In our description of the study methods and results we follow the consolidated health economic evaluation reporting standards (CHEERS) [35]  (see Additional file 1). The data for this health economic investigation were gathered as part of the study “Children of Parents with Mental Illness” CHIMPS [36].

Trial design

We conducted a multi-centre randomized clinical trial (RCT) at six of the originally seven study sites which are located in Germany to evaluate the effectiveness and cost-effectiveness of a family-focused intervention for children with parents having a mental illness [36]. We excluded one study site located in Switzerland because of the differences in the health and social care systems between both countries. We collected data from all participating family members at baseline and at 6-, 12- and 18-month follow-ups. We recruited families at in- and outpatient departments of psychiatric hospitals for adults and for children and adolescents. Families were eligible for study participation if they had at least one child between ages 3 and 19 and if at least one parent was treated because of a common or severe mental illness during the last 5 years. Children or adolescents could be included with or without having a diagnosis of a mental illness. Exclusion criteria for parents and children or adolescents were acute symptoms such as suicidal tendencies, risk of self-harm and danger to others, acute psychotic symptoms, and other mental states with an indication for inpatient treatment. Eligible families were randomly assigned to the intervention or control group after the baseline assessment had been completed. Further details of the trial design, recruitment and randomization procedures are published in the study protocol [36].

Intervention

Families in the intervention group received the intervention for children with a parent with mental illness (CHIMPS) [36, 37]. The aim of the intervention was the primary, secondary and tertiary prevention of mental illness in children or adolescents with at least one parent who had a common or severe mental illness. In case of children or adolescents without a diagnosis of a mental illness and without mental health problems at baseline the target of the intervention was the primary prevention of the onset of a mental disorder. In case of children or adolescents who already had mental health problems but did not fulfil the criteria of a diagnosis of a mental disorder at baseline the aim of the intervention was secondary prevention in the sense of detecting a potential mental disorder and giving advice for adequate treatment. In case of children or adolescents who already had a diagnosis of a mental disorder the aim of the study was tertiary prevention in the sense of improving the treatment. In addition, as a family focused program the intervention aims at improving psychological well-being in each family member.

CHIMPS is a manualized program [37] consisting on average of eight semi structured sessions (50–90 min) provided by a psychiatrist or psychotherapist over 6 months. Intervention providers were trained by the program developer. The program includes separate sessions with parents, each child and the entire family. The final number of sessions per family therefore depends on the number of participating family members. Further details of the CHIMPs intervention and the implementation of the program are provided in the study protocol [36].

Control condition

Families assigned to the control condition received no additional services beyond the routine medical and psychiatric treatment and the psychosocial care provided by the German health, social care, child welfare, and the educational system. Routine health care is financed by mandatory or private health insurance and includes medical in- and outpatient hospital treatment, ambulant treatment by office-based family doctors and specialized physicians including psychiatrists, ambulant psychotherapy, other ambulant therapies and medication. In addition to health care financed by health insurance, support for families with special needs is provided by child and youth welfare services, which are tax-based financed by communities [38]. For children and adolescents with particular educational needs, several types of school-based services, such as school social workers or school psychologists, are available, which are tax-based financed by the communities or by the federal states [38].

Perspective and scope of the health economic evaluation

In this article we present the health economic evaluation for the children and adolescents participating in the CHIMPS study. We will carry out a health economic evaluation for the participating parents in a separate analysis.

We conducted the health economic evaluation from the societal perspective. Therefore, we estimated total use and costs of health and psychosocial services including services provided by health care system, the child and youth welfare system and by the educational system. A detailed description of our cost assessment procedure is given in Waldmann et al. [38].

We conducted an incremental cost-utility analysis taking the child or adolescent as the unit of analysis from the perspective of the German health and social care welfare system. Therefore, only the data for children and adolescents from the six German study sites were included in this analysis. The analysis has a time frame of 24 months. For the incremental cost-utility analysis, we used an average 12-month time frame and two separate analyses for the first and second study years.

Discounting

Due to the short time frame, we applied no discounting of costs and effects.

MeasuresCosts for health-care and psychosocial service use

We assessed the total use of health care and psychosocial services of the children and adolescents by means of the Children and Adolescent Mental Health Service Use Inventory (CAMHSRI) [39] adapted for the German health and social care system [38]. Due to the broad spectrum of needs related to mental health problems in children or adolescents we included the cost of health care but also the costs of psychosocial care provided by the child and youth welfare system and the costs of educational support provided by the educational system [38]. We estimated costs for service units reported to be used by the participating children or adolescents on the basis of literature and internet search and by personal consultation of service providers, health insurances and other payers [38].

Intervention costs

We estimated the intervention costs per child and per family. Although the aims of the intervention differed between children and adolescents and their parents we estimated the intervention costs as a whole because it was not possible to distinguish between children or adolescent and parent focused parts of the intervention.

On average, each family received eight intervention sessions, one initiating session with parents and children (60 min), two sessions with both parents (60 min), one session with each child (50 min) and three group sessions for the entire family (90 min). The intervention could be provided by psychiatrists or psychologists. Therefore, we calculated the costs for the intervention staff as € 102.57 per hour, representing the average hourly rate of a psychiatrist (€ 132.7) and a psychologist (€ 88.56). Given a total intervention time of 7 h, total intervention costs amounted to € 717.99 per family. Since each family had on average 1.6 children, we estimated costs per child by dividing the total family costs by 1.6 with the result of € 448.74 rounded to € 450.

Outcomes

We measured the quality of life for children and adolescents by means of the KIDSCREEN-10 [40]. For the generation of quality adjusted life years we transformed the KIDSCREEN data into utility values by the algorithm provided by Chen et al. [41].

Statistical analyses

We performed all statistical analyses on an intention-to-treat (ITT) basis using the last observation carried forward (LOCF) method for the imputation of missing data.

Computation of average annual cost

We computed the average annual costs using the cost measures from baseline and the tree 6 months follow-up measures of 6 months cost as shown below:

$$Annual\,cost_ = \frac + Cost_ + Cost_ + Cost_ }}$$

where annual costtotal indicates the average annual cost of health and psychosocial care over 24 months and costt0 to costt3 indicate the 6 months cost measured retrospectively at baseline and the three follow-ups.

We collected information about service use retrospectively for the last 6 months before the time of assessment. Therefore the t0 cost assessment represents the cost over the 6 months before the baseline assessment. This makes the average annual costs computed by the formula above partly inert to being influenced by the intervention. The advantage of this approach is the availability of cost data in case of study drop-out after the baseline assessment. However, the disadvantage of this procedure is that the analysis becomes biased against the study hypothesis that total costs are influenced by the intervention. Therefore, we supplemented our overall analysis with two separate analyses for year one and year two. For this purpose we computed average annual cost for year one and for year two by means of the equations below:

$$\begin Annual \,cost_ & = Cost_ + Cost_ \\ Annual \,cost_ & = Cost_ + Cost_ \\ \end$$

where annual costyear 1 and annual costyear 2 indicate the average annual cost for the year one and year two and costt0 to costt3 indicate the 6 months cost measured retrospectively at baseline and the three follow-ups.

Computation of QALYs

We computed average annual QALYs as the area under the curve [30]. For the overall analysis we computed the QALY by dividing the sum of the utility scores estimated from the KIDSCREEN-10 questionnaire by four as shown below:

$$QALY_ = \frac + utility_ + utility_ + utility_ }}$$

where QALYtotal indicates the average quality adjusted life years over the total study period. Utilityt0 to utilityt3 indicate the utility estimates based on the transformed KIDSCREEN-10 measures.

Division of the sum of the four utility scores by four is needed because we performed two utility assessments per year which means that each utility measure represents 0.5 QALYs [30].

Analogous to the cost assessment we estimated separate QALYs for each year by the formulas:

$$\begin QALY_ & = \frac + utility_ }} \\ QALY_ & = \frac + utility_ }}. \\ \end$$

Statistical test of cost and QALY differences

For the assessment of the differences in cost and effects between study groups, we estimated linear regression models for costs and outcomes. We set the alpha error to p ≤ 0.05 taking into account that the children were clustered within families by including family identification as a cluster variable and by applying robust variance estimation [42]. In addition we took account for the skewed distribution of cost data by applying non-parametric bootstrapping with 2000 replications for estimating the 95% confidence intervals for the regression parameters [43] and we also estimated generalized linear models with gamma family distribution and logistic link functions [44] to confirm the inference of statistical differences between groups.

Incremental cost-utility analyses

We computed e incremental cost-utility ratios (ICUR) as annual average over the total 24-month study period and separately for the year one and two. We interpreted the ICUR on the basis of its location at the cost effectiveness plane (CEP) [30].

For estimating the ICUR variance we carried out nonparametric bootstrapping with 10.000 replications [30]. We estimated the probability of cost-effectiveness depending on willingness to pay (WTP) thresholds between € 0 and € 125.000 by means of the cost-effectiveness acceptability curve (CEAC) [30]. In addition we estimatedthe probability of obtaining a net monetary benefit by means of net-benefit regression curves with 95% confidence intervals [30].

We conducted all analyses with Stata 16.1 using the programs provided by Henry A. Glick for estimating the ICUR variance, the acceptability curve and the net-monetary benefit regression [30].