusion in the present study. The TADS sample comprised 439 adolescents aged 12-17 years with a primary diagnosis of major depressive disorder (MDD) according to DSM-IV criteria (American Psychiatric Association, 2000). The demographic and clinical characteristics of the TADS sample, design, data collection procedures, as well as inclusion and exclusion criteria are described in detail in previous publications (The TADS Team, 2003, 2005. TADS was completed in full compliance with the Department of Health and Human Services policy for the protection of human subjects (45 CFR 46). The protocol and consent documents were reviewed and approved by the Institutional Review Boards of each participating institution. All data collection, handling, and storage were done in compliance with the Privacy Act. A Federal Certificate of Confidentiality was obtained for the study. All participants (adolescents and caregivers) provided written informed consent or assent to participate in TADS. Written consent was obtained from parents on behalf of the adolescents where appropriate.
To be included in the current study, participants drawn from the TADS dataset had to have completed the baseline assessments of both hopelessness and parent-adolescent conflict. Further, we required that a caregiver also had completed a baseline assessment of parent-adolescent conflict. In the TADS dataset only one caregiver per adolescent reported on parent-adolescent conflict, and the vast majority of these caregiver informants were mothers, stepmothers, or grandmothers providing daily care for the adolescent (Curry et al., 2006). We therefore excluded those few participants who did not have a maternal caregiver respondent on parent-adolescent conflict. Of the 439 participants in the TADS dataset, two participants lacked all the required assessments at baseline. Three lacked a maternal caregiver informant, two lacked any caregiver report of conflict, seven lacked adolescent report of conflict, two lacked adolescent report of hopelessness, and six lacked both adolescent report of both conflict and hopelessness. This brought the final sample size to N = 417. This represents a 5.0% reduction in sample size due to missing assessments, which is unlikely to introduce substantial bias in estimates from a complete case analysis (Lee et al., 2021).

Measures
We used a latent variable modelling framework in this study, fitting measurement models based on item response theory rather than using scale scores. We hence do not report internal consistency estimates for scale scores in this section, but we report on assessment of measurement properties in the results section.

Parent-adolescent conflict
The Conflict Behaviour Questionnaire (CBQ, Prinz et al., 1979) was used to measure parent-adolescent conflict in TADS. The CBQ is a multi-informant measure covering multiple aspects of conflict. Parents complete it for their relationship with their adolescent, and the adolescent completes it separately for each parent. Items cover the frequency of conflictual interactions, the affective intensity of conflict, and typical conflict behaviours. The CBQ has two subscales, perception of the parent/adolescent and perception of the dyad. Example items from the perception of the parent/adolescent subscale are "My child/mother usually starts arguments" and "My child/mother blows up for no reason". Example items from the perception of the dyad subscale are "My child/mother and I speak to each other only when we have to", and "At least once a day we get angry at each other". In the current study, we only used items from the perception of the dyad subscale. On these items, the two informants are reporting about a shared experience-the way they typically interact. Discrepant reporting is therefore interpretable as an indicator of divergent perceptions of the state of their relationship and the typical qualities of their interactions. Differences in reporting on the perception of the parent/adolescent subscale are however not interpretable in the same way, because both informants are rating the behaviour of the other informant, hence reporting on two distinct sets of behaviours.

Hopelessness
The Beck Hopelessness Scale (Beck et al., 1974) was used to assess adolescent hopelessness. The BHS is a widely used self-report measure of hopelessness, also in adolescent populations (Lester, 2015). It comprises 20 statements rated as true or false. Example items are "My future seems dark to me" and "All I can see ahead of me is unpleasantness rather than pleasantness". There is considerable evidence for hopelessness as measured by the BHS as a unidimensional construct (Aish & Wasserman, 2001;Young et al., 1992). Three items have been found to have poor psychometric properties in multiple studies (Items 4, 8 and 13, see Kliem et al., 2018), and in accordance with the preregistration we did not include these in our analyses.

Analysis Plan
We conducted the analyses within a Bayesian framework, specifying and fitting models in Stan (Stan Development Team, 2019), using the R (R Core Team, 2019) package cmdstanr (Gabry & Češnovar, 2020). For readers unfamiliar with Bayesian data analysis, we suggest consulting one of the many introductory papers available (Baldwin & Larson, 2017;Rognli et al., 2023).

Modelling informant discrepancies and conflict as predictors of hopelessness
Like the in the original study (Rognli et al., 2021) we modelled informant discrepancies using latent difference scores (de Haan et al., 2018). A latent difference score model consists of a measurement model fitted to observed data from multiple informants, and a specific way of setting up the latent variables of that measurement model. The latent variable of the first type of informant is set to be equal to the latent variable of the second type of informant plus a latent difference score variable. This latent difference score then represents the part of the response of the second informant that is not equal to that of the first informant. Figure 1 illustrates the structure of the latent difference score model. We used a two-parameter logistic item response model (IRT model, de Ayala, 2009) fitted to the CBQ Perception of the Dyad subscale as the measurement model.
In the original study, the hopelessness variable was rated by a clinician on a three-point scale (the hopelessness item of a clinical interview for depression), and an ordinal regression model was used to evaluate the association between informant discrepancy and hopelessness. That model would not be appropriate for a multi-item self-report measure of hopelessness such as the BHS. In the current study, we therefore fitted a two-parameter logistic IRT model to the responses of the adolescent on the BHS, letting the latent hopelessness variable be the outcome variable of a linear regression model with informant discrepancy and/or reported conflict as the predictor. We fitted four different regression models with the following different predictor variables: Adolescent report of conflict, parent report of conflict, informant discrepancy, and informant discrepancy adjusted for adolescent report of conflict. We also fitted each of these models allowing the regression coefficients to vary with adolescent gender.

Prior distributions, model fitting and validation of computation
In a Bayesian analysis, the prior distribution encodes assumptions and external knowledge about each parameter (Gelman et al., 2013). In our main analysis, we used the posterior distributions from the original study to inform the prior distributions of the regression coefficients. For other parameters, we used weakly informative priors, which are distributions ruling out impossible parameter values (such as a standardised regression coefficient of 100) and downweighting highly implausible ones (Gelman et al., 2017). As a sensitivity analysis, we also fitted the models with weakly informative priors for the regression coefficients. Descriptions of all the prior distributions and the reasoning behind them are available in the supplementary  Table S1.
We coded the complete models in the Stan programming language. They consisted of IRT models for the CBQ and the BHS, with the latent trait parameters of the BHS model coupled to the latent trait or latent discrepancy score parameters of the CBQ model via linear regression. We fitted these models using the dynamic Hamiltonian Monte Carlo algorithm implemented in Stan version 2.26.1 (Stan Development Team, 2019). We ran four chains with 1000 warmup iterations, drawing 1000 samples from each chain. Running the diagnostic functions of the cmdstanr package (Gabry & Češnovar, 2020) indicated no problems with the computation or sampling, implying valid sampling from the posterior distribution. Stan and R code for the analysis is available at https://doi.org/10.17605/OSF.IO/VYBK8.

Results
We generally report summaries of the posterior distributions for model parameters. These are directly interpretable probability distributions for model parameters, conditional on the data.

Measurement Models and Distributions of Latent Variables
We investigated the fit of the measurement models, and assessed measurement invariance and reliability. We found satisfactory measurement properties and good model fit. Detailed descriptions of these procedures and their results are available in Appendix S2. There was considerable variability in the latent conflict variables and in informant discrepancy. The latent conflict variable (means of the posterior distribution for each case) ranged from −1.87 to 2.47 for adolescent report and −1.79 to 1.92 for parent report. The posterior means of the latent difference scores ranged from −2.40 to 2.27. The posterior mean of the correlation between adolescent report and informant discrepancy was −0.60 (90% CI −0.67 to −0.53). The latent hopelessness variable ranged from −1.56 to 1.47. All item parameter estimates from the IRT models are also available in Appendix S2.

Regression Model Fit and Sensitivity to Assumptions
Before interpreting parameter estimates from the regression model, we evaluated model fit using Posterior Predictive Checks, which is a recommended procedure in Bayesian data analysis . This means using the independent variable from the data and the fitted model to simulate new dependent variable datasets, which we compare to the observed distribution of the dependent variable. A well-fitting model should give simulated distributions of the dependent variable that resembles the observed distribution in shape and range, in this case the predicted distributions of BHS scores. These plots indicated satisfactory model fit, and are available as supplementary Fig. S3.
To check the sensitivity of our inferences to the use of informative prior distributions for the regression coefficients, we also fitted all models with weakly informative priors and compared the posterior distributions to those of the models fitted with informative priors. The means of the posterior distributions did not differ substantially, and the credible intervals were only marginally smaller with informative priors.
The posterior distributions of the difference between the regression coefficients for gender were all symmetrical around values very close to zero (posterior means ranged from −0.01 to 0.06, posterior standard deviations from 0.12 to 0.17), showing that the associations between conflict or informant discrepancy and hopelessness are unlikely to vary strongly with adolescent gender given these data. We therefore report posterior estimates from the models without gender-specific regression coefficients. Table 1 displays the parameter estimates from the four fitted models. We report both the posterior mean and standard deviation, and both 66% and 90% credible intervals. Mastrandrea et al. (2010) described 66% probability as "likely" and 90% probability as "very likely". We hence suggest these intervals can be interpreted as the ranges wherein the true parameter value is likely and very likely to be found. We also include the Bayesian version of R 2 , the proportion of variance explained by the model, calculated according to equation 3 in Gelman et al. (2019).

Regression Model Parameter Estimates
The estimates from the model with informant discrepancy as the predictor imply a considerable association between informant discrepancy and hopelessness, with hopelessness predicted to be higher when parents report less conflict than the adolescent does. This association holds when adjusting for adolescent report of conflict. Further, informant discrepancy shows a stronger association than the absolute level of conflict in the adjusted model, although the uncertainty about the magnitude of the parameters is larger. The posterior probability of a regression coefficient for informant discrepancy that is negative and of a larger magnitude than 0.1 is 0.99 for the unadjusted coefficient and 0.90 for the adjusted coefficient. This replicates the findings of Rognli et al., (2021) according to our preregistered definition that this probability would be >0.74 (https://doi.org/10.17605/OSF.IO/D72WG).
The estimates from the models with adolescent or parent report of conflict as separate predictors of hopelessness imply that adolescents reporting more conflict are more likely to experience hopelessness. However, parental report alone shows no association. Both findings are in line with a similar analysis of the same dataset by Becker-Weidman et al. (2009).
The proportions of variance explained by the models are small. This is as expected for a regression model predicting a multidetermined phenomenon such as hopelessness from one or two predictor variables.

Model Predictive Distributions
The implications of a fitted regression model is easier to understand by using it to simulate outcomes at different levels of the predictor (Gelman et al., 2020). The predicted distributions of BHS scores at different levels of informant discrepancy are displayed in Fig. 2, using the model with discrepancy adjusted for adolescent report of conflict and simulating 20,000 cases at each level. As is evident from the plots, the proportion of adolescents reporting moderate to severe hopelessness by endorsing half of the items or more (shown with dark grey bars) is predicted to increase substantially as parents report less conflict relative to the adolescent, both at high, average, and low levels of adolescentreported conflict.

Discussion
The results of this study replicates the findings in Rognliet al., (2021), which had a much lower sample size and poor gender balance. As expected with a larger sample size, there was less uncertainty in the parameter estimates. Taken together, the current replication study alongside our original study provide initial evidence for an association between informant discrepancy and hopelessness, where those adolescents who report more conflict than their parents (i.e. with higher informant discrepancy) are also more likely to feel hopeless, even when adjusting for the level of conflict reported by the adolescent. The magnitude of the association appears to be of practical importance, with the fitted model predicting substantial increases in severe hopelessness at high levels of informant discrepancy. However, more research is necessary to further understand how discrepancy in report of conflict is related to adolescent hopelessness.
The present findings indicate that the association between informant discrepancy and hopelessness does not vary considerably by adolescent gender. It is important to note that in Bayesian inference, a parameter estimate near zero, as we found for the difference in regression coefficients between genders, is as interpretable as any other estimate, unlike non-significant estimates near zero in null hypothesis significance testing (Kruschke, 2018).
Conflicts between caregivers and adolescents entail both representational and interactional aspects that reciprocally influence each other (Collins & Luebker, 1994). What happens during a particular conflict event, how it is resolved, and how the event is interpreted is all influenced by the expectations and previous experiences of the adolescent and the parent. In turn, the event also adds to that experience and changes or reinforces their representations of the relationship. We suggest that different interpretations of events will lead to diverging representations, with those representations making it more likely that subsequent events will also be interpreted differently, leading to further divergence of representations. This assumption is supported by an observational study linking informant discrepancy in report of conflict to observed lack of open communication (Ehrlich et al., 2016).
The primary limitation of this study is the cross-sectional nature of the data used, requiring stronger theoretical justification for causal interpretations, and increasing the uncertainty of such interpretations. Hence, it is important to consider other plausible interpretations of the association between hopelessness and discrepancy, and how well they fit with the findings and theory. Hopelessness could be a cause of adolescents interpreting conflictual interactions as more severe than the caregiver, driving up discrepancy. However, in that case we would expect to find adolescent report of conflict alone to be a stronger predictor of hopelessness. In the adjusted model, informant discrepancy appears to be the strongest predictor variable, which does not support this interpretation.
The association between hopelessness and discrepancy could also reflect depressive cognitive distortions acting as a third variable. It is however not plausible that all discrepancy in report of conflict is caused by adolescent depressive distortions. For that to be the case, one would have to assume that all caregivers perceive the state of their Mean Posterior mean, SD Posterior standard deviation, 90% CI 90% credible interval, the 5th and 95th percentiles of the posterior distribution; 66% CI 66% credible interval, the 17th and 83rd percentiles of the posterior distribution, ESS Bulk/Tail Effective Sample Size, the number of effectively independent draws, calculated separately for the bulk and the tail of the distribution, R 2 Proportion of variance explained by the model relationship with their adolescent "accurately", which is an unreasonable assumption. It is likely that in some caregiveradolescent dyads caregivers contribute more to informant discrepancies than the adolescent, while in other dyads, the adolescent contributes more. It is also a major limitation that all caregiver informants are maternal or female. The finding in Rognli et al., (2021) of an association between father-adolescent discrepancy and hopelessness of similar magnitude to that of motheradolescent conflict has hence not been replicated. Both the present study and that of Rognli et al., (2021) were conducted in clinical samples with a diagnosed depressive disorder. However, hopelessness is not restricted to depressed adolescents (Lester, 2015), and neither is discrepant reports of caregiver-adolescent conflict (Rote & Smetana, 2016). It is currently unknown whether the association replicated in the current study extends to nonclinical populations, and further investigation in nonclinical sample would be valuable. The primary strength of the study is conducting a planned replication with a large sample size.
Identifying modifiable variables associated with hopelessness among depressed adolescents has high relevance for clinical practice, because hopelessness is not simply a marker of depressive severity, but rather a difference in the clinical picture predicting suicidal behaviours and poor treatment outcomes (Wolfe et al., 2019). Discrepant conflict representations among parents and adolescents could very well be a relevant target of intervention for reducing hopelessness in depressed adolescents. Reduction in the level of discrepancy could possibly be achieved through very brief family therapy interventions, and probably with less effort than reductions in the level of conflict as such. Drawing direct clinical implications from the current evidence is in our view premature, but further investigation of the potential of such interventions in a clinical research context is warranted. Such interventions would also work as an experimental manipulation of discrepancy, allowing for

Data availability
Data and/or research tools used in the preparation of this paper were obtained from the National Institute of Mental Health (NIMH) Data Archive (NDA). NDA is a collaborative informatics system created by the National Institutes of Health to provide a national resource to support and accelerate research in mental health. Dataset identifier(s): https://doi.org/10.15154/1524730. This paper reflects the views of the authors and may not reflect the opinions or views of the NIH or of the Submitters submitting original data to NDA.

Code availability
Complete Stan and R code for the analysis is available at https://doi.org/10.17605/OSF.IO/VYBK8. Acknowledgements The authors are grateful to the TADS team, and to the participating adolescents and their families. We also thank Nikolai O. Czajkowski and Marianne Aalberg for their contributions to the paper that provided the basis for the present study.
Author Contributions E.W.R. conceived of the study, participated in the acquisition of data and performed the statistical analysis. K.W.F. acquired the data. Both authors interpreted the results of the analysis, collaborated on drafting and revising the paper, and read and approved the final version.
Funding Open access funding provided by Akershus University Hospital (AHUS).

Compliance with Ethical Standards
Conflict of Interest The authors declare no competing interests.
Ethics Approval TADS was completed in full compliance with the Department of Health and Human Services policy for the protection of human subjects (45 CFR 46). The protocol and consent documents were reviewed and approved by the Institutional Review Boards of each participating institution. All data collection, handling, and storage were done in compliance with the Privacy Act. A Federal Certificate of Confidentiality was obtained for the study.
Informed Consent All participants (adolescents and caregivers) provided written informed consent or assent to participate in TADS. Written consent was obtained from parents on behalf of the adolescents where appropriate.
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