A growing literature indicates that breakfast consumption is associated with several health outcomes among adolescents. Adolescents who eat breakfast often have a more favourable nutrient intake than adolescents with low breakfast frequency⁽ Reference Nicklas, Baranowski and Cullen ^{1 ,} Reference Rampersaud, Pereira and Girard ^{2 )}. Also, despite some inconsistency in findings⁽ Reference Mesas, Munoz-Pareja and Lopez-Garcia ^{3 )}, an association between low breakfast frequency and overweight among children and adolescents has been observed⁽ Reference Rampersaud, Pereira and Girard ^{2 ,} Reference Fabritius and Rasmussen ^{4 ,} Reference Szajewska and Ruszczynski ^{5 )}. Low breakfast frequency in childhood and adulthood is associated with metabolic risk factors in adulthood such as higher BMI, higher mean fasting insulin and higher LDL cholesterol concentrations⁽ Reference Smith, Gall and McNaughton ^{6 ,} Reference Wennberg, Gustafsson and Wennberg ^{7 )}. Additionally, there are indications in the literature that breakfast consumption is positively associated with children’s ability to concentrate in school⁽ Reference Rampersaud, Pereira and Girard ^{2 ,} Reference Hoyland, Dye and Lawton ^{8 ,} Reference Cooper, Bandelow and Nevill ^{9 )}. Further, low breakfast frequency in adolescence predicts low breakfast frequency in late adolescence and young adulthood⁽ Reference Pedersen, Holstein and Flachs ^{10 ,} Reference Merten, Williams and Shriver ^{11 )}. In the existing literature the definition of breakfast consumption varies⁽ Reference Rampersaud, Pereira and Girard ^{2 ,} Reference Merten, Williams and Shriver ^{11 –} Reference Sjöberg, Hallberg and Höglund ^{15 )}. Whereas others have used terms such as ‘breakfast pattern’, ‘skipping breakfast’ and ‘regularity of breakfast’, we apply the term ‘breakfast frequency’. This terminology directly reflects the applied breakfast measure in the present study.

The family is a significant setting for influencing the development of adolescents’ health behaviours⁽ Reference Tinsley ^{16 )}. In the family adolescents are influenced by their parents’ attitudes, beliefs and behaviours⁽ Reference Tinsley ^{16 )}. Breakfast is often consumed in the home and the family setting is therefore important when studying breakfast habits among adolescents. Others have highlighted the importance of investigating the influence of the family setting for adolescent breakfast frequency⁽ Reference Pearson, Biddle and Gorely ^{13 ,} Reference Sleddens, Kroeze and Kohl ^{17 )}. Breakfast frequency has been associated with the family setting characterized by physical factors such as food availability and food poverty in the home and sociodemographic factors such as socio-economic position⁽ Reference Pearson, Biddle and Gorely ^{13 )}. Further, sociocultural factors have been associated with breakfast frequency and especially parental breakfast consumption and family type have been investigated in several studies⁽ Reference Pearson, Biddle and Gorely ^{13 )}. A sociocultural factor that has had limited study is family functioning. Family functioning includes interpersonal interactions between parent and child such as problem solving, communication, roles, adaptability, warmth/closeness and behaviour control⁽ Reference Kitzman-Ulrich, Wilson and George ^{18 ,} Reference Broderick ^{19 )}. Low family functioning is associated with health outcomes and health behaviours such as overweight⁽ Reference Berge, Wall and Larson ^{20 ,} Reference Halliday, Palma and Mellor ^{21 )}, sedentary behaviour⁽ Reference Berge, Wall and Larson ^{20 )} and low intake of fruit and vegetables⁽ Reference Berge, Wall and Larson ^{20 ,} Reference Mellin, Neumark-Sztainer and Story ^{22 ,} Reference Neumark-Sztainer, Story and Resnick ^{23 )}.

Franco et al. suggested that adolescents who experience a high level of family communication and support are more susceptible to parents’ advice about breakfast consumption⁽ Reference Franko, Thompson and Bauserman ^{24 )}. A recent study by Berge et al. found that high family functioning (communication, closeness, problem solving, behavioural control) among US adolescents (mean age of 14·4 years) was associated with daily breakfast consumption⁽ Reference Berge, Wall and Larson ^{20 )}. Young and Fors found among US 9th–12th graders that the ability to communicate with parents about serious issues was positively associated with daily healthy breakfast (healthy not defined)⁽ Reference Young and Fors ^{25 )}. Also for family cohesion, involving measures of emotional bonding and supportiveness, positive associations have been found with frequent breakfast consumption among 13–16-year-old New Zealanders⁽ Reference Moore and Harre ^{26 )} and 9–19-year-old US adolescents⁽ Reference Franko, Thompson and Bauserman ^{24 )}. The existing studies have used different measures of family functioning and are based solely on populations of adolescents from the USA and New Zealand. When planning interventions it is important to get detailed insights into which aspects of family functioning are associated with breakfast frequency and whether the observed associations exist across settings.

The family setting is also characterized by sociodemographic factors and for several of these, associations with adolescent breakfast frequency have been observed. Low breakfast frequency is most common among girls and the prevalence increases with increasing age⁽ Reference Sjöberg, Hallberg and Höglund ^{15 ,} Reference Pedersen, Meilstrup and Holstein ^{27 ,} Reference Currie, Zanotti and Morgan ^{28 )}. Low socio-economic position⁽ Reference Sjöberg, Hallberg and Höglund ^{15 ,} Reference Höglund, Samuelson and Mark ^{29 –} Reference Vereecken, Dupuy and Rasmussen ^{32 )}, not living with two parents⁽ Reference Vereecken, Dupuy and Rasmussen ^{32 –} Reference Levin, Kirby and Currie ^{35 )} and being an immigrant⁽ Reference Delva, O’Malley and Johnston ^{36 –} Reference Jensen and Holstein ^{38 )} are associated with low breakfast frequency among adolescents.

A model that can be used to gain insight into causal mechanisms between for example the family setting and energy-related behaviour is Kremers’ Environmental Research framework for weight Gain prevention (EnRG) model⁽ Reference Kremers, de Bruijn and Visscher ^{39 )}. We consider breakfast frequency to be an example of weight-gaining behaviour. According to Kremers’ model, the causal background for energy balance-related behaviours is the physical and sociocultural characteristics of the settings in which people act. The model suggests that personal (e.g. sociodemographic factors) and behavioural characteristics act as modifying factors between the setting and behaviour⁽ Reference Kremers, de Bruijn and Visscher ^{39 ,} Reference Kremers ^{40 )}. Brug et al. highlighted that most studies have not examined the differences in environmental correlates for distinct subgroups as proposed by the Kremers’ model with regard to effect modifiers such as sociodemographic variables⁽ Reference Brug, Kremers and Lenthe ^{41 )}. Information on such modifying influences is important for developing efficient public health interventions. Based on this perspective, it can be hypothesized that sociodemographic factors such as high family social class and family structure buffer the influence of low family functioning on breakfast frequency. Information on such modifying or joint influences is important for designing well-targeted public health interventions. Berge et al. studied the modifying effect of ethnicity on the association between family functioning and breakfast consumption, finding no modifying effect⁽ Reference Berge, Wall and Larson ^{20 )}. Franko et al. studied the modifying effect of age on the association between family cohesion and frequency of breakfast consumption and found no modifying effect of age⁽ Reference Franko, Thompson and Bauserman ^{24 )}. Additional studies examining the modifying effect of other sociodemographic factors are still lacking.

Therefore, the aim of the current study was to gain more insight into which aspects of family functioning are associated with adolescent breakfast frequency by investigating the following research questions: (i) is there an association between family functioning (measured by close relations to parents, quality of family communication and family support) and breakfast frequency among adolescents? (ii) Are any observed associations modified by sociodemographic factors?

Methods

Study design and study population

We used Danish data from the international, cross-sectional, Health Behaviour in School-aged Children (HBSC) study⁽ Reference Currie, Nic Gabhainn and Godeau ^{42 )}. Data collection is conducted every fourth year in each participating country among students aged 11, 13 and 15 years (in Denmark, equivalent to 5th, 7th and 9th grade, respectively) in a random sample of schools (i.e. cluster sampling). Students completed the self-administered, internationally standardized and anonymous HBSC questionnaire at school⁽ Reference Roberts, Freeman and Samdal ^{43 )}. In 2014 we selected schools at random from a complete list of schools in Denmark. We used a regional-specific sampling to assure equal proportional representation of six geographical regions. We substituted every school that declined participation with another school chosen at random within the same region. In total we approached 168 schools of which forty-eight agreed to participate. In the majority of cases, the reason given for non-participation was that, at the time of recruitment, Danish schools were in the process of implementing a new and comprehensive school reform. Further, some schools had participated in similar surveys and did not have resources available for participation in yet another study. The school acceptance rate was higher among private than public schools (χ ² test, P=0·0328) but did not relate to school location or school size. We do not suspect that this non-participation pattern resulted in important student-related selection bias. The participating schools comprised 5292 students in 248 classes at grade 5, 7 and 9. Of the students present on the day of data collection, 4534 students submitted a satisfactorily completed questionnaire (based on subjective identification of questionnaires not filled in seriously). The response rate was 85·7 % (4534/5292). We have no information on reasons for non-participation among students. In the Danish data collection items on family communication were mainly included in the questionnaire applied in grade 7 and 9. The sample for the present study therefore comprises 3054 students in 7th and 9th grade from 167 classes in forty-one schools. The mean age of the participants in grade 7 and 9 was 13·8 (sd 0·4) years and 15·8 (sd 0·4) years, respectively.

The study was conducted according to the guidelines laid down in the Declaration of Helsinki. In Denmark there is no formal ethics agency that grants ethical approval of school-based surveys. We received study approval from the school headmaster, the parents’ school board and the students’ council in each of the participating schools. Since the school headmaster and the parents’ school board approved the study, we did not ask the parents for approval of the study. The students received oral and written information that participation was voluntary and anonymous. The study has been approved by the Danish Data Protection Agency (reference number 2015-621-0030).

Measurements

Dependent variable: breakfast frequency

Breakfast frequency was measured by a frequency question for weekdays. We dichotomized the variable following conceptual considerations and defined low breakfast frequency as consuming breakfast on fewer than four out of five weekdays (Table 1). The definition of low breakfast frequency varies⁽ Reference Rampersaud, Pereira and Girard ^{2 ,} Reference Merten, Williams and Shriver ^{11 –} Reference Sjöberg, Hallberg and Höglund ^{15 )}. According to the definition applied in the present study, breakfast can still be defined as frequent despite occasionally being skipped. Sensitivity analyses involving cut-off points defined by consuming breakfast on fewer than five, three, two and one weekday(s) were conducted. These showed no changes in the directions of associations. The breakfast frequency measure has been validated in a Danish study against 7 d, 24 h recall measures among 11–15-year-olds, demonstrating 87 % agreement and κ=0·65 for the dichotomized variable⁽ Reference Pedersen, Holstein and Laursen ^{44 )}. Also, the measure of breakfast frequency was included in a larger qualitative validation study of meal habits where face and content validity of the breakfast frequency item were tested among 11-, 13- and 15-year-old students. In total the first author conducted twenty gender-homogeneous focus group discussions at five schools with two to five students in each group. The objective was to learn about students’ perceptions and experiences of the measure immediately after they had answered the questionnaire. Further, we wished to understand how they perceived the concept of breakfast. We found high face validity as the students found it easy to answer the item. To clarify the content validity the students were asked about how they defined breakfast. The term ‘breakfast’ was a generally used term and the students generally defined it as food eaten in the morning before school (CA Johnson and TP Pedersen, unpublished results; available upon request).

Table 1 Item wording, response keys and categorization used in analyses

Independent variables: family functioning

Three dimensions of family functioning were measured⁽ Reference Kitzman-Ulrich, Wilson and George ^{18 ,} Reference Broderick ^{19 )}: (i) closeness, measured by the extent of close relations to parents; (ii) communication, measured by the quality of family communication; and (iii) support, measured by family support.

Close relations to parents

Close relations to parents was measured by asking the students how easy they find it to talk to each of their parents/step-parents about issues that really bother them (Table 1). Following conceptual considerations responses were dichotomized for each parent: close relations to parents (=‘very easy’ or ‘easy’) v. no close relations to parents (=‘difficult’, ‘very difficult’ or ‘don’t have or see this person’). Afterwards the variables were combined into close relations with at least two parents, close relations with one parent, and no close relations with parents. The item has proved useful and has been reported as such by different focus groups and teams in the international HBSC study⁽ Reference Brooks, Tabak and Zaborskis ^{45 ,} Reference Damsgaard, Holstein and Koushede ^{46 )}.

Quality of family communication

Quality of family communication was measured by an index constructed based on a short version of the clear communication scale from the Family Dynamics Measure II⁽ Reference White, Grzankowski and Paavilainen ^{47 )}. The students responded to four statements about the communication in their family. Based on conceptual considerations responses were dichotomized for each statement: ‘strongly agree’ or ‘agree’ (=1) v. ‘neither agree nor disagree’, ‘disagree’ or ‘strongly disagree’ (=0). Next the four dichotomized variables were coded into a sum score with five levels of quality of family communication: 0 (low level of quality of family communication) to 4 (high level of quality of family communication; Table 1). The short four-item version has been tested among 11−17-year-olds in the international HBSC study and showed good reliability (Cronbach’s α=0·8)⁽ Reference Brooks, Tabak and Zaborskis ^{45 )}. To test the reliability of the index in the present study sample we determined the index’s internal consistency by Cronbach’s α (=0·9), which indicated an excellent internal consistency in the index⁽ Reference Fayers and Machin ^{48 )}. Further, we tested the index for differential item function (DIF) to investigate whether or not the items in the index perform differently in subgroups⁽ Reference Fayers and Machin ^{49 )}. We tested for DIF in relation to the included sociodemographic variables, namely gender, age group, family social class, family structure and migration status. According to Scott et al., meaningful DIF should be considered if the significant odds ratio estimates are larger than 2 or lower than 0·5⁽ Reference Scott, Fayers and Aaronson ^{50 )}. We found DIF (OR=0·42; 95 % CI 0·25, 0·70) in the group of immigrants compared with natives for the statement: ‘When there is a misunderstanding we talk it over until it’s clear’. To explore the DIF with regard to migration status we compared the final analyses with analyses conducted on a sub-sample consisting of only natives. These showed no changes in the directions of associations.

Family support

Family support was measured by an index inspired by the Multidimensional Scale of Perceived Social Support (MSPSS)⁽ Reference Zimet, Dahlem and Zimet ^{51 )}. The scale covers social support from both family and friends, but in the present study we included only the family component. The students responded to four statements about family support. Following conceptual considerations responses were dichotomized for each statement: ‘strongly agree’ or ‘agree’ (=1) v. ‘neither agree nor disagree’, ‘disagree’ or ‘strongly disagree’ (=0). Afterwards the four dichotomized variables were coded into a sum score with five levels of family support: 0 (low level of family support) to 4 (high level of family support; Table 1). The MSPSS has shown a well-established scale construction with good validity and reliability⁽ Reference Brooks, Tabak and Zaborskis ^{45 ,} Reference Zimet, Dahlem and Zimet ^{51 ,} Reference Ng, Amer Siddiq and Aida ^{52 )}. The Danish version of the index is not fully comparable with the original MSPSS as we applied five response categories (‘strongly agree’, ‘agree’, ‘neither agree or disagree’, ‘disagree’, ‘strongly disagree’). The original MSPSS has seven categories from ‘strongly agree’ to ‘strongly disagree’. We tested the family support index for internal consistency by Cronbach’s α, which was high (=0·9). Further, we tested for DIF in relation to the sociodemographic subgroups and found no significant DIF.

Sociodemographic variables

We included gender, age group, socio-economic position, migration status and family structure in the analyses. Grade (7th and 9th) was used as a proxy for age group as the age variation within grades in Denmark is small. Socio-economic position was measured by family occupational social class. Students’ responses to items about their parents’ occupation were coded into family social class by the research staff and categorized into seven groups (social class I, II, III IV, V, economically inactive and unclassifiable). We followed the definitions of social class applied by the Danish National Institute of Social Research, which is almost identical to the UK Registrar General’s classification⁽ Reference Galobardes, Shaw and Lawlor ^{53 ,} Reference Hansen ^{54 )}. In the analyses family social class was dichotomized into high (I, II, III) and low social class (IV, V, economically inactive and unclassifiable). Sensitivity analyses with group III included in the low family social class category were performed and the estimates did not change notably. Further, before including unclassifiable responses (n 244) in the low family social class group, the analyses were performed with unclassifiable categorized in a separate group. This revealed an association between the category unclassifiable and breakfast frequency similar to the association between low family social class and breakfast frequency. Students’ migration status was classified as either native Danes or immigrants/descendants of immigrants, based on their responses to items about their own and their parents’ country of birth. Family structure was defined based on students’ reports of who they live with and categorized as traditional family (living with two biological parents) and other (single parent, reconstructed family, other family types; Table 1).

Statistical analyses

All analyses were conducted using the statistical software package SAS version 9·3. In the descriptive analysis of distributions χ ² tests of significance were used to examine differences in breakfast frequency by sociodemographic factors (gender, age group, family social class, family structure and migration status).

We used Cronbach’s α to test the internal consistency of the quality of family communication index and the family support index. To test for DIF we used logistic regression with each item in the index as dependent variable and the index and the sociodemographic variable as independent variables⁽ Reference Fayers and Machin ^{49 ,} Reference Scott, Fayers and Aaronson ^{50 )}.

Logistic regression models were generated to estimate the association between breakfast frequency and (i) close relations to parents, (ii) quality of family communication and (iii) family support. Initial analyses stratified by gender revealed same-direction associations for boys and girls, and analyses are therefore presented for the total sample. To account for the risk of data dependency due to the applied cluster design, we specified three-level hierarchical models (students nested within classes nested within schools) using SAS 9·3 PROC GLIMMIX. In the first step we analysed the associations unadjusted and in the second step we adjusted the analyses for the included sociodemographic variables. In initial analyses we included the sociodemographic variables one at a time and we conducted the analyses with family social class and family structure with and without dichotomizing the variables, but the associations between family functioning and low breakfast frequency did not alter.

In the third step we tested the associations for modification by sociodemographic factors. First, we examined the overall effect modification by including interaction terms between family functioning and sociodemographic factors in the model one at a time. Second, we examined the joint effect; that is, the combined effect of two variables for the three dimensions of family functioning and the sociodemographic variables. By including the combined effect it is possible to compare associations for the different combinations of the two variables with a common reference category whereby it is possible to identify protective or harmful combinations⁽ Reference Vandenbroucke, von Elm and Altman ^{55 ,} Reference de Mutsert, Jager and Zoccali ^{56 )}. Associations for all combinations were compared and those combinations that were identified as harmful were further investigated by testing for multiplicative effect modification ( $${\rm ratio\; of\; odds\; ratios}\,{\equals}\,{\rm OR}_{{{\plus}\!{\plus}}} /{\rm OR}_{{{\plus}{\minus}}}{\times}{\rm OR}_{{{\minus}{\plus}}}{\plus}1$$ ) and additive effect modification (relative excess risk due to interaction, $${\rm RERI}\,{\equals}\,{\rm OR}_{{{\plus}\!{\plus}}} {\minus}{\rm OR}_{{{\plus}{\minus}}} {\minus}{\rm OR}_{{{\minus}{\plus}}} {\plus}1$$ )⁽ Reference Knol and VanderWeele ^{57 ,} Reference Vanderweele and Knol ^{58 )}. The confidence intervals for the ratio of odds ratios and RERI were calculated as proposed by Hosmer and Lemeshow⁽ Reference Hosmer and Lemeshow ^{59 )}. Only the relevant combinations are presented in the figures.

Only twenty-two adolescents (0·7 %) did not answer the breakfast frequency item. Analyses of missing data on the family functioning measures were conducted by comparing sociodemographic differences between respondents and non-respondents and testing differences by χ ² tests of significance. We found that adolescents with missing information on the family functioning measures were characterized by more often reporting low breakfast frequency, being a boy, being 13 years old (not significant for the measure of close relations to parents), being from low social class, being an immigrant and living in another family structure than traditional (only significant for the measure of close relations to parents; P<0·05).

Results

Descriptive results

Nearly one-quarter of the adolescents consumed breakfast on fewer than four out of five weekdays (low breakfast frequency) and significantly more girls than boys reported low breakfast frequency (P<0·0001; Table 2). There was a significantly larger proportion of participants with low breakfast frequency among 15- than 13-year-olds (P=0·0023), adolescents from low family social class (P<0·0001), immigrants (P<0·0001) and other family structure than traditional families (P<0·0001).

Table 2 Gender-specific distribution of family functioning variables, sociodemographic variables and the proportion of low breakfast frequency among adolescents (n 3054) aged 13 and 15 years, Danish arm of the Health Behaviour in School-aged Children study, 2014

* Low breakfast frequency defined as eating breakfast on less than four days during weekdays.

Table 2 shows that a significantly larger proportion reported low breakfast frequency among adolescents with no close relations to parents (32·8 %) compared with adolescents with close relations to two or more parents (18·8 %; P<0·0001). A significantly larger proportion of adolescents reported low breakfast frequency when they experienced low quality of family communication (40·2 %) compared with adolescents who reported high quality of family communication (18·8 %; P<0·0001). A significantly larger proportion of adolescents reporting low family support had low breakfast frequency (38·9 %) compared with adolescents who reported high family support (19·5 %; P<0·0001).

Logistic regression analyses

Table 3 shows that inclusion of the sociodemographic variables in the statistical models attenuated the associations between the three measures of family functioning and breakfast frequency. Still, statistical significance remained. The adjusted analyses in Table 3 show that low breakfast frequency was associated with low family functioning when measured by three dimensions. The OR for low breakfast frequency was 1·81 (95 % CI 1·40, 2·33) among adolescents who reported no close relations to parents compared with adolescents who reported close relations to two or more parents. Among adolescents who had low level of quality of family communication the OR for low breakfast frequency was 2·28 (95 % CI 1·61, 3·22) compared with adolescents with high level of quality of family communication (lower level of score compared with uppermost level of score). The OR for low breakfast frequency was 2·09 (95 % CI 1·39, 3·15) among adolescents who reported low level of family support compared with adolescents who reported high level of family support (lower level of score compared with uppermost level of score).

Table 3 Odds ratios (95 % CI) for low breakfast frequency by family functioning, unadjusted and adjusted for sociodemographic variables, among adolescents (n 3054) aged 13 and 15 years, Danish arm of the Health Behaviour in School-aged Children study, 2014

Significant associations are shown in bold font.

The adjusted analyses of all three dimensions of family functioning showed associations between the included sociodemographic variables (gender, age group, family social class, migration status and family structure) and low breakfast frequency. Low breakfast frequency was more common among girls, 15-year-olds, adolescents from low family social class, immigrant adolescents and adolescents living in other family structures than traditional.

Effect modification analyses

The joint effect analysis suggested for all three dimensions of family functioning that the odds of having low breakfast frequency among adolescents with low compared with high family functioning were considerably higher among girls than among boys (Figs 1–3). This finding was supported by tests for effect modification. We found positive additive effect modification of no close relations to parents and being a girl, RERI=1·30 (95 % CI 0·19, 2·42). Further, we found positive multiplicative and additive effect modification of low level of quality of family communication and being a girl. The multiplicative ratio of odds ratios =2·32 (95 % CI 1·09, 4·96), RERI=2·89 (95 % CI 0·84, 4·95). We found positive effect modification of low level of family support and being a girl but the finding was not significant.

Fig. 1 Odds ratios (with 95 % CI represented by vertical bars) for low breakfast frequency by combinations of close relations to parents and gender, adjusted for sociodemographic variables*, among adolescents (n 3054) aged 13 and 15 years, Danish arm of the Health Behaviour in School-aged Children study, 2014. Effect modification of the combination of no close relations to parents and being a girl: ratio of odds ratios=3·36/(1·46×1·60)=1·44 (95 % CI 0·86, 2·42); relative excess risk due to interaction=3·36–1·46–1·60+1=1·30 (95 % CI 0·19, 2·42). *Only the combinations that had an effect are illustrated (ref., reference category)

Fig. 2 Odds ratios (with 95 % CI represented by vertical bars) for low breakfast frequency by combinations of quality of family communication and gender, adjusted for sociodemographic variables*, among adolescents (n 3054) aged 13 and 15 years, Danish arm of the Health Behaviour in School-aged Children study, 2014. Effect modification of the combination of low level of family communication and being a girl: ratio of odds ratios=4·78/(1·30×1·59)=2·32 (95 % CI 1·09, 4·96); relative excess risk due to interaction=4·78–1·30–1·59+1=2·89 (95 % CI 0·84, 4·95). *Only the combinations that had an effect are illustrated (ref., reference category)

Fig. 3 Odds ratios (with 95 % CI represented by vertical bars) for low breakfast frequency by combinations of family support and gender, adjusted for sociodemographic variables*, among adolescents (n 3054) aged 13 and 15 years, Danish arm of the Health Behaviour in School-aged Children study, 2014. Effect modification of the combination of low level of family support and being a girl: ratio of odds ratios =3·98/(1·64×1·61)=1·51 (95 % CI 0·65, 3·52); relative excess risk due to interaction=3·98–1·64–1·61+1=1·73 (95 % CI –0·54, 4·00). *Only the combinations that had an effect are illustrated (ref., reference category)

Further, the joint effect analyses suggested that the odds of having low breakfast frequency for adolescents with no close relations to parents compared with adolescents with close relations to two or more parents were considerably higher among immigrants than among native Danes, OR=5·96 (95 % CI 3·20, 11·09; figure not shown). Test for effect modification showed positive effect modification but the finding was not significant. Further, the odds of having low breakfast frequency for adolescents with low level of family support compared with adolescents with high level of family support were considerably higher among immigrants than among native Danes, OR=5·56 (95 % CI 1·85, 16·73; figure not shown). Further, test for effect modification revealed positive effect modification but the finding was not significant. Also the odds of having low breakfast frequency for adolescents with low compared with high family support were considerably higher among adolescents living in a family structure other than traditional as compared with adolescents from a traditional family structure, OR=4·35 (95 % CI 2·48, 7·62; figure not shown). Test for effect modification showed positive effect modification but the finding was not significant. The joint effect analyses with age group and family social class did not reveal any modifying effect.