The classical twin study compares similarity between monozygotic (MZ) twins with that of dizygotic (DZ) twins and is used to study the relative importance of genetic and environmental factors on a phenotype [12,13]. Another type of twin study is the co-twin control study where influences of environmental factors are studied among twins discordant for a trait [12,13], i.e. a matched case-control study. The strength of this type of study is the ability to control for socioeconomic factors, maternal and paternal age and environmental exposure in childhood. This type of design is thus more powerful to study independent effects than conventional case-control studies [12,13]. These studies may be based on MZ twins only, to account fully for genetic effects, but in our case we have included DZ twins also. The Danish Twin Registry (DTR) is the oldest population based twin register in the world and among the largest [14,15]. These twins have been found to be representative of the general population in Denmark with regard to many diseases and mortality [16,17].

A questionnaire on health and health related behavior was sent by mail to 46,418 twin individuals who were aged 20 - 71 years in 2002. After one reminder, 34,944 individuals (75.3%) had returned the questionnaire and from these data BMI was calculated based on self-reported height and weight.

The pairs discordant for BMI, i.e. one twin having a BMI > 30 kg/m² (obesity) and the other twin a BMI between 20 and 25 kg/m² (normal), were selected. Furthermore, twins in a pair should be of the same sex and their age in 2002 should not exceed 50 years. A total of 146 complete twin pairs fulfilled these criteria in 2006. Three subjects could not be contacted resulting in 143 complete pairs and 3 single persons, i.e. 289 twin individuals. These subjects were invited to participate in a structured interview and a physical examination which took place in their home or in a nearby nursing school in 2006 [18]. All were interviewed without any relatives, including the co-twin, being present and by the same interviewer. The structured interview consisted of a total of 145 questions from validated questionnaires [8,19-25].

The twins who would report being overweight before starting school and those who did not answer the questions on bullying would be excluded from further analysis with their co-twins.

The questionnaires dealt with various health related topics including mental and physical problems, the perception of stress, experiences of having been bullied in childhood, growth and height history, eating habits, perception of body shape and of parental care and neglect [8,19-25]. Having been a victim of bullying in school was assessed by means of the Olweus Bully/Victim Questionnaire (OBVQ) which has been used in a number of previous studies [26-28]. In 2006, a study demonstrated that the OBVQ instrument had satisfactory psychometric properties; including construct validity and reliability [28]. The OBVQ questionnaire comprises a total of 40 questions about social relations in school, including bullying and teasing [29]. We used the reduced version consisting of 13 questions (Table 1) since the twins had to recall their school experiences many years earlier [29].

For questions 1 - 11 the answer options consisted of 5 categories: Question one offered possibilities for answering from “Very bad” to “Very well”. Question two offered possibilities for answering from “No good friends” to “More than 5 good friends” and questions 3 - 11 offered possibilities for answering from: “No, I was not bullied” to “It happened several times a week”. For those who remembered never having been bullied the questionnaire stopped with question three. Answer options for question 12 was “Yes” or “No”, whereas for question 13 the possibilities were “No contact”, “Contact once” and “Contact several times” [29].

Only few individuals gave answers in the extreme categories and therefore the answer categories I-II and IIIV were subsequently merged for question 1, whereas answer categories I-III and IV-V were merged for question 2. For questions 3 - 10 answer categories II-V were merged, for question 11 answer categories I-II, and III-V and for question 13 answer categories II-III were merged.

The height and weight questionnaire was developed and used by the Finnish Twin Register and was used with permission from Professor Jaakko Kaprio.

The twin individuals were asked to report how their height and weight had developed during childhood compared to that of their co-twin and of peers.

The questions were covering the age groups: 0 - 6 years (before school age as Danish children start school at the age of six), 7 - 12 years, 13 - 16 years, 17 - 19 years, 20 - 23 years, last year, and finally the past six months.

The answer possibilities for height of co-twin and peers were: higher, similar or lower than co-twin/peers, and for the weights lighter, similar, a little more over-

weight or more overweight than the co-twin, or others at the same age.

The twin individuals were also asked to remember their weights in kg at ages 18, 20, 25, 30, 35, 40, 45 and 50 years up to the present age.

Physical measurements of height and weight were taken with the participants wearing light indoor clothes and no shoes [30]. The same standard folding ruler and bathroom scale were used throughout the study. Height was measured in meters with two decimals and weight measured in kilograms with one decimal by the same investigator.

From the answers to the questions about weight at different ages during adulthood and the weight measured in 2006 we calculated BMI from the age of 20 and with 5 years of intervals up until present age, while using the same height measurement taken in 2006. Since height does not change much from the age of 20 until the midfifties, this was considered a valid method [30,31].

The study was approved by the Scientific-Ethical Committee of Vejle and Funen Counties (J nr VF- 20030155). Each participant was guaranteed anonymity with regard to publication and they were guaranteed that nothing being said in the interview would be disclosed to the cotwin.

This design utilized the complete twin pairs who participated (n = 109) only and not the singletons (n = 18). Twin pairs, who reported to having been discordant for weight already when starting school, were also excluded from further analysis.

In the intra-pair analysis we tested if the twin, who was bullied in school (considered to be the “case”) had a higher probability of being the heaviest compared to the twin who was not bullied in school (considered to be the “control”). We also tested whether the probability increased with higher intra-pair differences in BMI.

The growth-curve model analyses the association between BMI from age 20 and the answers to the 13 questions about bullying using Wald test and a mixed-effects linear regression model. Each question was analyzed separately and adjustments were subsequently made for age and sex, allowing for a random intercept and a random slope.

By these procedures, unbiased standard errors, regression coefficients and p-values were derived [32]. A hierarchical model was also applied to test if the twin design had a significant influence on the growth in BMI.

The statistical analysis was carried out using Stata 9.2 (StataCorp, 2007). For the analysis of the intra-pair twin comparison the ptrend command in STATA was used. Finally the growth-curve model was analyzed by use of the xtmixed command, which allows for individuals having a random intercept and a random slope.