Aims/hypothesis Inverse associations between physical activity (PA) and type 2 diabetes mellitus are well known. However, the shape of the dose–response relationship is still uncertain. This review synthesises results from longitudinal studies in general populations and uses non-linear models of the association between PA and incident type 2 diabetes. Methods A systematic literature search identified 28 prospective studies on leisure-time PA (LTPA) or total PA and risk of type 2 diabetes. PA exposures were converted into metabolic equivalent of task (MET) h/week and marginal MET (MMET) h/week, a measure only considering energy expended above resting metabolic rate. Restricted cubic splines were used to model the exposure–disease relationship. Results Our results suggest an overall non-linear relationship; using the cubic spline model we found a risk reduction of 26% (95% CI 20%, 31%) for type 2 diabetes among those who achieved 11.25 MET h/week (equivalent to 150 min/week of moderate activity) relative to inactive individuals. Achieving twice this amount of PA was associated with a risk reduction of 36% (95% CI 27%, 46%), with further reductions at higher doses (60 MET h/week, risk reduction of 53%). Results for the MMET h/week dose–response curve were similar for moderate intensity PA, but benefits were greater for higher intensity PA and smaller for lower intensity activity. Conclusions/interpretation Higher levels of LTPA were associated with substantially lower incidence of type 2 diabetes in the general population. The relationship between LTPA and type 2 diabetes was curvilinear; the greatest relative benefits are achieved at low levels of activity, but additional benefits can be realised at exposures considerably higher than those prescribed by public health recommendations.

The standard two-stage approach for estimating non-linear dose–response curves based on aggregated data typically excludes those studies with less than three exposure groups. We develop the one-stage method as a linear mixed model and present the main aspects of the methodology, including model specification, estimation, testing, prediction, goodness-of-fit, model comparison, and quantification of between-studies heterogeneity. Using both fictitious and real data from a published meta-analysis, we illustrated the main features of the proposed methodology and compared it to a traditional two-stage analysis. In a one-stage approach, the pooled curve and estimates of the between-studies heterogeneity are based on the whole set of studies without any exclusion. Thus, even complex curves (splines, spike at zero exposure) defined by several parameters can be estimated. We showed how the one-stage method may facilitate several applications, in particular quantification of heterogeneity over the exposure range, prediction of marginal and conditional curves, and comparison of alternative models. The one-stage method for meta-analysis of non-linear curves is implemented in the dosresmeta R package. It is particularly suited for dose–response meta-analyses of aggregated where the complexity of the research question is better addressed by including all the studies.

Meta-analytical methods are frequently used to combine dose-response findings expressed in terms of relative risks. However, no methodology has been established when results are summarized in terms of differences in means of quantitative outcomes. We proposed a two-stage approach. A flexible dose-response model is estimated within each study (first stage) taking into account the covariance of the data points (mean differences, standardized mean differences). Parameters describing the study-specific curves are then combined using a multivariate random-effects model (second stage) to address heterogeneity across studies. The method is fairly general and can accommodate a variety of parametric functions. Compared to traditional non-linear models (e.g. E max, logistic), spline models do not assume any pre-specified dose-response curve. Spline models allow inclusion of studies with a small number of dose levels, and almost any shape, even non monotonic ones, can be estimated using only two parameters. We illustrated the method using dose-response data arising from five clinical trials on an antipsychotic drug, aripiprazole, and improvement in symptoms in shizoaffective patients. Using the Positive and Negative Syndrome Scale (PANSS), pooled results indicated a non-linear association with the maximum change in mean PANSS score equal to 10.40 (95 % confidence interval 7.48, 13.30) observed for 19.32 mg/day of aripiprazole. No substantial change in PANSS score was observed above this value. An estimated dose of 10.43 mg/day was found to produce 80 % of the maximum predicted response. The described approach should be adopted to combine correlated differences in means of quantitative outcomes arising from multiple studies. Sensitivity analysis can be a useful tool to assess the robustness of the overall dose-response curve to different modelling strategies. A user-friendly R package has been developed to facilitate applications by practitioners.

Several studies have analyzed the relationship between coffee consumption and mortality, but the shape of the association remains unclear. We conducted a dose-response meta-analysis of prospective studies to examine the dose-response associations between coffee consumption and mortality from all causes, cardiovascular disease (CVD), and all cancers. Pertinent studies, published between 1966 and 2013, were identified by searching PubMed and by reviewing the reference lists of the selected articles. Prospective studies in which investigators reported relative risks of mortality from all causes, CVD, and all cancers for 3 or more categories of coffee consumption were eligible. Results from individual studies were pooled using a random-effects model. Twenty-one prospective studies, with 121,915 deaths and 997,464 participants, met the inclusion criteria. There was strong evidence of nonlinear associations between coffee consumption and mortality for all causes and CVD (P for nonlinearity < 0.001). The largest risk reductions were observed for 4 cups/day for all-cause mortality (16%, 95% confidence interval: 13, 18) and 3 cups/day for CVD mortality (21%, 95% confidence interval: 16, 26). Coffee consumption was not associated with cancer mortality. Findings from this meta-analysis indicate that coffee consumption is inversely associated with all-cause and CVD mortality.

Background The possibility that lifestyle factors such as diet, specifically potassium intake, may modify the risk of stroke has been suggested by several observational cohort studies, including some recent reports. We performed a systematic review and meta‐analysis of existing studies and assessed the dose–response relation between potassium intake and stroke risk. Methods and Results We reviewed the observational cohort studies addressing the relation between potassium intake, and incidence or mortality of total stroke or stroke subtypes published through August 6, 2016. We carried out a meta‐analysis of 16 cohort studies based on the relative risk (RR) of stroke comparing the highest versus lowest intake categories. We also plotted a pooled dose–response curve of RR of stroke according to potassium intake. Analyses were performed with and without adjustment for blood pressure. Relative to the lowest category of potassium intake, the highest category of potassium intake was associated with a 13% reduced risk of stroke (RR=0.87, 95% CI 0.80–0.94) in the blood pressure–adjusted analysis. Summary RRs tended to decrease when original estimates were unadjusted for blood pressure. Analysis for stroke subtypes yielded comparable results. In the spline analysis, the pooled RR was lowest at 90 mmol of potassium daily intake (RRs=0.78, 95% CI 0.70–0.86) in blood pressure–adjusted analysis, and 0.67 (95% CI 0.57–0.78) in unadjusted analysis. Conclusions Overall, this dose–response meta‐analysis confirms the inverse association between potassium intake and stroke risk, with potassium intake of 90 mmol (≈3500 mg)/day associated with the lowest risk of stroke.