What is health? Contrary to simplistic notions of its being defined as the absence of disease, it is now increasingly understood that most outcomes of public health significance are continuous in nature (Keyes and Galea, 2016). This applies to both physical and mental health outcomes (Plomin et al., 2009; Keyes, 2002). The use of binary endpoints, while having utility in clinical applications, should not hinder investigation of the influences of health outcomes which are ultimately continuous. Further, analysing the determinants of health using continuous rather than binary outcomes is beneficial both practically (with more statistical power and less information loss) and substantively (greater aetiological understanding). Indeed, those at high risk of a developing an illness may comprise a minority of those who ultimately succumb (Rose, 2001).

Studies into the effect on continuous outcomes of exposures, be they risk factors in observational studies or interventions in randomised trials, typically focus on mean differences in the outcome, using linear regression. However linear regression assumes homoscedasticity, that is that the variability of the outcome is unrelated to the exposure, and often this is not the case. It is possible to extend regression analysis to model the variability as well as the mean, and this has benefits in terms of not only the model’s fit but also its interpretation. If for example the intervention in a trial can be shown to reduce variability in the outcome, this could reasonably be viewed as evidence of intervention success (Subramanian et al., 2018) independent of the intervention’s effect on the mean. Treatment for refractive vision errors—glasses, contact lenses, and/or corrective surgery—seeks to improve vision by shifting individuals towards a specified standard (e.g. 20/20 vision) (Vitale et al., 2006). Successful treatments alter the mean refraction, but they are even more successful if they also reduce the substantial variability in refraction arising from the mix of short- and long-sighted individuals.

Similarly, obesity interventions aim to reduce body mass index (BMI) and shift treated individuals from overweight (25–30 kg/m²), obese ( > 30 kg/m²), or severely obese ( > 45 kg/m²) to the normal range (20–25 kg/m²). However, here the effect of the intervention on variability is often to increase it. Even if not formally tested, visual comparisons of outcome distributions of some influential trials suggest that weight loss interventions increase rather than reduce BMI variability, (Truby et al., 2006) presumably since they are effective in some but not all participants.

Understanding if and how risk factors influence variability in health outcomes has aetiological significance, consistent with the goal of epidemiological science to understand the distribution of health (Porta, 2008). Risk factors could feasibly affect outcome variability yet not affect the mean—for example, one study found that breastfeeding was not related to mean childhood BMI, yet was related to lower childhood BMI variability (Beyerlein et al., 2008b). Similarly, sex may affect variability and/or average levels of an outcome—for instance, males may have greater variability than females in some cognitive traits (Hyde, 2014) and brain structures (Wierenga et al., 2022).

Identifying associations between risk factors and outcome variability may also be useful to identify the absence or presence of heterogeneity in susceptibility to interventions or risk factors and thus aid aetiological understanding. Indeed, the finding that substantial increases in mean BMI in recent decades have been matched by increases in BMI variability indicates that there may be differential susceptibility to the obesogenic environment (Flegal and Troiano, 2000; Johnson et al., 2015). In the context of randomised controlled trials, the finding of variability in treatment effects between individuals has been used to justify individualised approaches to treatment (personalised medicine). Reflecting the challenges of empirically testing this, however, five separate meta-analyses have tested heterogeneity in response to antidepressant therapy; despite using the same dataset, different methods and divergent conclusions were drawn (Luedtke and Kessler, 2021).

Another advantage of modelling varability arises in common situations where the outcome under study is non-linearly related to other outcomes of interest. For instance, BMI influences mortality and morbidity rates, but the relationship between BMI and mortality is thought to be J-shaped ( Bhaskaran et al., 2018) compared with those in the normal range, mortality risks are greater for those who are under- or overweight. In this case, the total effect of an intervention to reduce BMI on these wider outcomes is not fully captured by its average BMI effect. Rather, understanding the total distributional effect on BMI is required.

Figure 1 shows three hypothetical scenarios for an intervention to affect the distribution of an outcome. In the first case (Panel A), the intervention has an impact that is consistent across the population: all individuals are affected and to the same extent. In the second case (Panel B), the intervention has the same mean impact, but variability is also increased: some are positively affected, others negatively. In the third case (Panel C), the mean is again increased, but so is skewness. There is heterogeneity in response, with some seeing more positive responses than others. The policy implications may be different in each case. In the second and third scenarios, efforts could be directed to identify those who are (more) positively impacted, so as to increase the net benefit or cost-effectiveness of the intervention. Indeed, in a choice between interventions, an intervention generating lower expected benefits but smaller variability in outcomes may be chosen, in so far as reducing inequalities is seen as a policy goal in itself.

Figure 1

Download asset Open asset

Recent studies in biological (Sun et al., 2020; Nakagawa et al., 2014), environmental (Pitt et al., 2020), and economic science (Hohberg et al., 2020; Silbersdorff and Schneider, 2019; Silbersdorff et al., 2018) have begun to examine how risk factors relate to the distribution of the outcome of interest. However, there have been few epidemiological applications of this approach to date; (Beyerlein et al., 2008a) and fewer still that provide explanations for such findings, which are essential if such methods are to have utility. Indeed, one recent study which investigated the association between mental health symptoms and lower income explicitly avoided interpretation of its findings on variability, focusing instead on issues relating to the application of such methods (Silbersdorff and Schneider, 2019).

Regression methods that allow variability to be modelled are uncommon. One particular method, Generalised Additive Models for Location, Scale and Shape (GAMLSS) (Rigby and Stasinopoulos, 2005) has become the standard for constructing growth reference centiles, (Cole et al., 2009) where the aim is to model the outcome’s distribution as a function of age. It defines the distribution in terms of distribution moments, i.e. the mean, variance, and optionally skewness and kurtosis. This allows for factors influencing the higher moments to be identified in just the same way as for the mean, and it provides a simple and elegant interface for modelling variability in epidemiology.

Another arguably underutilised (Beyerlein, 2014) and related statistical approach to investigating risk factors for continuous outcomes is quantile regression. Recent epidemiological studies using this method have found that risk factors for higher BMI—particularly lower social class and physical inactivity—have sizably larger effect sizes at higher BMI centiles (Bann et al., 2020; Green and Rowe, 2020). This has potentially important policy implications—risk factors which have larger effects amongst those at highest health risk are likely to have a more favourable effect on population health than alternatives which do not (Bann et al., 2020). However, the reason for this phenomenon is not yet understood—it is likely to be logically consistent with results of GAMLSS analyses in which risk factors influence outcome means, variability and/or skewness.

In this paper, we provide a worked example of the use and interpretation of GAMLSS. Accompanying this is an online tutorial and full replication syntax for running GAMLSS in R (https://osf.io/5tvz6/). We investigate whether and how several established risk factors—sex, childhood socioeconomic circumstances, and physical inactivity (Stringhini et al., 2017)—relate to differences in outcome mean and variability. We choose two different continuous outcomes, an indicator of adiposity (body mass index, BMI) and mental wellbeing. These are two weakly correlated health outcomes, each of independent importance to population health. Each risk factor-outcome combination is the subject of previous (separate) literature which focuses largely on mean differences only. For instance, low socioeconomic position in childhood has been repeatedly related to higher BMI (Bann et al., 2018; Senese et al., 2009) and worse mental wellbeing in adulthood; (Wood et al., 2021; Simanek et al., 2021; Wood et al., 2017) greater physical activity has notable likely bi-directional links with lower BMI ; (Jakicic et al., 2019) and higher wellbeing; (Black et al., 2015; Choi et al., 2019; Pinto Pereira et al., 2014) while males and females seemingly have similar mean BMI and wellbeing, (Wood et al., 2017) this may mask differences in variability or skewness, as suggested in the sizable sex differences in overweight and obesity rates (Conolly et al., 2017).

The further investigation of differences in variability and skewness in these outcomes is therefore arguably of substantive interest, providing further motivation to the tutorial content. We highlight the contribution of GAMLSS by contrasting results with the more commonly used linear regression and (less commonly used) quantile regression models.

A total of 6007 participants had valid data for BMI and all risk factors, and 7104 for WEMWBS. Mean BMI was 28.4 (SD = 5.5), and mean WEMWBS 49.2 (8.3). Higher BMI was weakly associated with lower wellbeing (r = –0.07, p < 0.01). BMI was moderately right-skewed (Figure 2, left panel) and WEMWBS left-skewed (Figure 2, right panel). Visual and descriptive comparisons of the BMI and wellbeing distributions by risk factor suggest that differences in the outcome mean and variability are not always in the same direction.

Figure 2

Download asset Open asset

GAMLSS results for the binary risk factors are shown in Tables 1 and 2, with the results using the extra risk factor categories inSupplementary file 1. Associations were similar in the unadjusted and mutually adjusted analyses, so the former are described below.

Comparison with quantile regression findings

For BMI, the associations of lower social class and physical inactivity were stronger at upper quantiles (Table 3; e.g., manual social class had 3.7 (0.6) higher BMI at the the median, and 4.9 (0.7) at the 75th); estimates at higher centiles were also estimated less precisely than at lower centiles (larger SE). In contrast sex differences were present at lower centiles but absent at the 75th centile. These findings corresponded with those from GAMLSS using BCCG, with all BMI centiles plotted by risk factor group (Figure 3). This comparison highlights the utility of GAMLSS—risk factor differences in the mean, variability, and skewness can each be quantified and thus visually depicted.

Table 3

Outcome	Risk factor	25th centile	50th centile	75th centile
BMI @ Age 46	Male vs female	6.8 (0.5)	4.5 (0.6)	–0.8 (0.7)
	Father’s Class	3.7 (0.6)	3.7 (0.6)	4.9 (0.7)
	Exercise Level	1 (0.7)	3 (0.7)	4.3 (0.8)
WEMWBS @ Age 42	Sex	0 (0.7)	0 (0.5)	0 (0.3)
	Father’s Class	–4.5 (0.7)	–4 (0.5)	–1.8 (0.3)
	Exercise Level	–6.9 (0.5)	–6.1 (0.5)	–1.8 (0.5)

1. Note: results show the percentage difference (log-transformed x 100) in BMI or mental wellbeing (WEMWEBS; standard errors in parenthesis) at different centiles of the outcome distribution; estimates are mutually adjusted.

Figure 3

Download asset Open asset

For WEMWBS, the associations of lower social class and physical inactivity were also stronger at lower quantiles (Table 3), yet had larger standard errors. Sex was not associated with WEMWBS at any centile. These findings corresponded with those from GAMLSS (Figure 4).

Figure 4

Download asset Open asset

Using an underutilised analytical approach (GAMLSS), we present empirical evidence to support the idea that risk factors can relate to sizable differences in outcome variability, and even outcome skewness, in addition to differences in the outcome mean. Females had higher variability in BMI and mental wellbeing than males; lower social class and physical inactivity were each associated with higher variability in both BMI and mental wellbeing, despite having different directions of association with the mean (higher BMI yet lower mental wellbeing).

Our findings add to an emerging literature which has investigated associations between risk factors and outcome variability. Studies (Sun et al., 2020; Nakagawa et al., 2014; Pitt et al., 2020; Hohberg et al., 2020; Silbersdorff and Schneider, 2019; Silbersdorff et al., 2018; Beyerlein et al., 2008a) have reported that risk factors associated with higher means are also associated with higher outcome variability. For example, (Beyerlein et al., 2008a) found that multiple risk factors for high childhood BMI (such as more frequent television viewing and greater rapid infant weight gain) were related to both higher mean BMI and greater variability in BMI. However, previous studies have not utilised multiple outcomes or nationally representative samples, and have not systematically considered explanations for such findings or their implications.

Our findings help to reconcile findings from GAMLSS with those using quantile regression (Beyerlein et al., 2008a; Bann et al., 2020; Green and Rowe, 2020) which have reported stronger effect sizes for BMI risk factors at higher BMI centiles. This finding is both consistent with and helps explain the GAMLSS findings. For instance, lower social class and physical inactivity are related to higher BMI mean and variability, yet less BMI skewness; the net result is higher effect estimates at upper centiles which are less precisely estimated, as seen in quantile regression. While both analytical approaches have merit, GAMLSS has a number of attractive features for use in aetiological research: it enables each distribution moment to be separately investigated, and uses predetermined distribution families which enable computation of sparsely distributed variables.

Why are risk factors associated with differences in outcome variability? There are multiple possible explanations. First, risk factors may not be sufficient for an outcome to occur but rather only have a causal effect in the presence of other factors, for instance as posited in models such as the stress-diathesis model of mental health (Zuckerman, 1999). Such additional factors could also operate as effect modifiers which increase the strength of the risk factor. Factors such as genetic propensity to weight gain may for example modify the effect on weight gain of exposure to adverse socioeconomic circumstances (Tyrrell et al., 2017). Other environmental factors could operate similarly—such that the association between lower social class and higher BMI is weaker amongst those living in a local environment which is less ‘obesogenic’ (i.e. less conducive to physical inactivity and lower energy intake) (Drewnowski et al., 2007; Stafford et al., 2007). The net result of such divergent effects would be increased variability since the effects would range from zero to the upper bound of the effect. This explanation may also apply to mental wellbeing, given evidence for the myriad environmental (Ludwig et al., 2012; Wood et al., 2021) and genetic determinants (Luciano et al., 2018; de Moor et al., 2015) which could modify the effects observed in the current study.

Alternatively, between-person differences in confounding and/or measurement error may also lead to risk factors being associated with outcome variability. For example, in the present study physical activity was measured via a single item capturing reported activity of a moderate-vigorous intensity for at least 30 min per day; this is an imperfect reflection of the underlying exposure which may have a causal effect (e.g. total energy expenditure [across all intensities of activity] in the case of adiposity; (Bann et al., 2014) or time spent in specific activities conducive to wellbeing in the case of mental wellbeing [Black et al., 2015]). The net result would be higher variability in those reporting higher physical activity levels. A related issue is the extent to which the exposure captures the same ‘dose’ across participants in a given study. The physical activity measure used here counted the number of days that bouts of activity lasted at least 30 min; this likely reflects substantial variability in the level of exercise actually undertaken, thus leading to greater differences in outcome variability. This could partly explain the associations of lower social class with greater outcome variability, since social class is one dimension of socioeconomic position, such that there may be substantial between-person variation in other dimensions (e.g. parental education, income and/or wealth [Moulton et al., 2021; Galobardes et al., 2006]) which may each influence outcomes, leading to greater variability.

The study highlights the fact that analyses by GAMLSS and quantile regression lead to similar results at the selected quantiles of the outcome distribution—see Figures 3 and 4. However GAMLSS, by analysing the whole distribution, can in some cases provide more efficient estimates of the quantiles. Compare for example the standard errors of the median as obtained by the BCCG distribution (Tables 2 and 3) and quantile regression (Table 3); the GAMLSS standard errors are smaller.

All data are available to download from the UK Data Archive: https://beta.ukdataservice.ac.uk/datacatalogue/series/series?id=200001.

1. 1. Bann D
   2. Kuh D
   3. Wills AK
   4. Adams J
   5. Brage S
   6. Cooper R
   7. National Survey of Health and Development scientific and data collection team

   (2014) Physical activity across adulthood in relation to fat and lean body mass in early old age: findings from the Medical Research Council National Survey of Health and Development, 1946-2010

   American Journal of Epidemiology 179:1197–1207.

   https://doi.org/10.1093/aje/kwu033

   • PubMed
   • Google Scholar
2. 1. Bann D
   2. Johnson W
   3. Li L
   4. Kuh D
   5. Hardy R

   (2018) Socioeconomic inequalities in childhood and adolescent body-mass index, weight, and height from 1953 to 2015: an analysis of four longitudinal, observational, British birth cohort studies

   The Lancet. Public Health 3:e194–e203.

   https://doi.org/10.1016/S2468-2667(18)30045-8

   • PubMed
   • Google Scholar
3. 1. Bann D
   2. Fitzsimons E
   3. Johnson W

   (2020) Determinants of the population health distribution: an illustration examining body mass index

   International Journal of Epidemiology 49:731–737.

   https://doi.org/10.1093/ije/dyz245

   • PubMed
   • Google Scholar
4. 1. Barone Gibbs B
   2. Aaby D
   3. Siddique J
   4. Reis JP
   5. Sternfeld B
   6. Whitaker K
   7. Pettee Gabriel K

   (2020) Bidirectional 10-year associations of accelerometer-measured sedentary behavior and activity categories with weight among middle-aged adults

   International Journal of Obesity 44:559–567.

   https://doi.org/10.1038/s41366-019-0443-8

   • PubMed
   • Google Scholar
5. 1. Beyerlein A
   2. Fahrmeir L
   3. Mansmann U
   4. Toschke AM

   (2008a) Alternative regression models to assess increase in childhood BMI

   BMC Medical Research Methodology 8:59.

   https://doi.org/10.1186/1471-2288-8-59

   • PubMed
   • Google Scholar
6. 1. Beyerlein A
   2. Toschke AM
   3. von Kries R

   (2008b) Breastfeeding and childhood obesity: shift of the entire BMI distribution or only the upper parts?

   Obesity 16:2730–2733.

   https://doi.org/10.1038/oby.2008.432

   • PubMed
   • Google Scholar
7. 1. Beyerlein A

   (2014) Quantile regression-opportunities and challenges from a user’s perspective

   American Journal of Epidemiology 180:330–331.

   https://doi.org/10.1093/aje/kwu178

   • PubMed
   • Google Scholar
8. 1. Bhaskaran K
   2. Dos-Santos-Silva I
   3. Leon DA
   4. Douglas IJ
   5. Smeeth L

   (2018) Association of BMI with overall and cause-specific mortality: a population-based cohort study of 3·6 million adults in the UK

   The Lancet. Diabetes & Endocrinology 6:944–953.

   https://doi.org/10.1016/S2213-8587(18)30288-2

   • PubMed
   • Google Scholar
9. 1. Black SV
   2. Cooper R
   3. Martin KR
   4. Brage S
   5. Kuh D
   6. Stafford M

   (2015) Physical Activity and Mental Well-being in a Cohort Aged 60-64 Years

   American Journal of Preventive Medicine 49:172–180.

   https://doi.org/10.1016/j.amepre.2015.03.009

   • PubMed
   • Google Scholar
10. 1. Choi KW
    2. Chen CY
    3. Stein MB
    4. Klimentidis YC
    5. Wang MJ
    6. Koenen KC
    7. Smoller JW
    8. Major Depressive Disorder Working Group of the Psychiatric Genomics Consortium

    (2019) Assessment of Bidirectional Relationships Between Physical Activity and Depression Among Adults: A 2-Sample Mendelian Randomization Study

    JAMA Psychiatry 76:399–408.

    https://doi.org/10.1001/jamapsychiatry.2018.4175

    • PubMed
    • Google Scholar
11. 1. Cole TJ
    2. Stanojevic S
    3. Stocks J
    4. Coates AL
    5. Hankinson JL
    6. Wade AM

    (2009) Age- and size-related reference ranges: a case study of spirometry through childhood and adulthood

    Statistics in Medicine 28:880–898.

    https://doi.org/10.1002/sim.3504

    • PubMed
    • Google Scholar
12. Report

    1. Conolly A
    2. Saunders C
    3. Neave A

    (2017)

    Health Survey for England 2016: Adult overweight and obesity

    Health and Social Care Information Centre.

    • Google Scholar
13. 1. Davey Smith G

    (2011) Epidemiology, epigenetics and the “Gloomy Prospect”: embracing randomness in population health research and practice

    International Journal of Epidemiology 40:537–562.

    https://doi.org/10.1093/ije/dyr117

    • PubMed
    • Google Scholar
14. 1. de Moor MHM
    2. van den Berg SM
    3. Verweij KJH
    4. Krueger RF
    5. Luciano M
    6. Arias Vasquez A
    7. Matteson LK
    8. Derringer J
    9. Esko T
    10. Amin N
    11. Gordon SD
    12. Hansell NK
    13. Hart AB
    14. Seppälä I
    15. Huffman JE
    16. Konte B
    17. Lahti J
    18. Lee M
    19. Miller M
    20. Nutile T
    21. Tanaka T
    22. Teumer A
    23. Viktorin A
    24. Wedenoja J
    25. Abecasis GR
    26. Adkins DE
    27. Agrawal A
    28. Allik J
    29. Appel K
    30. Bigdeli TB
    31. Busonero F
    32. Campbell H
    33. Costa PT
    34. Davey Smith G
    35. Davies G
    36. de Wit H
    37. Ding J
    38. Engelhardt BE
    39. Eriksson JG
    40. Fedko IO
    41. Ferrucci L
    42. Franke B
    43. Giegling I
    44. Grucza R
    45. Hartmann AM
    46. Heath AC
    47. Heinonen K
    48. Henders AK
    49. Homuth G
    50. Hottenga JJ
    51. Iacono WG
    52. Janzing J
    53. Jokela M
    54. Karlsson R
    55. Kemp JP
    56. Kirkpatrick MG
    57. Latvala A
    58. Lehtimäki T
    59. Liewald DC
    60. Madden PAF
    61. Magri C
    62. Magnusson PKE
    63. Marten J
    64. Maschio A
    65. Medland SE
    66. Mihailov E
    67. Milaneschi Y
    68. Montgomery GW
    69. Nauck M
    70. Ouwens KG
    71. Palotie A
    72. Pettersson E
    73. Polasek O
    74. Qian Y
    75. Pulkki-Råback L
    76. Raitakari OT
    77. Realo A
    78. Rose RJ
    79. Ruggiero D
    80. Schmidt CO
    81. Slutske WS
    82. Sorice R
    83. Starr JM
    84. St Pourcain B
    85. Sutin AR
    86. Timpson NJ
    87. Trochet H
    88. Vermeulen S
    89. Vuoksimaa E
    90. Widen E
    91. Wouda J
    92. Wright MJ
    93. Zgaga L
    94. Porteous D
    95. Minelli A
    96. Palmer AA
    97. Rujescu D
    98. Ciullo M
    99. Hayward C
    100. Rudan I
    101. Metspalu A
    102. Kaprio J
    103. Deary IJ
    104. Räikkönen K
    105. Wilson JF
    106. Keltikangas-Järvinen L
    107. Bierut LJ
    108. Hettema JM
    109. Grabe HJ
    110. van Duijn CM
    111. Evans DM
    112. Schlessinger D
    113. Pedersen NL
    114. Terracciano A
    115. McGue M
    116. Penninx B
    117. Martin NG
    118. Boomsma DI
    119. Genetics of Personality Consortium

    (2015) Meta-analysis of Genome-wide Association Studies for Neuroticism, and the Polygenic Association With Major Depressive Disorder

    JAMA Psychiatry 72:642–650.

    https://doi.org/10.1001/jamapsychiatry.2015.0554

    • PubMed
    • Google Scholar
15. 1. Drewnowski A
    2. Rehm CD
    3. Solet D

    (2007) Disparities in obesity rates: analysis by ZIP code area

    Social Science & Medicine 65:2458–2463.

    https://doi.org/10.1016/j.socscimed.2007.07.001

    • PubMed
    • Google Scholar
16. 1. Elliott J
    2. Shepherd P

    (2006) Cohort profile: 1970 British Birth Cohort (BCS70)

    International Journal of Epidemiology 35:836–843.

    https://doi.org/10.1093/ije/dyl174

    • PubMed
    • Google Scholar
17. 1. Flegal KM
    2. Troiano RP

    (2000) Changes in the distribution of body mass index of adults and children in the US population

    International Journal of Obesity and Related Metabolic Disorders 24:807–818.

    https://doi.org/10.1038/sj.ijo.0801232

    • PubMed
    • Google Scholar
18. 1. Galobardes B
    2. Shaw M
    3. Lawlor DA
    4. Lynch JW
    5. Davey Smith G

    (2006) Indicators of socioeconomic position (part 1)

    Journal of Epidemiology and Community Health 60:7–12.

    https://doi.org/10.1136/jech.2004.023531

    • PubMed
    • Google Scholar
19. 1. Green MA
    2. Rowe F

    (2020) Explaining the widening distribution of Body Mass Index: A decomposition analysis of trends for England, 2002–2004 and 2012–2014

    Area 53:362–372.

    https://doi.org/10.1111/area.12675

    • Google Scholar
20. 1. Hohberg M
    2. Pütz P
    3. Kneib T

    (2020) Treatment effects beyond the mean using distributional regression: Methods and guidance

    PLOS ONE 15:e0226514.

    https://doi.org/10.1371/journal.pone.0226514

    • PubMed
    • Google Scholar
21. 1. Hyde JS

    (2014) Gender similarities and differences

    Annual Review of Psychology 65:373–398.

    https://doi.org/10.1146/annurev-psych-010213-115057

    • PubMed
    • Google Scholar
22. 1. Jakicic JM
    2. Powell KE
    3. Campbell WW
    4. Dipietro L
    5. Pate RR
    6. Pescatello LS
    7. Collins KA
    8. Bloodgood B
    9. Piercy KL
    10. 2018 PHYSICAL ACTIVITY GUIDELINES ADVISORY COMMITTEE*

    (2019) Physical Activity and the Prevention of Weight Gain in Adults: A Systematic Review

    Medicine and Science in Sports and Exercise 51:1262–1269.

    https://doi.org/10.1249/MSS.0000000000001938

    • PubMed
    • Google Scholar
23. 1. Johnson W
    2. Li L
    3. Kuh D
    4. Hardy R

    (2015) How Has the Age-Related Process of Overweight or Obesity Development Changed over Time? Co-ordinated Analyses of Individual Participant Data from Five United Kingdom Birth Cohorts

    PLOS Medicine 12:e1001828.

    https://doi.org/10.1371/journal.pmed.1001828

    • PubMed
    • Google Scholar
24. 1. Keyes CLM

    (2002) The Mental Health Continuum: From Languishing to Flourishing in Life

    Journal of Health and Social Behavior 43:207.

    https://doi.org/10.2307/3090197

    • Google Scholar
25. Book

    1. Keyes KM
    2. Galea S

    (2016) Population Health Science

    Oxford University Press.

    https://doi.org/10.1093/med/9780190459376.001.0001

    • Google Scholar
26. 1. Lewontin RC

    (1966) On the Measurement of Relative Variability

    Systematic Zoology 15:141.

    https://doi.org/10.2307/2411632

    • Google Scholar
27. 1. Luciano M
    2. Hagenaars SP
    3. Davies G
    4. Hill WD
    5. Clarke T-K
    6. Shirali M
    7. Harris SE
    8. Marioni RE
    9. Liewald DC
    10. Fawns-Ritchie C
    11. Adams MJ
    12. Howard DM
    13. Lewis CM
    14. Gale CR
    15. McIntosh AM
    16. Deary IJ

    (2018) Association analysis in over 329,000 individuals identifies 116 independent variants influencing neuroticism

    Nature Genetics 50:6–11.

    https://doi.org/10.1038/s41588-017-0013-8

    • PubMed
    • Google Scholar
28. 1. Ludwig J
    2. Duncan GJ
    3. Gennetian LA
    4. Katz LF
    5. Kessler RC
    6. Kling JR
    7. Sanbonmatsu L

    (2012) Neighborhood effects on the long-term well-being of low-income adults

    Science 337:1505–1510.

    https://doi.org/10.1126/science.1224648

    • PubMed
    • Google Scholar
29. 1. Luedtke A
    2. Kessler RC

    (2021) New Directions in Research on Heterogeneity of Treatment Effects for Major Depression

    JAMA Psychiatry 78:478–480.

    https://doi.org/10.1001/jamapsychiatry.2020.4489

    • PubMed
    • Google Scholar
30. 1. Mostafa T
    2. Wiggins RD

    (2015) The impact of attrition and non-response in birth cohort studies: a need to incorporate missingness strategies

    Longitudinal and Life Course Studies 6:131–146.

    https://doi.org/10.14301/llcs.v6i2.312

    • Google Scholar
31. 1. Mostafa T
    2. Narayanan M
    3. Pongiglione B
    4. Dodgeon B
    5. Goodman A
    6. Silverwood RJ
    7. Ploubidis GB

    (2021) Missing at random assumption made more plausible: evidence from the 1958 British birth cohort

    Journal of Clinical Epidemiology 136:44–54.

    https://doi.org/10.1016/j.jclinepi.2021.02.019

    • PubMed
    • Google Scholar
32. 1. Moulton V
    2. Goodman A
    3. Nasim B
    4. Ploubidis GB
    5. Gambaro L

    (2021) Parental Wealth and Children’s Cognitive Ability, Mental, and Physical Health: Evidence From the UK Millennium Cohort Study

    Child Development 92:115–123.

    https://doi.org/10.1111/cdev.13413

    • PubMed
    • Google Scholar
33. 1. Munafò MR
    2. Tilling K
    3. Taylor AE
    4. Evans DM
    5. Davey Smith G

    (2018) Collider scope: when selection bias can substantially influence observed associations

    International Journal of Epidemiology 47:226–235.

    https://doi.org/10.1093/ije/dyx206

    • PubMed
    • Google Scholar
34. 1. Nakagawa S
    2. Poulin R
    3. Mengersen K
    4. Reinhold K
    5. Engqvist L
    6. Lagisz M
    7. Senior AM
    8. O’Hara RB

    (2014) Meta‐analysis of variation: ecological and evolutionary applications and beyond

    Methods in Ecology and Evolution 6:143–152.

    https://doi.org/10.1111/2041-210X.12309

    • Google Scholar
35. 1. Pinto Pereira SM
    2. Geoffroy M-C
    3. Power C

    (2014) Depressive symptoms and physical activity during 3 decades in adult life: bidirectional associations in a prospective cohort study

    JAMA Psychiatry 71:1373–1380.

    https://doi.org/10.1001/jamapsychiatry.2014.1240

    • PubMed
    • Google Scholar
36. 1. Pitt D
    2. Trück S
    3. van den Honert R
    4. Wong WW

    (2020) Modeling risks from natural hazards with generalized additive models for location, scale and shape

    Journal of Environmental Management 275:111075.

    https://doi.org/10.1016/j.jenvman.2020.111075

    • PubMed
    • Google Scholar
37. 1. Plomin R
    2. Haworth CMA
    3. Davis OSP

    (2009) Common disorders are quantitative traits

    Nature Reviews. Genetics 10:872–878.

    https://doi.org/10.1038/nrg2670

    • PubMed
    • Google Scholar
38. Book

    1. Porta M

    (2008)

    A Dictionary of Epidemiology

    Oxford, UK: Oxford University Press.

    • Google Scholar
39. 1. Rigby RA
    2. Stasinopoulos DM

    (2005) Generalized additive models for location, scale and shape (with discussion)

    Journal of the Royal Statistical Society 54:507–554.

    https://doi.org/10.1111/j.1467-9876.2005.00510.x

    • Google Scholar
40. Book

    1. Rigby RA
    2. Stasinopoulos MD
    3. Heller GZ
    4. De Bastiani F

    (2019) Distributions for Modeling Location, Scale, and Shape

    Taylor Francis Group.

    https://doi.org/10.1201/9780429298547

    • Google Scholar
41. 1. Rose G

    (2001) Sick individuals and sick populations

    International Journal of Epidemiology 30:427–432.

    https://doi.org/10.1093/ije/30.3.427

    • PubMed
    • Google Scholar
42. 1. Senese LC
    2. Almeida ND
    3. Fath AK
    4. Smith BT
    5. Loucks EB

    (2009) Associations between childhood socioeconomic position and adulthood obesity

    Epidemiologic Reviews 31:21–51.

    https://doi.org/10.1093/epirev/mxp006

    • PubMed
    • Google Scholar
43. 1. Senn S

    (2016) Mastering variation: variance components and personalised medicine

    Statistics in Medicine 35:966–977.

    https://doi.org/10.1002/sim.6739

    • PubMed
    • Google Scholar
44. 1. Silbersdorff A
    2. Lynch J
    3. Klasen S
    4. Kneib T

    (2018) Reconsidering the income-health relationship using distributional regression

    Health Economics 27:1074–1088.

    https://doi.org/10.1002/hec.3656

    • PubMed
    • Google Scholar
45. 1. Silbersdorff A
    2. Schneider KS

    (2019) Distributional Regression Techniques in Socioeconomic Research on the Inequality of Health with an Application on the Relationship between Mental Health and Income

    International Journal of Environmental Research and Public Health 16:20.

    https://doi.org/10.3390/ijerph16204009

    • PubMed
    • Google Scholar
46. 1. Simanek AM
    2. Meier HCS
    3. D’Aloisio AA
    4. Sandler DP

    (2021) Objective and subjective childhood socioeconomic disadvantage and incident depression in adulthood: a longitudinal analysis in the Sister Study

    Social Psychiatry and Psychiatric Epidemiology 56:1201–1210.

    https://doi.org/10.1007/s00127-020-02013-5

    • PubMed
    • Google Scholar
47. 1. Stafford M
    2. Cummins S
    3. Ellaway A
    4. Sacker A
    5. Wiggins RD
    6. Macintyre S

    (2007) Pathways to obesity: identifying local, modifiable determinants of physical activity and diet

    Social Science & Medicine 65:1882–1897.

    https://doi.org/10.1016/j.socscimed.2007.05.042

    • PubMed
    • Google Scholar
48. 1. Stasinopoulos DM
    2. Rigby RA

    (2007) Generalized Additive Models for Location Scale and Shape (GAMLSS) in R

    Journal of Statistical Software 23:1–46.

    https://doi.org/10.18637/jss.v023.i07

    • Google Scholar
49. 1. Stringhini S
    2. Carmeli C
    3. Jokela M
    4. Avendaño M
    5. Muennig P
    6. Guida F
    7. Ricceri F
    8. d’Errico A
    9. Barros H
    10. Bochud M
    11. Chadeau-Hyam M
    12. Clavel-Chapelon F
    13. Costa G
    14. Delpierre C
    15. Fraga S
    16. Goldberg M
    17. Giles GG
    18. Krogh V
    19. Kelly-Irving M
    20. Layte R
    21. Lasserre AM
    22. Marmot MG
    23. Preisig M
    24. Shipley MJ
    25. Vollenweider P
    26. Zins M
    27. Kawachi I
    28. Steptoe A
    29. Mackenbach JP
    30. Vineis P
    31. Kivimäki M
    32. LIFEPATH consortium

    (2017) Socioeconomic status and the 25 × 25 risk factors as determinants of premature mortality: a multicohort study and meta-analysis of 1·7 million men and women

    Lancet 389:1229–1237.

    https://doi.org/10.1016/S0140-6736(16)32380-7

    • PubMed
    • Google Scholar
50. 1. Subramanian SV
    2. Kim R
    3. Christakis NA

    (2018) The “average” treatment effect: A construct ripe for retirement. A commentary on Deaton and Cartwright

    Social Science & Medicine 210:77–82.

    https://doi.org/10.1016/j.socscimed.2018.04.027

    • PubMed
    • Google Scholar
51. 1. Sun J
    2. Covaci A
    3. Bustnes JO
    4. Jaspers VLB
    5. Helander B
    6. Bårdsen BJ
    7. Boertmann D
    8. Dietz R
    9. Labansen AL
    10. Lepoint G
    11. Schulz R
    12. Malarvannan G
    13. Sonne C
    14. Thorup K
    15. Tøttrup AP
    16. Zubrod JP
    17. Eens M
    18. Eulaers I

    (2020) Temporal trends of legacy organochlorines in different white-tailed eagle (Haliaeetus albicilla) subpopulations: A retrospective investigation using archived feathers

    Environment International 138:105618.

    https://doi.org/10.1016/j.envint.2020.105618

    • PubMed
    • Google Scholar
52. 1. Tennant R
    2. Hiller L
    3. Fishwick R
    4. Platt S
    5. Joseph S
    6. Weich S
    7. Parkinson J
    8. Secker J
    9. Stewart-Brown S

    (2007) The Warwick-Edinburgh Mental Well-being Scale (WEMWBS): development and UK validation

    Health and Quality of Life Outcomes 5:63.

    https://doi.org/10.1186/1477-7525-5-63

    • PubMed
    • Google Scholar
53. 1. Truby H
    2. Baic S
    3. deLooy A
    4. Fox KR
    5. Livingstone MBE
    6. Logan CM
    7. Macdonald IA
    8. Morgan LM
    9. Taylor MA
    10. Millward DJ

    (2006) Randomised controlled trial of four commercial weight loss programmes in the UK: initial findings from the BBC “diet trials.”

    BMJ 332:1309–1314.

    https://doi.org/10.1136/bmj.38833.411204.80

    • PubMed
    • Google Scholar
54. 1. Tyrrell J
    2. Wood AR
    3. Ames RM
    4. Yaghootkar H
    5. Beaumont RN
    6. Jones SE
    7. Tuke MA
    8. Ruth KS
    9. Freathy RM
    10. Davey Smith G
    11. Joost S
    12. Guessous I
    13. Murray A
    14. Strachan DP
    15. Kutalik Z
    16. Weedon MN
    17. Frayling TM

    (2017) Gene-obesogenic environment interactions in the UK Biobank study

    International Journal of Epidemiology 46:559–575.

    https://doi.org/10.1093/ije/dyw337

    • PubMed
    • Google Scholar
55. 1. Vitale S
    2. Cotch MF
    3. Sperduto RD

    (2006) Prevalence of visual impairment in the United States

    JAMA 295:2158–2163.

    https://doi.org/10.1001/jama.295.18.2158

    • PubMed
    • Google Scholar
56. 1. Wierenga LM
    2. Doucet GE
    3. Dima D
    4. Agartz I
    5. Aghajani M
    6. Akudjedu TN
    7. Albajes-Eizagirre A
    8. Alnaes D
    9. Alpert KI
    10. Andreassen OA
    11. Anticevic A
    12. Asherson P
    13. Banaschewski T
    14. Bargallo N
    15. Baumeister S
    16. Baur-Streubel R
    17. Bertolino A
    18. Bonvino A
    19. Boomsma DI
    20. Borgwardt S
    21. Bourque J
    22. den Braber A
    23. Brandeis D
    24. Breier A
    25. Brodaty H
    26. Brouwer RM
    27. Buitelaar JK
    28. Busatto GF
    29. Calhoun VD
    30. Canales-Rodríguez EJ
    31. Cannon DM
    32. Caseras X
    33. Castellanos FX
    34. Chaim-Avancini TM
    35. Ching CR
    36. Clark VP
    37. Conrod PJ
    38. Conzelmann A
    39. Crivello F
    40. Davey CG
    41. Dickie EW
    42. Ehrlich S
    43. Van’t Ent D
    44. Fisher SE
    45. Fouche J-P
    46. Franke B
    47. Fuentes-Claramonte P
    48. de Geus EJ
    49. Di Giorgio A
    50. Glahn DC
    51. Gotlib IH
    52. Grabe HJ
    53. Gruber O
    54. Gruner P
    55. Gur RE
    56. Gur RC
    57. Gurholt TP
    58. de Haan L
    59. Haatveit B
    60. Harrison BJ
    61. Hartman CA
    62. Hatton SN
    63. Heslenfeld DJ
    64. van den Heuvel OA
    65. Hickie IB
    66. Hoekstra PJ
    67. Hohmann S
    68. Holmes AJ
    69. Hoogman M
    70. Hosten N
    71. Howells FM
    72. Hulshoff Pol HE
    73. Huyser C
    74. Jahanshad N
    75. James AC
    76. Jiang J
    77. Jönsson EG
    78. Joska JA
    79. Kalnin AJ
    80. Klein M
    81. Koenders L
    82. Kolskår KK
    83. Krämer B
    84. Kuntsi J
    85. Lagopoulos J
    86. Lazaro L
    87. Lebedeva IS
    88. Lee PH
    89. Lochner C
    90. Machielsen MW
    91. Maingault S
    92. Martin NG
    93. Martínez-Zalacaín I
    94. Mataix-Cols D
    95. Mazoyer B
    96. McDonald BC
    97. McDonald C
    98. McIntosh AM
    99. McMahon KL
    100. McPhilemy G
    101. van der Meer D
    102. Menchón JM
    103. Naaijen J
    104. Nyberg L
    105. Oosterlaan J
    106. Paloyelis Y
    107. Pauli P
    108. Pergola G
    109. Pomarol-Clotet E
    110. Portella MJ
    111. Radua J
    112. Reif A
    113. Richard G
    114. Roffman JL
    115. Rosa PG
    116. Sacchet MD
    117. Sachdev PS
    118. Salvador R
    119. Sarró S
    120. Satterthwaite TD
    121. Saykin AJ
    122. Serpa MH
    123. Sim K
    124. Simmons A
    125. Smoller JW
    126. Sommer IE
    127. Soriano-Mas C
    128. Stein DJ
    129. Strike LT
    130. Szeszko PR
    131. Temmingh HS
    132. Thomopoulos SI
    133. Tomyshev AS
    134. Trollor JN
    135. Uhlmann A
    136. Veer IM
    137. Veltman DJ
    138. Voineskos A
    139. Völzke H
    140. Walter H
    141. Wang L
    142. Wang Y
    143. Weber B
    144. Wen W
    145. West JD
    146. Westlye LT
    147. Whalley HC
    148. Williams SC
    149. Wittfeld K
    150. Wolf DH
    151. Wright MJ
    152. Yoncheva YN
    153. Zanetti MV
    154. Ziegler GC
    155. de Zubicaray GI
    156. Thompson PM
    157. Crone EA
    158. Frangou S
    159. Tamnes CK
    160. Karolinska Schizophrenia Project (KaSP) Consortium

    (2022) Greater male than female variability in regional brain structure across the lifespan

    Human Brain Mapping 43:470–499.

    https://doi.org/10.1002/hbm.25204

    • PubMed
    • Google Scholar
57. 1. Wood N
    2. Bann D
    3. Hardy R
    4. Gale C
    5. Goodman A
    6. Crawford C
    7. Stafford M

    (2017) Childhood socioeconomic position and adult mental wellbeing: Evidence from four British birth cohort studies

    PLOS ONE 12:e0185798.

    https://doi.org/10.1371/journal.pone.0185798

    • PubMed
    • Google Scholar
58. 1. Wood N
    2. Hardy R
    3. Bann D
    4. Gale C
    5. Stafford M

    (2021) Childhood correlates of adult positive mental well-being in three British longitudinal studies

    Journal of Epidemiology and Community Health 75:177–184.

    https://doi.org/10.1136/jech-2019-213709

    • PubMed
    • Google Scholar
59. Book

    1. Zuckerman M

    (1999) Diathesis-Stress Models

    American Psychological Association.

    https://doi.org/10.1037/10316-000

    • Google Scholar

Author details

1. David Bann

   Centre for Longitudinal Studies, Social Research Institute, University College London, London, United Kingdom

   Contribution

   Conceptualization, Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Resources, Visualization, Writing - original draft, Writing - review and editing

   For correspondence

   david.bann@ucl.ac.uk

   Competing interests

   No competing interests declared

   "This ORCID iD identifies the author of this article:" 0000-0002-6454-626X

2. Liam Wright

   Centre for Longitudinal Studies, Social Research Institute, University College London, London, United Kingdom

   Contribution

   Formal analysis, Investigation, Methodology, Resources, Software, Visualization, Writing - review and editing

   Competing interests

   No competing interests declared

3. Tim J Cole

   Great Ormond Street Institute of Child Health, University College London, London, United Kingdom

   Contribution

   Conceptualization, Investigation, Methodology, Visualization, Writing - review and editing

   Competing interests

   No competing interests declared

• 1,556

  views

• 213

  downloads

• 7

  citations

Views, downloads and citations are aggregated across all versions of this paper published by eLife.