Social Inequality in Adolescent Life Satisfaction: Comparison of Measure Approaches and Correlation with Macro-level Indices in 41 Countries

Depósito de Investigación de la Universidad de Sevilla https://idus.us.es/ This version of the article has been accepted for publication, after peer review and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s11205-018-1860-0 1 A comparison of family affluence based approaches to measure inequality 1 in adolescent life satisfaction in 41 countries and correlation with macro- 2 level indices 3 Abstract. Family affluence plays a crucial role in adolescent well-being and is potential source of health 4 inequalities. There are scarce research findings in this area from a cross-national perspective. This study introduces 5 several methods for measuring family affluence inequality in adolescent life satisfaction (LS) and assesses its 6 relationship with macro-level indices. The data (N=192,718) were collected in 2013/2014 in 39 European 7 countries, Canada, and Israel, according to the methodology of the cross-national Health Behavior in School-aged 8 Children (HBSC) study. The 11-, 13- and 15-year olds were surveyed by means of self-report anonymous 9 questionnaires. Fifteen methods controlling for confounders were tested to measure social inequality in adolescent 10 LS. In each country, all measures indicated that adolescent from more affluent families showed higher satisfaction 11 with their life than did those from less affluent families. According to the Poisson regression estimations, for 12 instance, the lowest inequality in LS was found among adolescents in Malta, while the highest inequality in LS 13 was found among adolescents in Hungary. The ratio between the mean values of LS score at the extreme highest 14 and lowest family affluence levels (Relative Index of Inequality) derived from the regression-based models 15 distinguished for its positive correlation with the Gini index, and negative correlation with Gross National Income, 16 Human Development Index and the mean Overall Life Satisfaction score. The measure allows in-depth exploration 17 of the interplay between individual and macro-socioeconomic factors affecting adolescent well-being from a cross- 18 national perspective. 19 Keywords. Adolescents Life satisfaction Family affluence Health inequality Measures Relative index of 20 inequality 21 22 1 Introduction 23 Family socioeconomic status (SES) including family affluence plays a crucial role in young people’s well-being 24 and has a great impact on the development of their personality and aspirations. There is evidence that the richer, 25 wealthier or higher SES of the family provides better health and well-being among children and adolescents (Levin 26 et al. 2011; Viner et al. 2012). Differences in family SES across social groups and populations are a potential 27 source of social inequalities in both health and quality of life (QoL) among young people (Koster et al. 2005; 28 Hanson and Chen 2007; WHO 2010), this being of a major concern for public health and social policies in each 29 country (Hosseinpoor et al. 2015). 30 Recent scientific literature extensively develops concepts and theory on social inequalities in health (Bartley 31 2004; Arcaya et al. 2015; Alonge and Peters 2015), however, findings are mostly based on research with adult 32 populations (Mackenbach et al. 2008; Hosseinpoor et al. 2012; Choi et al. 2015). The effect of within country 33 income inequality on adult QoL and well-being has also been analyzed (Diener and Biswas-Diener 2002; Schütte 34 et al. 2014). It was found that adult life satisfaction (LS) is dependent on income level, which allows for basic 35 needs to be met. From a cross-national perspective, it was demonstrated that national income was a greater 36 predictor of individual LS among adults (Schyns 2002). As for children and young people, the data on social 37 disparities in health, LS or QoL is clearly lacking and this population has received considerably less attention in 38 the literature (Levin et al. 2011). Thus, it is useful to examine whether the findings from previous studies in 39 adulthood may also apply to young people. 40 Socioeconomic inequalities in health and health behaviors during adolescence is one of the foci of the cross- 41 national study Health Behavior in School-aged Children (HBSC) which involves a wide network of researchers 42 from more than 40 countries and regions (HBSC 2017). The previous editions of the study have highlighted the 43 effect of socioeconomic differences on the way young people grow and develop (Currie et al. 2012; Inchley et al. 44 2016). A significant positive association between LS and family affluence was found for both genders in nearly 45 all participating countries and regions. 46 The existence of social inequality in adolescent health depends on the age-appropriate measure of family 47 socioeconomic conditions, in addition to its numerical account depending on the method for evaluating the extent 48 of social inequality (Spencer 2006). The Family Affluence Scale (FAS) is a measure that has been proposed in the 49 HBSC framework; it has been demonstrated as a valid indicator for evaluating the socioeconomic position of the 50 adolescents in cross-national surveys (Currie et al. 2008; Torsheim et al. 2016). The scale includes items on 51 common material assets or activities of the adolescent family (HBSC 2013) (see more in Methods). However, the 52 lack of an appropriate method for assessing socioeconomic inequalities in adolescent health is the principal cause 53 of the lack of consensus in the literature of how health inequalities manifest within and between countries. 54 Manuscript (excluding all authors contact details) Click here to view linked References 2 Moreover, the lack of a valid method for measure socioeconomic inequalities in adolescents could cause these 55 disparities to be underestimated (Alonge and Peters 2015; Elgar et al.2016). In this context, although some cut-off 56 points have been suggested in order to classify groups in three categories (low-, mid- and high-level material 57 wealth), due to the differences among the FAS distribution across countries a new method for employing the scale 58 is being developed. As it was employed in the last HBSC report (Inchley et al. 2016), groups are created now by 59 using ridit-scores, selecting the 20% of the population with the lowest scores as the group with low affluence, and 60 the 20% of the population with the highest scores as the group with high family affluence in each country. The 61 population with scores in the middle 60% of the distribution is considered as the group with medium affluence. 62 The range in health outcome distribution between high and low-affluence groups was only used to measure the 63 extent of health inequality, while its statistical significance was based on linear trends across all three family 64 affluence groups. Although this common approach is simple to interpret and does not require any strong 65 assumption about the distribution of the health measure or its measurement scale (the range approach), it is limited 66 to exploring causal models of health inequalities given that it omits intermediate groups when there are more than 67 two groups (Wagstaff et al. 1991; Alonge and Peters 2015). In addition, it does not account for the sample size of 68 the groups. Finally, using a measure within two marginal groups of the population may not reflect health 69 inequalities in relation to country’s income inequality and welfare benefits (Schyns 2002; Bartley 2004; Spinakis 70 et al. 2011). 71 Furthermore, family structure and other factors may be potential confounders of the relationship between 72 family affluence and LS among children and adolescents (Levin et al. 2011). Indeed, Burton and Phipps (2010) 73 found positive association between family income and young teen happiness. The influence of gender in LS has 74 been widely evidenced too. For example, gender has been found to be a predictor of adolescent LS, with boys 75 more likely to show high LS (Reiss 2013; Moksnes and Espnes 2013; Klanšček et al. 2014). Along the same lines, 76 previous findings have shown that older adolescents tend to report lower life satisfaction (Kunst and Mackenbach 77 1995). This drawback may disappear if the model is rigorously adjusted for confounders to assess health 78 inequalities between family affluence groups. 79 Several analyses of the HBSC data, using a multilevel approach, have shown the existence of cross-national 80 variation in the relationship between family affluence and adolescent LS (Levin et al. 2011). Such analyses have 81 also highlighted the importance of identifying and addressing country-level socioeconomic factors during 82 adolescence. These findings suggest a possible relationship between social inequality in LS among adolescents 83 and socioeconomic indices in a cross-national perspective. However, cross-national research in the field, especially 84 with adolescent populations, is still scant and limited by measurement problems. Since the last HBSC report 85 (Inchley et al. 2016) there have been no further attempts to compare adolescent health inequalities in detail. It is 86 surprising that so little attention has been paid to the question of how social inequality is best measured among 87 adolescents. 88 To overcome these shortcomings, our research has focused on adopting a broader concept of measuring and 89 evaluating social inequalities in health (Wagstaff et al. 1991). Until recently, the two approaches to measuring 90 health inequality are regression-based measures (e.g. the Slope Index) and aggregate measures (e.g. Health 91 Concentration Index) (Wagstaff et al 1991; Kunst and Mackebach 1995; Mackenbach and Kunst 1997; Regidor 92 2004a; 2004b). Therefore, there is little experience in adopting these approaches for assessing social inequalities 93 in adolescent health (Due et al. 2009). Indeed, to date none have compared different health inequality measures 94 with respect to correlations between their accounts and country-level socioeconomic indicators across adolescent 95 samples. 96 The aim of our study is twofold: 97 1. To compare socioeconomic inequality in adolescent LS across countries employing different measures. 98 2. To determine the correlations between outcomes of tested measures and country level socioeconomic 99 indices (e.g. Gross National Income, Gini index, etc.). 100 101 2 Data and Methods 102 2.1 Subjects and study design 103 The data presented here were obtained from the Health Behavior in School-aged Children (HBSC) study, a cross- 104 national survey with support from the World Health Organization (WHO, Europe) which was completed in 105 2013/2014 in 42 countries, including 40 European countries and regions (considered alone as countries, i.e. 106 England, Scotland and Wales), Canada, and Israel. More detailed background information about the study is 107 provided in its international report (Inchley et al. 2016) and website: www.hbsc.org (HBSC 2017). 108 The population selected for sampling was 11-, 13- and 15-year old adolescents. Participants were selected 109 using a clustered hierarchical sampling design, where the initial sampling unit was the school class. Data collection 110 methods ensured that the samples of students were representative by age and gender. Specifically, the analyses 111 presented here are based on the total number of 192,718 individual records (children with valid LS and FAS) 112 3 obtained from 41 countries via HBSC Data Centre (Bergen University, Norway). Table 1 indicates the samples by 113 countries (Armenia was excluded from the analysis due to deviance in FAS assessment). 114 The data were collected by means of self-report standardized questionnaires. The surveys were administrated 115 in school classrooms ensuring students’ confidentiality. Response rates at the school, class and student level exceed 116 80% in the majority of countries (Inchley et al. 2016). 117 The study conformed to the principles outlined in the Declaration of Helsinki. National and local educational 118 institutions agreed upon the study protocol. Ethical approval was obtained for each national survey according to 119 the national guidance and regulations at the time of data collection. Researchers strictly followed the standardized 120 international research protocol to ensure consistency in survey instruments, data collection and processing 121 procedures (HBSC 2013). 122 2.2 Measures 123 At the individual level, the outcome variable was LS, and the explanatory variables were family FAS, family 124 structure, gender and age. The analysis was stratified by country. 125 Students’ LS was rated using the measurement technique known as the Cantril (1965) ladder. They were asked to 126 take a look at the drawn ladder, with steps numbered from zero (“0”) at the bottom to ten (“10”) at the top, with 127 the instruction to suppose the top of the ladder represents the best possible life, and the bottom of the ladder 128 represents the worst possible life. Respondents were asked to indicate the step of the ladder at which they would 129 place their lives at present. Thus, the response was scored from 0 to 10 (an ordinary variable y), which was also 130 dichotomized into a binary variable Y with codes: Y = 0 for LS score ≤ 5 (low LS), and Y = 1 for LS score > 5 131 (high LS). Both ordinary and binary variables were used as an outcome variable in the models of health inequality 132 measure. In addition, their inverses (z=10 – y, and Z = 0 for LS score > 5 (high LS) and Z = 1 for LS score ≤ 5 133 (low LS)) were used in regression-based models in order to adopt the Poisson and negative binomial distributions. 134 On average, the proportion of missing cases for LS was 3.7%. 135 Family wealth was measured by the Family Affluence Scale (FAS), which was specially developed for the 136 international nature of the HBSC study (Currie et al. 2008; Torsheim et al. 2016). The scale is simple and easy to 137 answer even for young adolescents. FAS includes six questions with answers (assignment of points shown in 138 parentheses): Does your family own a car, van or truck? “no” (0), “yes one” (1), “yes two or more” (2); Do you 139 have your bedroom for yourself? “no” (0), “yes (1); During the past 12 months, how many times did you travel 140 away on holiday (vacation) with your family? “not at all” (0), “once” (1), “twice“ (2), “more than twice” (3); How 141 many computers does your family own? “none” (0), “one” (1), “two” (2), “more than two” (3); How many 142 bathrooms (room with a bath/shower or both) are in your home? "none" (0), "one" (1), "two" (2), "tree or more" 143 (3); Does your family have a dishwasher at home? "no" (0), "yes" (1). A FAS score was calculated by summing 144 the points to these six questions. Because the groups of respondents scored by 0 – 2 points and by 12 – 13 points 145 were small they were combined into the FAS=1 group and the FAS=11 group, respectively. The groups of 146 respondents scored from 3 to 11 points were assigned to groups FAS=2 through FAS=10, correspondingly. On 147 average the proportion of missing cases in the total sample for FAS was 8.3% (for details see Online Resource 1). 148 To identify family structure, respondents were given a checklist to mark the people living in their home. 149 Respondents were coded as living with “Both parents” (1) if both the mother and father were ticked in a checklist, 150 “Not both parents” (2) in all other cases. 151 At the country level, we used the indices reported in the Human Development Report (2015). Data referring 152 to the year 2014 were compiled. The Gini coefficient served as an indicator of country-level economic inequality. 153 The coefficient reflects the distribution of income among the population and varies between 0 (perfectly equal 154 distribution) and 100 (the worst inequality of incomes). The Gross National Income (GNI) per capita served as a 155 measure of economic level of each country (GNI in US dollars is calculated according to the World Bank Atlas 156 method of conversion from national currency to US dollar terms). The Human Development Index (HDI) was 157 employed as a summary measure of human development. It measures the average achievements in a country in 158 three basic dimensions of human development: a long and healthy life, access to knowledge, and a decent standard 159 of living. And finally, we used the Overall Life Satisfaction (OLS) mean score based on the responses of adult 160 population (ages 15 and older) to a question about satisfaction with freedom of choice and life in a Gallup World 161 Poll (the survey question is identical to the HBSC study). The same values of indices have been used for the two 162 Belgian regions and the numbers for the United Kingdom have been assigned to England, Scotland and Wales. 163 None of these indices were available for Greenland and Gini index was not found for Malta, leaving these countries 164 out of analyses that include country level indices. 165 2.3 Statistical analysis and methods of the measurement of social inequality 166 All analyses were performed with SPSS (version 20.0; SPSS Inc, Chicago, IL, 2010). P<0.05 was considered 167 statistically significant. Descriptive statistics (means and proportions with 95% confidence interval – 95 % CI) 168 4 were estimated by country. Associations between country-level assessments were estimated using Spearman 169 correlation coefficient ρ. 170 Two data files were used in analysis. The first file included 192,718 individual records from all countries. 171 The second file (Online Resource 1) included 42 records, which represented aggregated data by 41 countries, and 172 grand totals, which were estimated from individual records weighting them by the country sample size. The data 173 of files were merged by country and FAS group if necessary to update individual records with aggregated variables 174 (e.g. midpoints of FAS distribution). 175 In order to select appropriate methods for assessing inequality on adolescent LS the following requirements 176 for each measure were taken into account: 177 1. Incorporation of the actual sample size of each FAS category. 178 2. Obtaining a statistical model with the appropriate goodness of fit. 179 3. Adjustment for possible confounders. 180 4. Estimation of statistical properties (average and variation) using standard SPSS procedures. 181 To fulfill the first requirement, the ordinal FAS measure was transformed into a continuous X variable scaled 182 from 0 to 1, while incorporating appropriate population weights for each FAS category, as defined by Kunst and 183 Mackenbach (1995). The FAS categories were ranked from lowest to highest; the weight of each category was 184 proportional to its population size within a FAS scale category. The X variable was plotted on the horizontal axis 185 representing the cumulative distribution of the population for each FAS category. Then, the dependent variable 186 (e.g. y, Y or other) was plotted at the midpoint of each FAS group proportion range. The midpoints were calculated 187 for each country separately and for the total sample as the ridit scores in the following way: 188 189 where ui (i = 1, 2, …, g) is a proportion of corresponding FAS group in the sample, and g is the number of FAS 190 groups. 191 Then two types of summary statistics from the individual records data file were produced: 192 1 Regression-based measures (models ‘R’), and 193 2 Aggregate measures of dissimilarity of distributions (models ‘A’). 194 For the HBSC data, altogether 15 measures of social inequality in adolescent LS were chosen and tested. 195 Table 2 presents models and measures that have been employed in the literature to date (Wagstaff et al. 1991; 196 Spinakis et al. 2011; Regidor 2004a; 2004b) and originally proposed by authors of the present study. Detailed 197 description of the measures is presented in Appendix. 198 3 Results 199 The characteristics of samples by gender and family structure are outlined in Online Resource 1. In the total sample 200 48.8% of students were boys and 51.2% were girls. A negligible range between proportions of students’ gender 201 was common in all countries, except Ireland for which the percentage of boys to girls (38.9% vs. 61.1%) was taken 202 into account. Family structure distribution showed a wide variation across countries, ranging from 54.1% of 203 adolescents living with both parents in Greenland to 93.2% in Albania (71.8% in the total sample). 204 With respect to countries, mean FAS ranged from 3.94 (95% CI: 3.88; 4.00) in Albania to 8.80 (95% CI: 8.74; 205 8.86) in Norway; its average in the total sample was 6.92 (95% CI: 6.91; 6.93) (Table 1). The means of LS score 206 ranged from 7.08 (95% CI: 7.01; 7.14) in Belgium (Flemish) to 8.26 (95% CI: 8.20; 8.31) in Republic of Moldova; 207 the average in the total sample was 7.61 (95% CI: 7.60; 7.62). The proportion of adolescents reporting high LS 208 ranged from 79.9% (95% CI: 78.8; 81.0) in Czech Republic to 93.2% (95% CI: 92.5; 93.9) in Albania (85.8% in 209 the total sample (95% CI: 85.6; 85.9)). Figure 1 shows the asymmetric negatively-skewed distribution of LS scores 210 in the total sample (skewness = – 1.028). 211 There was a tendency for negative correlation at the country level between the means of FAS and that of the 212 LS score (ρ= – 0.218; p = 0.172), while no correlation was found between mean of FAS score and proportions of 213 high LS (ρ = 0.019; p = 0.908). In contrast, both correlations were positive in all countries at the individual level. 214 Midpoints of FAS were calculated for the total sample and for each country, reveling differences among 215 countries. The extend of inequality in adolescent LS employing all the proposed models was assessed also for the 216 total sample and for each of the 41 countries (see Online Resource 1). The impact of family affluence, family 217 structure (living with both parents), gender, and age on adolescent LS was assessed by regression-based models 218 comparing their goodness of fit. Results of this analysis revealed a dominant effect of family affluence over family 219 structure, gender, and age, with these last variables also showing a significant effect on adolescent LS. In 220 comparison with linear and logistic regression-based models, Poisson and negative binomial regression-based 221 models had a much better goodness of fit (deviance value/df was closer to 1) regressing both LS score and bivariate 222 LS. Results of this analysis in the total sample are shown in Table 3. 223 ),,…3, 2, = (,2/ ;2/ 1 1 11 giuuX uX i i kki      5 For every country, all proposed measures indicated that adolescents from more affluent families have higher 224 life satisfaction in comparison with their peers from less affluent families. However, regarding the first objective 225 of this study, results showed variation in the amount of inequalities found in LS between countries, with these 226 results also depending on the measure employed for assessing FAS inequalities. For example, according to the RII 227 of Poison regression for the LS score (Model R3) the lowest inequality in LS was found among adolescents in 228 Malta (RII = 1.024; 95% CI: 0.926; 1.134), while the highest inequality in LS was found among adolescents in 229 Hungary (RII = 1.812; 95% CI: 1.684; 1.950). However, countries were ordered differently by their values of 230 calculated LS inequality depending on the measure of inequality employed. Table 4 shows average values of 231 inequality in LS measured by 15 different methods and nominates three countries with the lowest and highest 232 values of the corresponding measures. Among the countries with the lowest social inequality in LS, Malta was 233 nominated in 13, Belgium (Fl.) and Netherlands in 11 of 15 measures. Among the countries with the highest social 234 inequality in LS, Hungary was nominated in 13 of 15 measures providing the significantly highest assessments of 235 proposed measures. Relatively high estimations of social inequality in LS were also revealed in samples of students 236 from Israel and the Republic of Moldova. For each country and in the total sample, the statistical estimations of 237 family affluence inequality in adolescent LS, measured by 15 different methods, are presented in Online Resource 238 1. 239 At the country level, the measures were positively correlated (data not presented). Most of Spearman 240 correlation coefficients showed significance at the level p ≤ 0.01. An exception was HCI, which had a weak 241 correlation with other measures. The regression-based measures for LS scores, as well as regression-based 242 measures for binary LS score, were highly correlated (ρ > 0.9) within their groups, meaning that these indicators 243 perform an almost identical role in the measurement of inequality. 244 The second goal of the present study was to examine the relationship between different measures of social 245 inequality in adolescent LS and several country-level socioeconomic indices. For this purpose, four macro-level 246 indices were chosen (the Gini coefficient, GNI, HDI, and OLS mean score), whose data were made available for 247 HBSC participating countries. Table 5 shows the correlation between these indices and proposed measures of 248 health inequality that were calculated at the country level. Any of the proposed measures of inequalities in LS 249 showed a positive correlation with the Gini index, although there were no significant estimations of Spearman 250 correlation. In addition, the proposed measures showed significant negative correlations with GNI, HDI, and OLS 251 mean scores with the exception of HCI (Model A1), that showed a non-significant but positive correlation with 252 GNI, HDI and OLS. In this respect, regression-based measures (models ‘R’) for LS scores demonstrated a 253 noticeable correlation with macro-level indices. For instance, RII of Poisson regression for the LS score (Model 254 R3) positively correlated with the Gini index (ρ = 0.100, p = 0.544), and negatively correlated with GNI (ρ = – 255 0.516, p = 0.001), HDI (ρ = – 0.495, p = 0.001) and OLS mean scores (ρ = – 0.404, p = 0.010). In contrast to the 256 regression-based models, the range-based inequality measure (Model A5) did not correlate with country-level 257 socioeconomic indices. 258 4 Discussion and Conclusion 259 Although cross-national variation in socioeconomic inequalities in LS among adults has been examined in many 260 studies (Diener and Biswas-Diener 2002; Schyns 2002; Schütte et al. 2014), the literature to date in that field of 261 research among adolescents is scarce (Levin et al. 2011). Thus the rationale of the present study was based on the 262 need to get new insight into the social inequalities in adolescent LS across different countries. Within this context 263 the aim of our study was twofold. Firstly, we sought to compare socioeconomic inequality in adolescent LS across 264 countries employing different measures and controlling the effect of possible confounders (age, gender and family 265 structure); and secondly, we examine if there were any correlations between outcomes of tested measures of LS 266 inequalities among adolescents and country level socioeconomic indices (e.g. Gross National Income, Gini index, 267 etc.). 268 The origin of the present study attempted to choose an appropriate method to measure social inequality in 269 health and use it to measure family affluence inequality in LS among adolescents within data collected across 270 HBSC countries (HBSC 2013; Inchley et al. 2016). Although numerous approaches and methods to measure 271 inequality in health have been presented in literature (Wagstaff et al. 1991; Bartley 2004; Spinakis et al. 2011; 272 Arcaya 2015; Alonge and Peters 2015), little is known about their adequateness for application in specific cases. 273 Thus, results responding the two research questions in this study were calculated using different approach for 274 measuring FAS-based inequalities in order to compare the results obtained. As our data consisted of national 275 samples, the main requirement for the selected methods was their adjustment for socioeconomic conditions and 276 possible confounders. 277 Health inequalities are most frequently investigated with respect to the various socioeconomic groups that 278 are formed in the society (Spinakis et al. 2011). This led several researchers to investigate inequalities using more 279 sophisticated measures of inequality. The experts for measurement of health inequalities in the European Union 280 have concluded that odds ratio (OR) of the logistic regression present the most adequate solution to the problem 281 6 of measuring inequalities with respect to social categories (Spinakis et al. 2011). The well-known RII and SII are 282 similar solutions that are also related to easy statistical modeling techniques (Kunst and Mackenbach 1995; 283 Mackenbach and Kunst 1997). However, their application poses restrictions for linearity; otherwise, the magnitude 284 of these indices would be biased (Regidor 2004b). Finally, there are some indices that are more known to the 285 researchers involved in measuring inequalities in general (e.g. the HCI) (Wagstaff et al. 1991; Regidor 2004a; 286 2004b). As suggested in much literature (Spinakis et al. 2011), different measures can give information about 287 different aspects of health inequalities. The interpretation of health inequality can also be quite different, depending 288 on the measure used. Several authors recommend that in order to have a fuller understanding of health inequalities, 289 it is better to use more than one measure and combine their outcomes (Wagstaff et al. 1991; Spinakis et al. 2011). 290 These findings highlight the importance of methodological issues in measuring social inequality in adolescent LS 291 and in the exploration of the interplay between individual and macro-socioeconomic factors on adolescent well- 292 being from the cross-national perspective. 293 The recent HBSC report (Inchley et al. 2016) has already applied a range-based measure to evaluate 294 inequality in health behavior outcomes among adolescents by comparing two marginal family affluence groups in 295 each of the countries. Due to a large variation of this summary statistic across countries, including analysis of 296 inequalities in LS, we adjusted data for sample size of family affluence groups in each country. As recommended 297 by Kunst and Mackenbach (1997), we used regression-based models for this purposes. Owing to the very 298 asymmetric distribution of the LS variable, we applied a novel solution of adapting a negative binomial regression 299 for the present study. In contrast with linear regression and logistic regression, the assessment of model goodness 300 of fit confirmed the appropriateness of using this regression as well as the Poisson regression. 301 Several aggregate measures of health inequality were introduced as alternatives to the regression-based 302 measures. In addition to the well-known measures, such as the HCI and range based, we introduced two new 303 measures: difference between averages of the midpoints in groups of subjects with high LS and low LS (Model 304 A2), and loss of positive cases due to health inequalities (Model A3). Although these two measures were based on 305 common statistical approaches, their assessments across countries had a weak correlation with country-level 306 socioeconomic indices, likely due to inadequate dichotomization of LS score. 307 As there were several possible confounders mediating the relationship between family affluence and LS, all 308 proposed models of social inequality in health were adjusted for them. In the present study family structure, gender, 309 and age were regarded as confounders. The prevalence and mediating influence of these variables differed cross- 310 nationally (Inchley et al. 2016). The current study found that gender, age, and family structure defined inequalities 311 in adolescent LS considerably, however in a smaller magnitude than family affluence. It was documented that 312 gender has a moderating effect in the relationship between adult LS and income (Diener and Biswas-Diener 2002; 313 Schyns 2002) and this was also observed among adolescents in analysis of relationship between family affluence 314 and LS among boys and girls (Levin et al. 2011). Family structure also confounds the relationship, as missing at 315 least one of the parents is more likely to result in lower family affluence. Even after adjusting models for gender, 316 age, and family structure (living with both parents) we found a consistent inequality in LS related to different level 317 of family affluence. 318 This study revealed a substantial variation in the strength of family affluence inequality in LS among 319 adolescents across countries, however, this variance and ordered rank of countries differ by the inequality measure 320 chosen. Most of all, the difference is seen when comparing the regression-based measures with aggregate 321 measures, as well as when comparing the regression-based models for the LS score with those for the binary LS 322 estimation. Theoretically, linear, Poisson, and negative binomial regression based measures should generate 323 identical assessments, but this was not achieved due to the dissimilarity between real LS score distributions and 324 corresponding theoretical distribution (e.g. the key assumption of linear regression is a normal distribution of at 325 least the dependent variable, but our data did not fulfill this requirement; violence of requirements for linear 326 regression is reflected by poor model goodness-of-fit). 327 Finally, our study examined if several methods of inequality measurements reveal different patterns of 328 association between family affluence inequality in adolescent LS and country level socioeconomic indices. In this 329 study we report that regression-based models for the ordinal LS score are relevant for measuring family affluence 330 inequality in adolescent LS. The outcomes of these measures correlate with country-level socioeconomic indices, 331 such as Gini index, GNI, HDI and OLS mean score. The measure based on Poisson regression model for LS score 332 is the one that better shows this association. Bearing in mind that this model demonstrated an appropriate goodness 333 of fit we recommend applying this model for practical purposes in the measurement of social inequalities in health 334 in similar studies. The use of the Poisson regression in the analysis of inequalities in health has already been 335 justified in several studies (Mackenbach and Kunst 1997; Mackenbach et al. 2008; Hosseinpoor et al. 2012). 336 In contrast to the models for the ordinal LS score, the measures of inequality with the models for the binary 337 LS did not demonstrate an impressive correlation with country-level socioeconomic indices. This is also noted for 338 the range-based inequality measure (Model A5) that was described in the HBSC report (Inchley et al. 2016). The 339 failure of this model might be explained by inadequate dichotomization of the LS score, when too high of a 340 proportion of subjects with high LS was provided. Indeed, further research is required to meet the challenge of 341 optimizing the scaling of the LS score. 342 7 In our study we found a positive correlation between family affluence inequality in LS among adolescents 343 and in the Gini index. Moreover, the results indicated higher inequality in those countries that had a more unequal 344 income distribution of income. The negative correlation with GNI gives indication on higher inequality in poorer 345 countries. These results resonate with the findings of a study by Levin et al. (2011) for the HBSC survey in 2006; 346 they are also in line with the previous findings among adults (Diener and Biswas-Diener 2002; Schyns 2002). Our 347 study, in addition to the findings described in the above references, revealed that inequality under consideration 348 also had a relationship with summary country-level statistics like the HDI, as well as with responses of adult 349 population to the identical question about LS. We note that family affluence inequality in adolescent LS had a 350 reduced magnitude in countries with declared a higher HDI and OLS mean score. 351 Limitations 352 We hereby note two kinds of limitations of this study. 353 The limitations of the first kind are related to the survey methodology. There are differences between 354 countries in various aspects of data collection, and some of these might affect the size of inequalities in health and 355 LS. The main concern was the family affluence assessment, which was constructed by students’ self-reported items 356 that are sensitive to the cultural and structural surroundings. Some studies have shown, however, that the FAS, 357 that was used in our study, is a reliable measure among adolescents and concurs with parental reports (Boyce et 358 al. 2006). Psychometric validation of the revised FAS and weakness of the measure has been described previously 359 (Torsheim et al. 2016). Boyce et al. (2006) compared FAS measurements internationally and recommended the 360 inclusion of FAS in aggregate analyses in studies on health inequalities. 361 The limitations of the second kind are related to the data processing and analysis of the relationship between 362 individual LS, family affluence, and country-level socioeconomic indices, in particular. While data are available 363 from many countries, the most appropriate approach for the analysis of such relationships might be the multilevel 364 modeling, such as those demonstrated in other studies (Due et al. 2009; Levin et al. 2011). In the present study we 365 did not use the multilevel modeling because of specific objectives in our study. Future work is recommended to 366 examine potential mediators in order to identify groups of adolescents with the highest social inequality in LS. 367 Conclusions 368 This study revealed a substantial variation of the magnitude of family affluence inequality in adolescent LS across 369 countries. However, the variance and ordered rank of countries varied also by the inequality measurement chosen. 370 We suggested that regression-based measures (e.g. the Poisson regression-based model) for LS scores are the most 371 suitable for assessment of family affluence inequality in adolescent LS. Our findings indicate the need for 372 continued research about social inequalities in adolescent health, and particularly in the exploration of the interplay 373 between individual and macro-socioeconomic factors on adolescents’ well-being from the cross-national 374 perspective. Research in this field is considered to be crucial for adolescent health by all policy planners. 375 376 Appendix 377 Regression-based measures. We considered eight regression-based models to measure inequality in adolescent 378 LS. They measure absolute and relative differences in the estimation of the outcome variable at the extreme 379 values of FAS. Four models explored the relationship between LS score and FAS, while the remaining four 380 models examined the prevalence of low and high LS (dichotomized LS score) across 11 FAS group midpoints. 381 All models were adjusted for gender, age and family structure variables (equations presented below omit these 382 variables). 383 Model R1 was based on the linear regression for the mean value of LS score: 384 , 385 where X represents midpoints of FAS in the scale of cumulative distribution ranging from 0 to 1,  is the 386 intercept (mean value of LS score at the extreme lowest hypothetical FAS (at X = 0), and β denotes the regression 387 slope, which designated the Slope Index of Inequality (SII). Specifically, the SII is interpreted as the average 388 increase in mean LS score in the population ranked from the extreme lowest FAS group to the extreme highest 389 FAS group. A positive SII indicates an increase in adolescent LS corresponding to an increase in family wealth. 390 Kunst and Mackenbach (Kunst and Mackenbach 1995; Mackenbach and Kunst 1997) defined the Relative Index 391 of Inequality (RII): 392 RII = (  + β) /  (1) 393 Xy   8 as a measure of the influence of socioeconomic status on a health index. In the present study, it estimates the ratio 394 between the mean value of LS score at the extreme highest FAS level (at X = 1) and at the extreme lowest FAS (at 395 X = 0). 396 To calculate RII instead of the formula (1) we used the identity derived by Moreno-Batancure et al. (2015): 397 , (2) 398 where is an average of LS score, which is relatively less sensitive to adjusting for confounders than intercept  399 in formula (1). Confidence interval (CI) for the RII was calculated using the formulas defined by Hayes and Berry 400 (2002). 401 Model R2 was based on the linear regression for the proportion of high LS in the population ranked from the 402 lowest FAS group to the highest. This model is an analog of the Model R1, in which the LS score was replaced by 403 a binary measure: Y = 0 (low LS), Y = 1 (high LS). This model has been used in the literature to measure inequalities 404 in health, such as mortality, self-assessed health (Mackenbach et al. 2008) and overweight prevalence (Due et al 405 2009; Devax and Sassi 2013). The SII and RII were calculated with the same formulas used for the model R1. 406 Here, RII represents the ratio between those reporting high LS at the top rank of FAS (at X=1) and at rank zero (at 407 X = 0). 408 As distributions of outcome variables (LS score or binary LS) might differ from a normal distribution, it is 409 preferable to generate RII values and their 95% CI using the Poisson regression and, alternatively, negative 410 binomial regression. 411 Model R3 was based on the Poisson regression, which is commonly used in epidemiology to analyze health 412 outcomes in Poisson counts. In the present study, the model was as follows: 413 , 414 where X and correspond to the values in model R1, and A and b are the parameters of Poisson regression. Then, 415 RII = exp(b). In this context, the model R3 is equivalent to the model R1, and the RII meaning is the same. 416 Model R4 was based on the Poisson regression for the proportion of high LS. This model is an analog of the 417 model R3 for a binary variable: Y = 0 (low LS), Y = 1 (high LS). 418 Models R5 and R6 were based on the negative binomial regression for the mean value of the LS score and 419 for the proportion of a high LS. Similarly, to the models R3 and R4, the same estimations were computed. 420 Model R7 was based on the ordinal logistic regression for LS score, which estimates the association between 421 the odd of the ordinal LS score y and continuous X value: 422 423 where P(y>i) and P(y≤i) (i = 0, 1, ..., 9) denote the probability of the LS greater than i scores and probability of 424 the LS score equal or lower i scores, correspondingly, and X represents family affluence in the scale of FAS 425 cumulative distribution. A measure of health inequality derived by this model is OR = exp (c). A positive c value 426 (or OR > 1) predicts the amount of increase in ratio P(y>i)/P(y≤i) while family affluence changes from the extreme 427 lowest level (at X = 0) to the extreme highest level (at X = 1). 428 Model R8 was based on the binary logistic regression for the high LS group. The model estimates the 429 association between continuous X value and binary LS: Y = 0 (low LS), Y = 1 (high LS). A measure of health 430 inequality derived from this model is OR = exp (B), where B is the coefficient for X in the binary logistic regression 431 equation. 432 All regression-based measures were calculated using the SPSS Generalized Linear Models procedure, using 433 the model goodness of fit by a deviance (value/df). In order to adopt Poisson and negative binomial distributions 434 the procedure was run with the inverse LS score (z=10 – y, or Z = 0 (high LS) and Z = 1 (low LS)) as a response 435 variable and the transformation 1 – Xi as a covariate. The sampling variability estimations were obtained from the 436 procedure. 437 The aggregate measures of dissimilarity of distributions were alternatives to the regression-based measures. 438 Model A1. The Health Concentration Index (HCI), or Concentration Index, has been widely used as a measure 439 of income-related health inequality (Wagstaff et al. 1991; Regidor 2004b; Spinakis et al. 2011; Alonge and Peters 440 2015). The HCI is based on the concentration curve (as well as the the Gini coefficient is based on Lorenz curve). 441 The concentration curve plots the cumulative proportion of the population, value X as defined above, along the 442 horizontal axis against the cumulative proportion of binary health measure (high life satisfaction) along the vertical 443 axis. HCI is defined as twice the net area between the concentration curve and the diagonal (45o) line of equity. It 444 is computed using the following formula: 445 , (3) 446 where A denotes the net area between the concentration curve and the diagonal, AUC denotes the area under 447 the concentration curve, yi is the cumulative proportion of the binary health measure in the ith FAS group, xi is the 448 cumulative proportion of the population in the ith FAS group, and g is the number of FAS groups. Note that x0 = 449 0 and y0 = 0. 450 )2/()2( SIIySIIyRII  y bXAy ln y , )( )( ln cXC iyP iyP i   2/))((21AUC21)AUC2/1(22 1 011      g iiiii yyxxAHCI 15 Table 4 Average value of different measures of social inequality in adolescent life satisfaction in the total 608 sample and in selected countries 609 Model and measure Average value in the total sample Average value in selected countries 3 countries with the lowest average value 3 countries with the highest average value R1 SII of linear regression for the LS score 0.703 0.058 Malta 0.319 Netherlands 0.322 Belgium (Fl.) 1.452 Hungary 1.091 Luxembourg 1.076 Israel R1 RII of linear regression for the LS score 1.327 1.022 Malta 1.111 Belgium (Fl.) 1.140 Netherlands 1.795 Hungary 1.665 Rep. of Moldova 1.664 Israel R2 SII of linear regression for the binary LS 11.139 3.705 Albania 4.489 Netherlands 5.322 Malta 24.323 Hungary 19.173 Portugal 17.077 Poland R2 RII of linear regression for the binary LS 2.055 1.347 Malta 1.361 Belgium (Fl.) 1.517 Netherlands 5.974 Hungary 3.862 Israel 3.641 Rep. of Moldova R3 RII of Poisson regression for the LS score 1.343 1.024 Malta 1.116 Belgium (Fl.) 1.149 Netherlands 1.812 Hungary 1.735 Rep. of Moldova 1.700 Israel R4 RII of Poisson regression for the binary LS 2.208 1.407 Belgium (Fl.) 1.478 Malta 1.645 Finland 4.964 Hungary 4.072 Rep. of Moldova 3.707 Israel R5 RII of negative binomial regression for the LS score 1,345 1.029 Malta 1.113 Belgium (Fl.) 1.139 Netherlands 1.830 Hungary 1.734 Rep. of Moldova 1.679 Israel R6 RII of negative binomial regression for the binary LS 2.203 1.399 Belgium (Fl.) 1.510 Malta 1.637 Netherlands 4.923 Hungary 4.042 Rep. of Moldova 3.642 Israel R7 OR of ordinal logistic regression for the LS score 1.949 0.997 Malta 1.323 Belgium (Fl.) 1.346 Netherlands 4.077 Hungary 2.788 Latvia 2.668 Ukraine R8 OR of logistic regression for the binary LS 2.573 1.540 Belgium (Fl.) 1.606 Malta 1.771 Finland 6.944 Hungary 4.701 Rep. of Moldova 4.595 Israel A1 Health Concentration Index (HCI) 0.066 -0.002 Albania 0.030 Greenland 0.036 Romania 0.112 Ireland 0.106 Israel 0.098 Poland A2 Difference in averages of midpoints 0.074 0.035 Belgium (Fl.) 0.038 Malta 0.046 Netherlands 0.148 Hungary 0.118 Rep. of Moldova 0.118 Israel A3 Loss of positive cases (high LS) 6.273 -0.003 Croatia 1.738 Finland 1.770 Czech Republic 20.028 Rep. of Moldova 16.651 Ukraine 13.880 Poland A4 Difference in LS score between the lowest 20% and highest 20% of FAS score 0.548 0.050 Malta 0.157 Belgium (Fl.) 0.235 Netherlands 1.227 Hungary 0.883 Slovakia 0.868 Israel A5 Difference in proportion of high LS between the highest 8.918 1.375 Albania 2.807 Malta 20.797 Hungary 15.008 Slovakia 16 20% and lowest 20% of FAS score 3.558 Netherlands 14.782 Portugal 610 611 17 Table 5 Spearman correlation between measures of social inequality in adolescent life satisfaction and several 612 socioeconomic indices: country level estimations 613 Model and measure Gini coefficient Gross National Income Human Development Index Overall Life Satisfaction R1 SII of linear regression for the LS score 0.142 – 0.447** – 0.437** – 0.345* R1 RII of linear regression for the LS score 0.119 – 0.519** – 0.500** – 0.408** R2 SII of linear regression for the binary LS 0.210 – 0.215 – 0.189 – 0.180 R2 RII of linear regression for the binary LS 0.122 – 0.188 – 0.166 – 0.104 R3 RII of Poisson regression for the LS score 0.100 – 0.516** – 0.495** – 0.404** R4 RII of Poisson regression for the binary LS 0.127 – 0.185 – 0.160 – 0.124 R5 RII of negative binomial regression for the LS score 0.090 – 0.511** – 0.490** – 0.398* R6 RII of negative binomial regression for the binary LS 0.133 – 0.172 – 0.148 – 0.109 R7 OR of ordinal logistic regression for the LS score 0.119 – 0.521** – 0.480** – 0.407** R8 OR of logistic regression for the binary LS 0.122 – 0.186 – 0.165 – 0.118 A1 Health Concentration Index 0.174 0.169 0.228 0.179 A2 Difference in averages of midpoints 0.123 – 0.209 – 0.188 – 0.137 A3 Loss of positive cases (high LS) 0.093 – 0.472** – 0.427** – 0.338* A4 Difference in LS score between the lowest 20% and highest 20% of FAS score 0.123 – 0.370* – 0.309 – 0.250 A5 Difference in proportion of high LS between the highest 20% and lowest 20% of FAS score 0.184 – 0.122 – 0.084 – 0.140 * p ≤ 0.05; ** p ≤ 0.01. 614 615 616 617 Fig. 1 Distribution of life satisfaction score in the total sample. 0 1 2 3 4 5 6 7 8 9 10 Life satisfaction score 0 5 10 15 20 25 % Figure Click here to download Figure Measuring inequality 22AUG2017 Figure.docx Attachment to Manuscript Click here to access/download Attachment to Manuscript Online Resource 1.xls