Assessing public support for extending smoke-free policies beyond enclosed public places and workplaces: protocol for a systematic review and meta-analysis 67 3 One of the assumptions in meta-analysis is that effect sizes are independent, i.e. the effect size of one study does not imply the direction or magnitude of the effect size in another study.33 Multiple estimates of public support in a specific country may violate the independence assumption, therefore we will conduct a three-level meta-analysis.34 A three-level meta-analysis is an extended version of a random-effects meta-analysis and includes sampling variation at the first level, within-country heterogeneity at the second level and between-country heterogeneity at the third level. The analytic model is as follows: 1) Where is the estimation of the true effect size for public support, the average population effect, is the within-country variance, is the between-country variance, and the sampling variance. 34 In each model, heterogeneity will be quantified by the I² statistic per level. We intend to use R 3.6.5 (R Foundation for Statistical Computing, 2020) using the packages meta and metaphor for all analysis. 35, 36 A second analysis will be performed on all studies presenting the change in public support following implementation of the actual policy under study. If relevant analyses will be performed twice, once including estimates for public support in general and once for public support specifically related to children, e.g. public support for smoking bans in cars and public support for smoking bans in cars if children are present (see the Outcomes and prioritisation section). The secondary objective is to identify and quantify determinants that are associated with public support. The determinants of public support will be evaluated at three levels: 1. Quantify within-study determinants of public support Public support may differ between population subgroups. Therefore, we will conduct subgroup analyses according to: • Gender (men vs. women) • Smoking status (current smokers vs. former smokers vs. nonsmokers, and/or current smokers vs. non-smokers (including former smokers), depending on data availability) • Parental status (yes vs. no, depending on data availability) • Age group (younger vs. older, categorisation depending on data availability)
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