We used data from the Swiss Youth Epidemiological Study on Mental Health (S-YESMH), a nationally representative, cross-sectional study of Swiss young adults’ mental health and wellbeing that was funded by the Swiss National Science Foundation and approved by the Ethics Committee of the Canton of Vaud (2017–00522). In order to obtain answers from participants of both Swiss and Non-Swiss nationality from all states (cantons), we developed a sampling plan stratified by canton, sex, and Swiss nationality that oversampled Non-Swiss participants, for which we adjusted in our statistical analyses. Based on this plan, the Swiss Federal Statistical Office provided us a random sample of 9805 young adults legally residing in Switzerland born between 1996 and 2000 (17–21 years old on December 31, 2017) who were randomly selected from the population register within each stratum specified by the sampling plan. Participants who were not able to complete the survey in German, French, or Italian were excluded from the survey. From the 9286 valid addresses in the sample at the time of data collection, 3840 participants (41.4%) completed the online survey.
The data were collected via a cross-sectional online survey from February to August 2018 by the market research organization LINK Institute (www.link.ch). We sent an invitation letter by postal mail to every person sampled. This letter described the study, stated that the survey was voluntary and that answers would never be linked to participant contact information, and provided free hotline numbers for participants to contact the study team, LINK Institute, or mental health organizations if they had additional questions about the study or mental health in general. Participants could access the survey by entering the web address and password provided or by scanning an individualized QR code on the invitation letter. The survey duration was around 25 min and included questions on socio-demographic characteristics, symptoms of several common psychological disorders and suicide, somatic symptoms, service use, quality of life, sources of stress, social support, and alcohol and drug use. After three weeks, a first reminder letter was sent to participants who had not responded to the survey. Two weeks after this, LINK Institute called those who had not participated to encourage them to participate. Those who provided their e-mail address during the telephone call, but had not filled out the survey, were reminded to participate by e-mail. We sent a second reminder letter that included an optional paper version of the questionnaire one month after the telephone reminders began. Finally, we sent a last reminder letter four months after sending the initial invitation letter.
Symptoms of common mental disorders (CMDs)
The common mental disorders in focus in this study were depression, anxiety, and attention deficit hyperactivity disorder (ADHD). Two Patient Health Questionnaire (PHQ) screeners were used to assess symptoms of CMDs: the Generalized Anxiety Disorder 7 (GAD-7) for anxiety  and the PHQ-9 for depression . Both are widely used in clinical settings and have been validated in populations across the world [22,23,24] (note: though the German, French, and Italian versions have been validated, they have not all been validated in Switzerland specifically). For the PHQ-9, sensitivity is 80% and specificity is 92%, while the sensitivity of the GAD-7 is 89% and its specificity is 82% . In this study, Cronbach’s alpha was 0.85 for the PHQ-9 and 0.87 for the GAD-7. These screeners ask about symptoms of anxiety and depression, respectively, over the past two weeks using a four-point rating scale for which 0 indicates ‘not at all’ and 3 indicates ‘always’. Based on the literature, we dichotomized total scores for these screeners into moderate anxiety and above (scores greater than or equal to 10) and moderate depression and above (scores greater than or equal to 10) . ADHD symptoms were assessed using the Adult ADHD Self-Report Scale Screener (ASRS-v1.1), a validated six-item instrument about symptoms of ADHD during the past 6 months [25,26,27]. This instrument has adequate sensitivity (68.7%) and is highly specific (99.5%) . Cronbach’s alpha was 0.6 in this study. We dichotomized total scores into ‘no ADHD’ (scores below 14) and ‘ADHD’ (scores 14–24) . We also created a variable ‘anxiety, depression, or ADHD’ that included any participant who screened positive for at least one of these disorders.
Because the instruments used to measure CMDs assessed self-reported symptoms, we do not have sufficient information to establish a formal clinical diagnosis. In this study, we thus refer to people who report symptoms of the CMDs under study and probably suffer from them.
Risky substance use
We assessed risky alcohol and substance use with questions about the usual quantity and frequency of substance consumption using the questionnaire from the Cohort Study on Substance Use Risk Factors (C-SURF), a study of young men in Switzerland [29, 30]. Risky alcohol use was defined as the frequency of risky single-occasion drinking over the last 12 months. For men, risky single-occasion drinking meant consuming at least six standard drinks on a single occasion, and for women, four standard drinks (the definition of a standard drink was clarified using pictures with examples). We calculated two dichotomous variables for risky alcohol use: risky alcohol use at least monthly and risky alcohol use at least weekly based on the frequency of risky single-occasion drinking in each time period. Risky drug use was calculated for different classes of illicit substances. Risky cannabis use was defined as using cannabis at least 2–3 times per week; risky use of non-prescribed prescription drugs was defined as using prescription drugs not prescribed by a doctor at least two to three times per year; and risky illicit drug use was defined as using any other illicit drug at least four times throughout the participant’s lifetime.
Other mental health outcomes
Current suicidal ideation was measured using the question from the PHQ-9 “How often have you been bothered by thoughts that you would be better off dead or of hurting yourself in some way over the last two weeks?” Answers were dichotomized into no suicidal ideation (answer choice “not at all”) and suicidal ideation (combined answer choices “several days,” “more than half the days,” and “nearly every day”). We assessed lifetime suicide attempts using the question from the Swiss Health Survey 2017 “Have you ever attempted to take your life?” .
Mental health-related quality of life was measured using the Short-Form 12 Health Survey, Version 2 (SF-12) . We calculated the Mental Component Summary score following the standard procedure using norm-based methods described in the SF-12 user manual. A score of 50 represents the average for the U.S. population in 1998, with higher scores indicating better quality of life.
Perceived need for and utilization of mental health care services
Questions on perceived need for health and mental health care service utilization were assessed using questions modified from the World Health Organization World Mental Health Composite International Diagnostic Interview (WHO WMH-CIDI) . Lifetime perceived need for health care services was assessed by the yes/no question “Has there ever been a time in your life that you believe you required help for problems with your emotions, nerves, mental health, or your use of alcohol or drugs?” Lifetime mental health care service utilization was assessed by asking whether the participant had ever spoken with a health professional (i.e., psychiatrist, general practitioner, nurse, psychologist, care personnel, or counselor) in person or on the phone for problems with emotions, nerves, or use of alcohol or drugs. For current mental health care service utilization, we asked the same question for the period including the last four weeks.
To measure the treatment gap, we first identified those who screened positive for CMDs and then measured their use of mental health care services by asking those who reported a perceived lifetime need for mental health care services a yes/no question about whether this need had been met. In addition, we looked at the percentage of participants who met the criteria for a disorder, yet had not used health care services either in the last four weeks or at any point during their lifetime.
Service availability was represented by the regional psychiatrist density, which we defined as the number of psychiatrists per 100,000 inhabitants in the seven large Nomenclature of Territorial Units for Statistics 2 (NUTS-2) regions defined by the Swiss Federal Statistical Office (i.e., Lake Geneva region, Espace Mittelland, Northwestern Switzerland, Zurich, Eastern Switzerland, Central Switzerland, and Ticino) [34, 35].
Income and other socio-demographic variables
We asked participants about their approximate monthly household income level. Less than 6000 CHF was classified as low, around 6000 CHF was classified as middle, and more than 6000 CHF was classified as high for Swiss households. All other answers were classified as unknown. The Swiss Federal Statistical Office provided all other socio-demographic variables, including age, sex, nationality, and language region.
All statistical analyses were conducted using R version 3.4.2  and SPSS version 25 . We adjusted our estimates to account for the stratified sampling design described above and non-response using the R package “survey” . We used the package to specify our survey design. The sampling probabilities were computed for simple random sampling within strata as specified by the sampling plan. The true population sizes for each stratum were provided by the Swiss Federal Statistical Office. Because the percentage of missing values was limited to less than 2% for all variables, we did not impute any values.
To describe the study participants, we calculated weighted mean values and proportions for age, sex, Swiss nationality, and language region as well as the prevalence of CMDs, risky substance use, perceived need for help, and professional mental health service utilization (lifetime and current) by sex and Swiss nationality. We compared the mental health outcomes current suicidal ideation, lifetime suicide attempts, and mental health-related quality of life between participants who did and did not screen positive for one or more CMDs.
To calculate the treatment gap, we used these estimates to determine the percentage of participants who screened positive for CMDs who either did not perceive a need for care or had not used professional mental health services.
We examined the association of risky alcohol and drug use with perceived need for care and service utilization by performing logistic regression analyses for each drug individually, first alone and then adjusting for relevant socio-demographic and health care service characteristics.