Types of studies

Randomised controlled trials with between‐subjects (parallel‐group) or within‐subjects (cross‐over) designs, conducted in laboratory or field settings. We excluded non‐randomised studies because our recent scoping review indicated that a sufficient number of eligible randomised controlled trials would be available to address our aim to synthesise evidence for intervention effects (Hollands 2013a). A key issue is that, compared with randomised controlled trials, non‐randomised studies rely on more stringent and sometimes non‐verifiable assumptions in order to confer confidence that, with successful implementation of the study design, the risk of systematic differences between comparison groups beyond the intervention of interest (i.e. confounding) is sufficiently low to permit valid inferences about causal effects.

Types of participants

Adults and children directly engaged with the manipulated products. We set no exclusion criteria in relation to demographic, socioeconomic or clinical characteristics or prognostic factors. We excluded studies involving non‐human participants (animal studies).

Types of interventions

Interventions eligible to be considered in this review were those that involved comparison of the effects of exposure to at least two sizes or sets of visible physical dimensions (that is volume, shape, height, width or depth) of either a portion of the same food (including non‐alcoholic beverages), alcohol or tobacco product, its package or individual unit size, or an item of tableware used to consume it. An eligible study could therefore include multiple eligible comparisons. For example, in a three‐arm between‐subjects study comparing the effects of exposure to a 200 g, 300 g or 400 g portion of pasta with sauce, eligible comparisons are: 200 g versus 300 g; 300 g versus 400 g; and 200 g versus 400 g (see also Data synthesis).

'Portion' refers to the overall amount (volume, weight or both) of a product that is presented for selection or consumption (for example, 200 g versus 300 g of pasta, 275 ml versus 440 ml of beer, or a packet of 10 versus 20 cigarettes). 'Package' refers to the different ways of packaging a specific portion, including that used for service, consumption or storage (for example, boxes, bags, cans or bottles). For example, the same portion of a food could be served within one large bag or multiple smaller bags. 'Individual unit' refers to the unit of a product that is presented within a given portion (for example, individual sweets or candies, biscuits or cookies, or cigarettes). 'Tableware' refers to crockery, cutlery or glassware used for serving or consuming food or drink (for example, plates, bowls, knives, forks, spoons or glasses). Packages and tableware as defined in this way have the capacity to limit or increase the portion or individual unit size of the consumed product and may therefore influence any corollary effects on selection and consumption.

We excluded the following:

• Interventions in which product size and/or shape may have been altered indirectly as a result of a higher‐level intervention but were not directly manipulated, to safeguard implementation fidelity (e.g. organisational‐level interventions to encourage the introduction of small‐scale environmental changes to alter product selection or consumption).

• Interventions in which the behavioural responses of participants (that is, selection or consumption levels or rates) were regulated by either explicit instructions to participants or some other action of the researcher (e.g. participants exposed to a product were given instructions on how much they should consume or a target rate of consumption). In such cases, selection or consumption of the manipulated product cannot be considered unregulated (ad libitum).

• Studies that compared packages, portions, individual units or tableware of different types or with different functions. For example, we excluded studies that made comparisons between different, differently sized eating utensils (e.g. straw versus spoon; chopsticks versus fork) whilst studies that made comparisons between different sizes of the same eating utensil were included (e.g. small spoon versus large spoon).

• Studies in which there were concurrent interventions unrelated to sizing that were intrinsically confounded with the comparison(s) of interest. For example, we excluded two‐arm studies in which one comparison group received a specified portion size and the other group received a smaller portion plus a concurrent nutritional labelling intervention.

Types of outcome measures

Primary outcomes

Behavioural endpoints

Eligible studies had to incorporate one or more measures of unregulated (ad libitum) consumption or selection (with or without purchasing) of food, alcohol or tobacco products. By unregulated, we refer to behaviour of participants that is not regulated by either explicit instructions or some other action of the researcher. Eligible studies may have measured consumption or selection in terms of quantities of manipulated products and/or quantities of non‐manipulated products. For example, a study investigating the effects of exposure to a large versus small portion of a pasta entrée, provided as part of a lunch meal, may have measured consumption in terms of energy intake from the entrée itself, or from a non‐manipulated vegetable side dish served with the entrée, or from the total lunch meal (that is, both manipulated and non‐manipulated components), or from all meals taken over the course of a whole day. Similarly, quantities consumed or selected may have been measured over a time period less than (immediate) or exceeding one day (longer‐term).

Our choice of eligible outcome constructs reflected a focus on the assessment of the effects of eligible interventions in terms of the types and amounts of food, alcohol and tobacco people consume, coupled with recognition that amount selected (with or without purchasing) is an important intermediate endpoint in pathways to consumption. We anticipated encountering a range of measures of these outcome constructs within included studies, and presented the following examples in the published protocol for this review.

1. Consumption (intake) of a product

We assessed the amount of energy (e.g. calories), substances (e.g. carbon monoxide, alcohol, saturated fat), or products (e.g. food, drink or tobacco) consumed, measured in applicable natural units (e.g. kcals, kilojoules, grams). Objective measurement may involve calculating the amount of a product consumed by subtracting the amount remaining after consumption from the amount presented to the participant. Alternatively, it may involve direct observation of the individual by outcome assessors. Subjective measurement would involve participant self report.

2. Selection of a product

a) Without purchase

b) With purchase

As per consumption, we assessed the amount of energy, substances or products selected for consumption, measured in applicable natural units. Depending on the study setting, a product may be selected with or without this act enjoining a purchase (that is, a transfer of money to the vendor).

Conceptual model

To supplement study eligibility criteria, we developed a provisional conceptual model that was published in the protocol for this review (Hollands 2014). This conceptual model was design‐oriented in the sense that its purpose was to help direct the review process by providing a simplified visual representation of the causal system of interest: the proposed causal pathway between eligible interventions and their outcomes (behavioural endpoints), and potential moderators of that relationship (effect modifiers) given that differential effects were plausible (Anderson 2011; Anderson 2013). We used the provisional conceptual model to inform the development of search strategies, data extraction forms and a provisional framework for the statistical analysis of outcome data collected from the eligible studies (see Search methods for identification of studies and Data collection and analysis). We iteratively revised the provisional conceptual model based on theory and evidence encountered in eligible studies during the course of the review process, and documented all revisions including the rationale for each revision and supporting evidence (see Data collection and analysis). We used the provisional and subsequent iterations of the conceptual model as a reference point for the design (in the protocol) and conduct (post‐protocol) of all stages of the systematic review up to and including data synthesis, and as a conceptual basis for explicit reporting of the methods and assumptions employed within the synthesis (Anderson 2013). In practice, iterative refinement of the conceptual model primarily involved incorporating further potential effect modifiers identified from theory and evidence presented in included study reports, which became candidates for consideration in the meta‐regression analysis (see Data collection and analysis). The final version of the conceptual model is shown Figure 1.

Figure 1

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Final conceptual model. The 28 constructs included in the provisional conceptual model (Hollands 2014) and retained in this final version are shown in plain type. The 22 constructs added to this final conceptual model based on theory and evidence encountered during the review process are shown in red type. The 2 constructs included in the provisional conceptual model (Hollands 2014) but excluded from this final version are shown in strikethrough plain type. See Table 1 for a full record of the conceptual model development process.

Within the conceptual model (Figure 1) we distinguished between three sets of potential effect modifiers: study characteristics; intervention characteristics; and participant characteristics. Within our analytic framework for quantitative synthesis of outcome data collected from the included studies (see Data collection and analysis), potential effect‐modifying impacts of participant characteristics could in practice only be investigated based on between‐study comparisons, due to lack of reporting of results by participant subgroups within the included studies.

Electronic searches

We conducted electronic searches for eligible studies within each of the following databases:

• Cochrane Central Register of Controlled Trials (CENTRAL 2015, Issue 1) (1992 to 30 January 2015);

• MEDLINE (OvidSP) (including MEDLINE In‐Process) (1946 to 30 January 2015);

• EMBASE (OvidSP) (1980 to 30 January 2015);

• PsycINFO (OvidSP) (1806 to 30 January 2015);

• Applied Social Sciences Index and Abstracts (ProQuest) (1987 to 30 January 2015);

• Food Science and Technology Abstracts (Web of Knowledge) (1969 to 22 November 2012);

• Science Citation Index Expanded (Web of Knowledge) (1900 to 30 January 2015);

• Social Sciences Citation Index (Web of Knowledge) (1956 to 30 January 2015);

• Trials Register of Promoting Health Interventions (EPPI Centre) (2004 to 30 January 2015).

We developed a MEDLINE search strategy by combining sets of controlled vocabulary and free‐text search terms based on the eligibility criteria described above (see Criteria for considering studies for this review). This was externally peer‐reviewed by an information retrieval specialist and Co‐convenor of the Cochrane Information Retrieval Methods Group and revised based on their peer‐review comments. We tested the MEDLINE search strategy for its sensitivity to retrieve a reference set of 48 records of reports of potentially eligible studies known to be indexed in MEDLINE that were identified by our preceding scoping review (Hollands 2013a). We adapted the final MEDLINE search strategy for use to search each of the other databases listed above based on close examination of database thesauri and scope notes if available. We imposed no restrictions for publication date, publication format or language and incorporated no study design filters. Full details of final search strategies for each database, along with search dates and yields (for both the original search and the updated search), are provided in Appendix 1.

Searching other resources

We conducted electronic searches of two grey literature resources using search strategies adapted from the final MEDLINE search strategy:

• Conference Proceedings Citation Index ‐ Science (Web of Knowledge) (1990 to 30 January 2015);

• Conference Proceedings Citation Index ‐ Social Science & Humanities (Web of Knowledge) (1990 to 30 January 2015);

• Open Grey ‐ www.opengrey.eu (1980 to 30 January 2015).

We also searched trial registers (ClinicalTrials.gov and the World Health Organization International Clinical Trials Registry Platform (ICTRP)) to identify registered trials, and the websites of the following key organisations in the area of health and nutrition:

• Centers for Disease Control and Prevention, USA;

• EU Platform for Action on Diet, Physical Activity and Health;

• International Obesity Task Force;

• Rudd Centre for Food Policy and Obesity, USA;

• UK Department of Health;

• World Health Organization.

In addition, we searched the reference lists of all eligible study reports that had been identified using the other search methods described above and undertook forward citation tracking (using Google Scholar and PubMed) to identify further eligible studies or study reports.

Selection of studies

We imported title‐abstract records retrieved by the electronic searches to EPPI Reviewer 4 (ER4) systematic review software (Thomas 2010). We identified, reviewed manually and removed duplicate records using ER4's automatic de‐duplication feature with the similarity threshold set initially to 0.85 and finally to 0.80 following satisfactory manual checks of incomplete duplicate groups. Two researchers working independently (GJH, IS) undertook duplicate screening of title‐abstract records. We coded title‐abstract records as 'provisionally eligible', 'excluded' or 'duplicate' by applying the eligibility criteria described above (see Criteria for considering studies for this review). Disagreements in the coding of title‐abstract records were identified and resolved by discussion to reach consensus between the two researchers (GJH, IS).

We obtained copies of corresponding full‐text study reports for all title‐abstract records coded as 'provisionally eligible'. Two researchers working independently (GJH, IS) undertook duplicate screening of full‐text study reports. We coded full‐text study reports as 'eligible' or 'excluded' by applying the eligibility criteria described above (see Criteria for considering studies for this review). Coding disagreements were again identified and resolved by discussion to reach consensus between the two researchers, with a third researcher (DO) acting as arbiter when needed. We recorded bibliographic details of study reports excluded at the full‐text screening stage, along with the primary reason for exclusion, in a Characteristics of excluded studies table. We identified and linked multiple full‐text reports of the same study. We also identified full‐text reports comprising multiple eligible studies. We documented the flow of records and studies through the systematic review process using a PRISMA flow diagram (Moher 2009).

Data extraction and management

We developed an electronic data extraction form based on the Cochrane Public Health Review Group's template (http://ph.cochrane.org/review‐authors). We piloted an initial draft form using a selection of 10 included studies and then amended this in consultation with other members of the review team. One researcher (GJH or IS) extracted data on characteristics of included studies, while two researchers working independently (GJH, IS) extracted outcome data in duplicate. We only collected outcome data relating to comparison groups eligible for consideration in this review, but Characteristics of included studies tables record details of all study arms (conditions). Discrepancies in extracted outcome data were identified and resolved by checking against the study report, discussion and consensus between two researchers (GJH, IS). We sought key data missing from reports of included studies by contacting study authors.

At the protocol stage, we intended to collect the data summarised immediately below in this section. This represented the core data set (comprising 28 pre‐specified moderator constructs for potential examination using meta‐regression analyses; see Data synthesis) that we could reasonably anticipate would need to be collected based on our study eligibility criteria (see Criteria for considering studies for this review) and provisional conceptual model (Hollands 2014).

Assessment of risk of bias in included studies

We assessed risk of bias in the included studies using the Cochrane 'Risk of bias' tool addressing eight specific domains, namely: random sequence generation and allocation concealment (selection bias); blinding of participants and personnel (performance bias); blinding of outcome assessors (detection bias); incomplete outcome data (attrition bias); selective outcome reporting (reporting bias); and baseline comparability of participant characteristics between groups and consistency in intervention delivery (other bias) (Higgins 2011b). The last domain refers to whether information and specific instructions provided to participants were standardised between conditions and whether participant (non‐)compliance with the study protocol was appropriately managed.

Two researchers working independently (GJH, IS) applied the Cochrane 'Risk of bias' tool to each included study. We recorded supporting information for judgements of risk of bias (high, low or unclear) in the form of verbatim text extracted from study reports, supplemented with reviewer comments. We identified and resolved discrepancies between the two researchers' judgements or supporting information by discussion to reach consensus. We derived a summary risk of bias judgement (high, low or unclear) for each specific outcome, for inclusion as a study‐level covariate in the final stage of the meta‐regression analysis (see Data synthesis). We also considered summary risk of bias in determining the strength of inferences drawn from the results of the data synthesis and in developing conclusions and recommendations concerning the design and conduct of future research. We derived the summary risk of bias judgement from the four domains judged to be most critical in this specific review, namely: random sequence generation (selection bias); allocation concealment (selection bias); blinding of participants and personnel (performance bias); and baseline comparability of participant characteristics between groups (other bias). It was derived using an algorithm suggested in Section 8.7 (Table 8.7a) of the Cochrane Handbook for Systematic Reviews of Interventions (Higgins 2011b). Specifically, if the judgement in at least one of these four domains was 'high risk of bias' then we determined summary risk of bias to be high. If no judgements of 'high' risk were made in these four domains, but the judgement in at least one of these domains was 'unclear risk of bias' then we determined the summary risk of bias to be unclear. We only judged summary risk of bias 'low' if judgements in all four of these domains were 'low risk of bias'.

Measures of treatment effect

We calculated the standardised mean difference (SMD) with 95% confidence intervals to express the size of the intervention effect in each study relative to the variability observed in that study. We classified included study results according to two categories of timing of outcome measurement: immediate outcomes (that is ≤ 1 day) versus longer‐term outcomes (that is > 1 day).

Unit of analysis issues

In the case of cluster‐randomised controlled trials, where an analysis was reported that accounted for the clustered study design, we estimated the effect on this basis. Where this was not possible and the information was not available from the authors, then we carried out an 'approximately correct' analysis according to current guidelines (Higgins 2011a). We imputed estimates of the intra‐cluster correlation (ICC) using estimates derived from similar studies included in the review. We also computed inflated standard errors for outcome data from cluster‐randomised controlled trials based on reported test statistics (f values, t values or P values) and used these data in all statistical analyses. Where test statistics were not available, we imputed inflated standard errors from unadjusted standard errors based on ratios of adjusted to unadjusted standard errors obtained from similar studies included in the review.

For included studies with a within‐subjects design, we calculated the standardised mean difference for continuous outcomes using the methods described in Section 16.4 of the Cochrane Handbook for Systematic Reviews of Interventions (Higgins 2011a). Similar to our approach for cluster‐randomised controlled trials, we sought to compute deflated standard errors for outcome data from studies with a within‐subjects design based on reported test statistics, or on ratios of inflated to unadjusted standard errors obtained from similar studies included in the review. However, in studies with a within‐subjects design, these ratios exceeded one, which is counter‐intuitive and suggests there was no statistical advantage in using within‐subjects designs in this area. We therefore reverted to use of unadjusted standard errors for studies with a within‐subjects design in all statistical analyses.

Final outcome values served as the primary unit of analysis. Only one included study reported outcome data using changes from baseline as the metric (Ahn 2010). For this study we computed final values based on reported data, supplemented with additional information supplied by the authors.

Dealing with missing data

Where data were missing due to participant dropout we conducted available case analyses and recorded any issues of missing data within the assessments conducted using the Cochrane 'Risk of bias' tool.

Assessment of heterogeneity

We assessed statistical heterogeneity in results by inspection of a graphical display of the estimated treatment effects from included studies along with their 95% confidence intervals, and by formal statistical tests of homogeneity (Chi²) and measures of inconsistency (I²) and heterogeneity (τ²).

Assessment of reporting biases

We drew funnel plots (plots of effect estimates versus the inverse of their standard errors) to inform assessment of reporting biases. We conducted statistical tests to formally investigate the degree of asymmetry using the method proposed by Egger et al (Egger 1997). We interpreted the results of statistical tests based on visual inspection of the funnel plots. Asymmetry of the funnel plot may indicate publication bias or other biases related to sample size, though it may also represent a true relationship between trial size and effect size.

Data synthesis

We described and summarised the findings of included studies to address the two stated objectives of the review. We provide a narrative synthesis describing the interventions, participants, study characteristics and effects of eligible interventions upon pre‐specified outcomes (see Criteria for considering studies for this review).

Our statistical analysis of the results of included studies used a series of random‐effects and fixed‐effect models to estimate summary effect sizes as SMDs with 95% confidence intervals. We determined the final configuration of our statistical analysis based on the final version conceptual model (Figure 1). We conducted the statistical analysis using STATA (StataCorp, College Station, TX, 2014) and it comprised the following stages:

Stage 1. A standard meta‐analysis to estimate summary effect sizes for all eligible interventions versus all comparators, using metan (Harris 2008).

Stage 2. A meta‐regression analysis with type of product (food, alcohol, tobacco) as a covariate.

Stage 3. A meta‐regression analysis with study characteristics as additional covariates.

Stage 4. A meta‐regression analysis with intervention characteristics as covariates. At the protocol stage, we considered the option of conducting multivariate analysis to deal with studies with multiple treatment arms in order for direct comparisons between each treatment arm and a control condition to be modelled, using mvmeta (White 2011). In practice, we did not judge this appropriate and we conducted all meta‐regression analyses using metareg (Harbord 2008).

Stage 5. A meta‐regression analysis with participant characteristics and 'Risk of bias' assessment as covariates.

We only incorporated outcome data from independent comparisons into the statistical analysis. For example, from an included study that measured energy consumed from a lunch meal in four groups of participants served with a 275 g, a 367 g, a 458 g or a 550 g sandwich (Rolls 2004a), available pairwise comparisons are: 275 g versus 367 g, 275 g versus 458 g, 275 g versus 550 g, 367 g versus 458 g, 367 g versus 550 g, and 458 g versus 550 g. However, since these comparisons are not independent from one another, only the incremental comparisons (which are independent) were incorporated: 275 g versus 367 g, 367 g versus 458 g, and 458 g versus 550 g. Our decision to incorporate only outcome data from incremental comparisons into the statistical analysis effectively assumes a linear 'dose‐response' relationship between portion size and consumption/selection for portions of the sizes investigated in included studies. This assumption was judged reasonable by topic expert members of the review team and it is also conservative in terms of its impact on estimates of summary effect sizes. Some groups of study participants feature in two incremental comparisons (e.g. the 367 g group features in both the 275 g versus 367 g comparison and the 367 g versus 458 g comparison), therefore we halved sample sizes for groups featuring in two incremental comparisons to adjust their weighting in the analysis for this non‐independence.

Preliminary examination of outcome data revealed substantive variation in effect sizes between comparisons identified from studies that manipulated portion, package, individual unit or tableware size and those identified from studies that manipulated tableware shape. We did not judge comparisons of size conceptually comparable to comparisons of shape among the set of studies included in this review: size comparisons consisted in larger versus smaller sizes (of a portion, package, individual unit or item of tableware), whilst shape comparisons consisted in shorter, wider versus taller, narrower glasses or bottles (tableware). We therefore took the post‐hoc decision to conduct separate meta‐analyses for size and shape respectively, for both consumption and selection outcomes. (This decision effectively removed the covariate that differentiated between size and shape manipulations from subsequent meta‐regression analyses ‐ see below and Table 1). Preliminary analyses also revealed substantive variation in effect sizes between those measured in children and those measured in adults (as well as variation in effect sizes between adults of different ages), and between comparisons involving food products and those involving tobacco products. We therefore estimated supplementary summary effect sizes for these subgroups to illustrate these variations in effects. In describing the effects of size and shape interventions on selection and consumption, our narrative synthesis is disaggregated as appropriate to reflect these variations and to incorporate supplementary effect sizes estimated to illustrate them (see Effects of interventions).

We used the following procedures for meta‐regression analyses. First, for each of the two outcomes (consumption and selection), we conducted a series of univariable analyses using random‐effects models to test for a statistical association between each covariate and the study‐level effect size (SMD). All variables identified in the final version of the conceptual model (see Table 1) were candidate covariates for univariable analyses. Blinded to data extracted for covariates from study reports by two researchers (GJH, IS), topic experts within the review team selected six baseline participant characteristics to be prioritised when contacting study authors to request data on potential effect modifiers that appeared to have been measured but were missing from study reports. This selection was based on what were expected to be the most important modifiers of the effects of the intervention, primarily based on topic experts' knowledge of theory and evidence for determinants of between‐person variation in levels of food and energy intake (since the majority of studies included in this review focused on food ‐ see Description of studies). The six selected covariates (variable type) were: age (continuous), gender (categorical), BMI (continuous), dietary restraint (continuous), dietary disinhibition (continuous) and hunger (continuous). All six had been pre‐specified in the original version of the conceptual model (Figure 1) and had been measured at baseline in at least one included study. We decided in advance of conducting univariable meta‐regression analyses that candidate covariates would be excluded if they had been measured in fewer than 10 independent comparisons feeding into an analysis (insufficient data) or if there was no variation in the value of the covariate between independent comparisons feeding into an analysis (absence of variation, which precluded estimation). Based on these exclusion criteria, we conducted two series of univariable meta‐regression analyses to investigate potential modifiers of the effects of larger versus smaller portions, packages, individual units or tableware on: (a) consumption of food and tobacco; and (b) on the selection (without purchase) of food. We did not conduct other planned series of univariable meta‐regression analyses due to insufficient data following application of the exclusion criteria outlined above.

Second, we estimated random‐effects models to identify the collections of study‐level covariates that best explained the between‐studies component of the variance in study‐level estimates of effect size. As with univariable analyses, it proved possible in practice to implement this analysis to investigate potential modifiers of the effects of larger versus smaller portions, packages, individual units or tableware on: (a) consumption of food and tobacco; and (b) on the selection (without purchase) of food. We did not conduct other planned second stage analyses due to insufficient data. We selected variables for inclusion in models using a stepwise forward selection procedure. We selected first the covariate which had the largest value of R² (a measure of the proportion of the between‐studies component of the variance explained by the model) based on the results of the preceding series of univariable analyses. Next, we added each of the other covariates observed to be statistically associated with the study‐level effect size in the results of the preceding univariable analyses to the model in sequence (in an order corresponding to Stages 2 to 4 of the statistical analysis plan, outlined above in this section). Each covariate was retained in the final model if its incorporation contributed to an increase in the value of the R² but was otherwise dropped from the model. Consequently, once this procedure was completed, the final model specification maximised the value of R².

To facilitate interpretation of estimated effect sizes (Schünemann 2011), we re‐expressed a series of SMD values ranging between 0.1 and 2.5 in terms of selected metrics of food or tobacco selection/consumption. Baseline values (SMD = 0.0) reflect estimated average (mean) consumption levels among representative samples of UK adults or children and associated among‐participant variation (that is, the standard deviation). Two researchers (IS and HBL) estimated average (mean) food energy intake, non‐alcoholic beverage consumption and cigarette consumption (among smokers) using unweighted data from the UK National Diet and Nutrition Survey Years 1‐4, collected using 24‐hour dietary recall in a nationally representative UK population sample (National Centre for Social Research 2012). One researcher (IS) also estimated an alternative estimate of average cigarette consumption (among smokers) based on unweighted data from the UK Opinions and Lifestyle Survey 2012 (Office for National Statistics 2012). We used these data to re‐express SMD values in terms of the proportionate (%) and absolute changes from baseline values in terms of each selected metric and tabulated these data for illustrative purposes (see Effects of interventions). We also compared re‐expressed values among UK adults and children to those based on published estimates among equivalent US samples.

Sensitivity analysis

We conducted a sensitivity analysis to explore the impact of outcome data imputed due to missing data. In practice, standard deviations were the only component of outcome data that needed to be imputed for some independent comparisons due to missing data. Therefore, this sensitivity analysis in practice involved re‐estimating fixed‐effect and random‐effects meta‐analyses (for both selection and consumption outcomes – all comparisons) using imputed values for standard deviations that were (1) double and (2) half those used in the 'base case' analyses reported in the Effects of interventions section. At the protocol stage, we had also planned to conduct a sensitivity analysis to explore the separate analysis of studies of food and tobacco products. In practice, we estimated supplementary summary effect sizes for these subgroups of studies (see Data synthesis), which was functionally equivalent to this planned sensitivity analysis.