Numerous meta‐analyses in healthcare research combine results from only a small number of studies, for which the variance representing between‐study heterogeneity is estimated imprecisely. A Bayesian approach to estimation allows external evidence on the expected magnitude of heterogeneity to be incorporated.The aim of this paper is to provide tools that improve the accessibility of Bayesian meta‐analysis. We present two methods for implementing Bayesian meta‐analysis, using numerical integration and importance sampling techniques. Based on 14 886 binary outcome meta‐analyses in the Cochrane Database of Systematic Reviews, we derive a novel set of predictive distributions for the degree of heterogeneity expected in 80 settings depending on the outcomes assessed and comparisons made. These can be used as prior distributions for heterogeneity in future meta‐analyses.The two methods are implemented in R, for which code is provided. Both methods produce equivalent results to standard but more complex Markov chain Monte Carlo approaches. The priors are derived as log‐normal distributions for the between‐study variance, applicable to meta‐analyses of binary outcomes on the log odds‐ratio scale. The methods are applied to two example meta‐analyses, incorporating the relevant predictive distributions as prior distributions for between‐study heterogeneity.We have provided resources to facilitate Bayesian meta‐analysis, in a form accessible to applied researchers, which allow relevant prior information on the degree of heterogeneity to be incorporated. © 2014 The Authors. Statistics in Medicine published by John Wiley & Sons Ltd.

Hazard ratios can be approximated by data extracted from published Kaplan–Meier curves. Recently, this curve approach has been extended beyond hazard-ratio approximation with the capability of constructing time-to-event data at the individual level. In this article, we introduce a command, ipdfc, to implement the reconstruction method to convert Kaplan–Meier curves to time-to-event data. We give examples to illustrate how to use the command.

Uncertainty remains about whether personal financial incentives could achieve sustained changes in health-related behaviors that would reduce the fast-growing global non-communicable disease burden. This review aims to estimate whether: i. financial incentives achieve sustained changes in smoking, eating, alcohol consumption and physical activity; ii. effectiveness is modified by (a) the target behavior, (b) incentive value and attainment certainty, (c) recipients' deprivation level. Multiple sources were searched for trials offering adults financial incentives and assessing outcomes relating to pre-specified behaviors at a minimum of six months from baseline. Analyses included random-effects meta-analyses and meta-regressions grouped by timed endpoints. Of 24,265 unique identified articles, 34 were included in the analysis. Financial incentives increased behavior-change, with effects sustained until 18months from baseline (OR: 1.53, 95% CI 1.05-2.23) and three months post-incentive removal (OR: 2.11, 95% CI 1.21-3.67). High deprivation increased incentive effects (OR: 2.17; 95% CI 1.22-3.85), but only at >6-12months from baseline. Other assessed variables did not independently modify effects at any time-point. Personal financial incentives can change habitual health-related behaviors and help reduce health inequalities. However, their role in reducing disease burden is potentially limited given current evidence that effects dissipate beyond three months post-incentive removal.

Background Overeating and harmful alcohol and tobacco use have been linked to the aetiology of various non‐communicable diseases, which are among the leading global causes of morbidity and premature mortality. As people are repeatedly exposed to varying sizes and shapes of food, alcohol and tobacco products in environments such as shops, restaurants, bars and homes, this has stimulated public health policy interest in product size and shape as potential targets for intervention. Objectives 1) To assess the effects of interventions involving exposure to different sizes or sets of physical dimensions of a portion, package, individual unit or item of tableware on unregulated selection or consumption of food, alcohol or tobacco products in adults and children. 2) To assess the extent to which these effects may be modified by study, intervention and participant characteristics. Search methods We searched CENTRAL, MEDLINE, EMBASE, PsycINFO, eight other published or grey literature databases, trial registries and key websites up to November 2012, followed by citation searches and contacts with study authors. This original search identified eligible studies published up to July 2013, which are fully incorporated into the review. We conducted an updated search up to 30 January 2015 but further eligible studies are not yet fully incorporated due to their minimal potential to change the conclusions. Selection criteria Randomised controlled trials with between‐subjects (parallel‐group) or within‐subjects (cross‐over) designs, conducted in laboratory or field settings, in adults or children. Eligible studies compared at least two groups of participants, each exposed to a different size or shape of a portion of a food (including non‐alcoholic beverages), alcohol or tobacco product, its package or individual unit size, or of an item of tableware used to consume it, and included a measure of unregulated selection or consumption of food, alcohol or tobacco. Data collection and analysis We applied standard Cochrane methods to select eligible studies for inclusion and to collect data and assess risk of bias. We calculated study‐level effect sizes as standardised mean differences (SMDs) between comparison groups, measured as quantities selected or consumed. We combined these results using random‐effects meta‐analysis models to estimate summary effect sizes (SMDs with 95% confidence intervals (CIs)) for each outcome for size and shape comparisons. We rated the overall quality of evidence using the GRADE system. Finally, we used meta‐regression analysis to investigate statistical associations between summary effect sizes and variant study, intervention or participant characteristics. Main results The current version of this review includes 72 studies, published between 1978 and July 2013, assessed as being at overall unclear or high risk of bias with respect to selection and consumption outcomes. Ninety‐six per cent of included studies (69/72) manipulated food products and 4% (3/72) manipulated cigarettes. No included studies manipulated alcohol products. Forty‐nine per cent (35/72) manipulated portion size, 14% (10/72) package size and 21% (15/72) tableware size or shape. More studies investigated effects among adults (76% (55/72)) than children and all studies were conducted in high‐income countries ‐ predominantly in the USA (81% (58/72)). Sources of funding were reported for the majority of studies, with no evidence of funding by agencies with possible commercial interests in their results. A meta‐analysis of 86 independent comparisons from 58 studies (6603 participants) found a small to moderate effect of portion, package, individual unit or tableware size on consumption of food (SMD 0.38, 95% CI 0.29 to 0.46), providing moderate quality evidence that exposure to larger sizes increased quantities of food consumed among children (SMD 0.21, 95% CI 0.10 to 0.31) and adults (SMD 0.46, 95% CI 0.40 to 0.52). The size of this effect suggests that, if sustained reductions in exposure to larger‐sized food portions, packages and tableware could be achieved across the whole diet, this could reduce average daily energy consumed from food by between 144 and 228 kcal (8.5% to 13.5% from a baseline of 1689 kcal) among UK children and adults. A meta‐analysis of six independent comparisons from three studies (108 participants) found low quality evidence for no difference in the effect of cigarette length on consumption (SMD 0.25, 95% CI ‐0.14 to 0.65). One included study (50 participants) estimated a large effect on consumption of exposure to differently shaped tableware (SMD 1.17, 95% CI 0.57 to 1.78), rated as very low quality evidence that exposure to shorter, wider bottles (versus taller, narrower bottles) increased quantities of water consumed by young adult participants. A meta‐analysis of 13 independent comparisons from 10 studies (1164 participants) found a small to moderate effect of portion or tableware size on selection of food (SMD 0.42, 95% CI 0.24 to 0.59), rated as moderate quality evidence that exposure to larger sizes increased the quantities of food people selected for subsequent consumption. This effect was present among adults (SMD 0.55, 95% CI 0.35 to 0.75) but not children (SMD 0.14, 95% CI ‐0.06 to 0.34). In addition, a meta‐analysis of three independent comparisons from three studies (232 participants) found a very large effect of exposure to differently shaped tableware on selection of non‐alcoholic beverages (SMD 1.47, 95% CI 0.52 to 2.43), rated as low quality evidence that exposure to shorter, wider (versus taller, narrower) glasses or bottles increased the quantities selected for subsequent consumption among adults (SMD 2.31, 95% CI 1.79 to 2.83) and children (SMD 1.03, 95% CI 0.41 to 1.65). Authors' conclusions This review found that people consistently...