Family-based Telemedicine vs. Inpatient Anorexia Nervosa Treatment (FIAT)

Measured by the eating disorder examination-questionnaire (EDE-Q). The scores of the EDE-Q are presented on a scale between 0 and 6, where higher scores mean higher presence of symptoms.

Measured by the compulsive exercise test (CET). Items are rated on a 6-point Likert type scale from 0 (never true) to 5 (always true), with higher scores correspond with stronger symptoms.

Measured by the Revised Children's Anxiety and Depression Scale (RCADS). Scores are presented between 0 (never) to 3 (always). The total score is converted into a T-score. Higher T-scores indicate higher presence of symptoms.

Measured by the modified over aggression scale (MOAS) in addition with a set serious adverse events list. Higher scores on the MOAS indicate more severe cases of aggressive behaviors.

Measured by structural interview.

Measured by structural interview.

Measured by the anorexia nervosa stages of change questionnaire (ANSOCQ). Each item can scored between 1 and 5. Higher scores indicate higher levels of motivation.

One item "On a scale of 1 to 10, how severe would you rate yourself as suffering from anorexia?" where a higher score indicates more insight into the illness.

Measured by the eating disorder quality of life (EDQOL). Each item can be scored on a 6-point scale ranging from 0 ("never") to 5 ("always"). Higher scores indicate lower quality of life.

Measured by the EQ-5D-Y-5L. Items are scored on 5 levels ("no problems" to "extreme problems") except one, which is scored on a vertical visual analogue scale (endpoints are "the best health you can imagine" and "the worst health you can imagine"). Higher scores indicate more problems.

Measured by the caregiver strain questionnaire (CGSQ-SF11). Items are scored on a 5-point Likert scale (0= not at all, 4= very much). Higher scores indicate greater strain.

Measured by a structured questionnaire about financial strain during treatment. The first question ("Has your child's treatment put a financial strain on you?") is scored on a 4-point Likert scale (1= not at all; 4= extremely). A higher score indicates greater financial strain. The second question ("Have you had any loss of earnings due to your child's illness?") is binary scored (yes/no) and follows up the "yes" condition with the question "how many days were you not able to work?".

Measured by the Client Service Receipt Inventory (CSRI). Assessing the use of various services in the respective units (e.g., days or hours).

Measured by an adapted version of the treatment satisfaction questionnaire by Lindstedt et al. (2020). The following topics are assessed and scored:

1. Helpfulness of therapy-elements. Higher scores indicate less helpfulness
2. Patient-therapist-interaction. Higher scores indicate less positive experiences of interaction.
3. Treatment goals importance. Higher scores indicate less importance of proposed treatment goals.
4. Achievement of treatment goals. Higher scores indicate less achievement of proposed treatment goals.
5. Change in symptoms (before treatment vs. after treatment). Higher scores indicate more positive change in symptoms.

Measured by an adapted version of the treatment satisfactory questionnaire by Krautter \& Lock (2004). The questions assess the subjective effectiveness of the treatment and treatment satisfaction. Items are scored on all topics on a 5-point Likert scale (0= very ineffective; 4= very effective). Higher scores indicate higher effectiveness. Additionally, the following questions are scored on a 5-point Likert scale (0= not at all; 4= yes, totally) :

1. "Do you agree that the team that treated your child is competent?"
2. "Would you recommend this treatment?"

Measured by an adapted version of the treatment satisfactory questionnaire by Krautter \& Lock (2004). The questions assess the subjective effectiveness of the treatment and treatment satisfaction. Two open questions ("What did you find helpful in this treatment?"; "What did you not find helpful in this treatment?") can be answered via free-text.

Measured by asking first whether any suicidal thoughts or behaviors were present in the past 28 days (yes/no). The yes condition is followed up by several questions assessing the presence (yes/no) of:

• passive suicidal thoughts.
• active suicidal thoughts.
• active suicidal thoughts with plan.
• active suicidal thoughts with plan and preparation.
• active suicidal thoughts with plan and intention to act upon it.
• suicidal behaviors, stopped by oneself.
• suicidal behaviors, stopped by others.
• suicidal behaviors, carried out, light physical damage.
• suicidal behaviors, carried out, medium physical damage.
• suicidal behaviors, carried out, severe physical damage.
• suicidal behaviors, carried out, death.

Both children and parents are asked. The children answer for their own thoughts/behaviors, the parents for their child's thoughts/behaviors.