Table 2.

Assessment of potential biases in calculation of population attributable fractions (PAFs)

	Source of potential bias	Direction	Magnitude	Notes
1	BMI treated as categorical rather than continuous data	Unclear	Small	The ‘proportional shift’ method (the use of categorical rather than continuous data in the calculation of attributable fractions) has been shown to be associated with the potential for both underestimation and overestimation of effect size. However, the greater the number of categories, the lower the risk of such uncertainty:42 we employ a relatively large number (six) of BMI categories.
2	Declining survey response rates	Underestimation of obesity effect	Unclear	Both surveys are large and deemed nationally representative, and both are weighted to adjust for non-response: however, in the case of the English survey, this weighting was only introduced in 2003, and therefore was not applied to the 1995 data; furthermore, despite the use of such weights, the data may still be potentially affected by a ‘healthy respondent’ bias.43 The latter, however, is difficult to quantify.
3	Broad age bands with potential for residual confounding	Overestimation of obesity effect	Unclear	Some of the change in BMI between the two time periods will be due to ageing, and this may not be captured because of the large age bands employed.
4	Exclusion of those aged 16–34 and 90+ years	Underestimation of obesity effect	Small	The exclusion of these sections of the adult population would suggest potential underestimation of effect size, especially given that overweight and obesity levels increased among both age groups between 1995 and 2008.44 However, the level of underestimation is likely to be small, given the relatively small number of deaths that occur in the younger age group overall, and the likely number of deaths from relevant causes for those aged 90 and above. Furthermore, sensitivity analyses using HRs approximated from the Bhaskaran et al study32 which covered both age groups (the age bands used were 16–49, 50–69, 70–79 and 80+ years) suggested fewer deaths were attributable to the change in BMI than was the case using the HRs for 35–89-year olds only. The calculated PAF for the 80+ years group was also very small in those analyses (eg, 0.004 for English data).
5	HRs not generalisable to Scotland and England	Overestimation of obesity effect	Small	The HRs used in the analyses (from the work published by the Global BMI Mortality Collaboration (GBMC)) were calculated from a meta-analysis of 89 European studies, a considerable number of which were from the UK.23 Assuming no effect modification from country/study-specific context, the HRs should be appropriate for use in our analyses of UK data, despite the higher levels of overweight and obesity observed in the UK. However, sensitivity analyses using alternative HRs approximated from the study by Bhaskaran et al,32 which were calculated from data for over 3.5 million adults in England (and based on c.18-year follow-up), resulted in smaller PAFs and therefore fewer deaths attributable to BMI changes over time in England, suggesting that the use of the GBMC HRs may have slightly overestimated the effect size.
6	HRs prone to confounding	Overestimation of obesity effect	Unclear	HRs from the GBMC study are not adjusted for socioeconomic deprivation, levels of physical activity or diet and thus represent a likely overestimation of effect size, although one that is difficult to quantify.
7	Changes in BMI due to pre-existing ill-health	Overestimation of obesity effect	Negligible	By excluding smokers and ex-smokers, those with chronic disease at time of recruitment, and participants who died within the first 5 years of follow-up, the GBMC study (the HRs from which are used here) largely removed this risk.
8	Interpolated data for age 65–89 years in 1995 Scottish survey data	Unclear	Unclear	Analyses comparing the estimated figure for 1995 with observed trend data in other years of the survey do not suggest any obvious inaccuracies, and there are no other data from other Scottish surveys that can be compared. However, the PAF for the 70–89 years age group is negative in the Scottish data (−0.008), but positive in the English data (0.028) which contrasts with the other two age groups where the PAFs are very similar in the two data sets. The extent to which this may relate to the interpolation is unknown.
9	Use of single-year comparison time points in calculation of PAFs	Unclear	Small	Sensitivity analyses using 3-year averages (1994–1996 instead of 1995, and 2007–2009 instead of 2008) suggest a minimal impact.
10	Lengthy follow-up period	Overestimation of obesity effect	Unclear	The potential for overestimation of effect size has been highlighted for studies with long follow-up periods on the basis that important ‘mediators’ (eg, systolic blood pressure, cholesterol) may decrease over time among those with initially recorded high BMI.33 45 It is unclear whether—or to what extent—this may apply here.

BMI, Body Mass Index.