Accounting for centre-effects in multicentre trials with a binary outcome - when, why, and how?

BACKGROUND: It is often desirable to account for centre-effects in the analysis of multicentre randomised trials, however it is unclear which analysis methods are best in trials with a binary outcome. METHODS: We compared the performance of four methods of analysis (fixed-effects models, random-effects models, generalised estimating equations (GEE), and Mantel-Haenszel) using a re-analysis of a previously reported randomised trial (MIST2) and a large simulation study. RESULTS: The re-analysis of MIST2 found that fixed-effects and Mantel-Haenszel led to many patients being dropped from the analysis due to over-stratification (up to 69% dropped for Mantel-Haenszel, and up to 33% dropped for fixed-effects). Conversely, random-effects and GEE included all patients in the analysis, however GEE did not reach convergence. Estimated treatment effects and p-values were highly variable across different analysis methods. The simulation study found that most methods of analysis performed well with a small number of centres. With a large number of centres, fixed-effects led to biased estimates and inflated type I error rates in many situations, and Mantel-Haenszel lost power compared to other analysis methods in some situations. Conversely, both random-effects and GEE gave nominal type I error rates and good power across all scenarios, and were usually as good as or better than either fixed-effects or Mantel-Haenszel. However, this was only true for GEEs with non-robust standard errors (SEs); using a robust ‘sandwich’ estimator led to inflated type I error rates across most scenarios. CONCLUSIONS: With a small number of centres, we recommend the use of fixed-effects, random-effects, or GEE with non-robust SEs. Random-effects and GEE with non-robust SEs should be used with a moderate or large number of centres

Adjusting for multiple prognostic factors in the analysis of randomised trials

Background: When multiple prognostic factors are adjusted for in the analysis of a randomised trial, it is unclear (1) whether it is necessary to account for each of the strata, formed by all combinations of the prognostic factors (stratified analysis), when randomisation has been balanced within each stratum (stratified randomisation), or whether adjusting for the main effects alone will suffice, and (2) the best method of adjustment in terms of type I error rate and power, irrespective of the randomisation method. Methods: We used simulation to (1) determine if a stratified analysis is necessary after stratified randomisation, and (2) to compare different methods of adjustment in terms of power and type I error rate. We considered the following methods of analysis: adjusting for covariates in a regression model, adjusting for each stratum using either fixed or random effects, and Mantel-Haenszel or a stratified Cox model depending on outcome. Results: Stratified analysis is required after stratified randomisation to maintain correct type I error rates when (a) there are strong interactions between prognostic factors, and (b) there are approximately equal number of patients in each stratum. However, simulations based on real trial data found that type I error rates were unaffected by the method of analysis (stratified vs unstratified), indicating these conditions were not met in real datasets. Comparison of different analysis methods found that with small sample sizes and a binary or time-to-event outcome, most analysis methods lead to either inflated type I error rates or a reduction in power; the lone exception was a stratified analysis using random effects for strata, which gave nominal type I error rates and adequate power. Conclusions: It is unlikely that a stratified analysis is necessary after stratified randomisation except in extreme scenarios. Therefore, the method of analysis (accounting for the strata, or adjusting only for the covariates) will not generally need to depend on the method of randomisation used. Most methods of analysis work well with large sample sizes, however treating strata as random effects should be the analysis method of choice with binary or time-to-event outcomes and a small sample size

A comparison of methods to adjust for continuous covariates in the analysis of randomised trials

BACKGROUND: Although covariate adjustment in the analysis of randomised trials can be beneficial, adjustment for continuous covariates is complicated by the fact that the association between covariate and outcome must be specified. Misspecification of this association can lead to reduced power, and potentially incorrect conclusions regarding treatment efficacy. METHODS: We compared several methods of adjustment to determine which is best when the association between covariate and outcome is unknown. We assessed (a) dichotomisation or categorisation; (b) assuming a linear association with outcome; (c) using fractional polynomials with one (FP1) or two (FP2) polynomial terms; and (d) using restricted cubic splines with 3 or 5 knots. We evaluated each method using simulation and through a re-analysis of trial datasets. RESULTS: Methods which kept covariates as continuous typically had higher power than methods which used categorisation. Dichotomisation, categorisation, and assuming a linear association all led to large reductions in power when the true association was non-linear. FP2 models and restricted cubic splines with 3 or 5 knots performed best overall. CONCLUSIONS: For the analysis of randomised trials we recommend (1) adjusting for continuous covariates even if their association with outcome is unknown; (2) keeping covariates as continuous; and (3) using fractional polynomials with two polynomial terms or restricted cubic splines with 3 to 5 knots when a linear association is in doubt

Shallow waters: social science research in South Africa's marine environment

This paper provides an overview of social science research in the marine environment of South Africa for the period 1994–2012. A bibliography based on a review of relevant literature and social science projects funded under the SEAChange programme of the South African Network for Coastal and Oceanic Research (SANCOR) was used to identify nine main themes that capture the knowledge generated in the marine social science field. Within these themes, a wide diversity of topics has been explored, covering a wide geographic area. The review suggests that there has been a steady increase in social science research activities and outputs over the past 18 years, with a marked increase in postgraduate dissertations in this field. The SEAChange programme has contributed to enhancing understanding of certain issues and social interactions in the marine environment but this work is limited. Furthermore, there has been limited dissemination of these research results amongst the broader marine science community and incorporation of this information into policy and management decisions has also been limited. However, marine scientists are increasingly recognising the importance of taking a more holistic and integrated approach to management, and are encouraging further social science research, as well as interdisciplinary research across the natural and social sciences. Possible reasons for the lack of communication and coordination amongst natural and social scientists, as well as the limited uptake of research results in policy and management decisions, are discussed and recommendations are proposed.Web of Scienc

The risks and rewards of covariate adjustment in randomized trials: an assessment of 12 outcomes from 8 studies

Adjustment for prognostic covariates can lead to increased power in the analysis of randomized trials. However, adjusted analyses are not often performed in practice

Nitrogen and sulphur management: challenges for organic sources in temperate agricultural systems

A current global trend towards intensification or specialization of agricultural enterprises has been accompanied by increasing public awareness of associated environmental consequences. Air and water pollution from losses of nutrients, such as nitrogen (N) and sulphur (S), are a major concern. Governments have initiated extensive regulatory frameworks, including various land use policies, in an attempt to control or reduce the losses. This paper presents an overview of critical input and loss processes affecting N and S for temperate climates, and provides some background to the discussion in subsequent papers evaluating specific farming systems. Management effects on potential gaseous and leaching losses, the lack of synchrony between supply of nutrients and plant demand, and options for optimizing the efficiency of N and S use are reviewed. Integration of inorganic and organic fertilizer inputs and the equitable re-distribution of nutrients from manure are discussed. The paper concludes by highlighting a need for innovative research that is also targeted to practical approaches for reducing N and S losses, and improving the overall synchrony between supply and demand

The use of scenarios and models to evaluate the future of nature values and ecosystem services in Mediterranean forests

Science and society are increasingly interested in predicting the effects of global change and socio-economic development on natural systems, to ensure maintenance of both ecosystems and human well-being. The Intergovernmental Platform on Biodiversity and Ecosystem Services has identified the combination of ecological modelling and scenario forecasting as key to improving our understanding of those effects, by evaluating the relationships and feedbacks between direct and indirect drivers of change, biodiversity, and ecosystem services. Using as case study the forests of the Mediterranean basin (complex socio-ecological systems of high social and conservation value), we reviewed the literature to assess (1) what are the modelling approaches most commonly used to predict the condition and trends of biodiversity and ecosystem services under future scenarios of global change, (2) what are the drivers of change considered in future scenarios and at what scales, and (3) what are the nature and ecosystem service indicators most commonly evaluated. Our review shows that forecasting studies make relatively little use of modelling approaches accounting for actual ecological processes and feedbacks between different socio-ecological sectors; predictions are generally made on the basis of a single (mainly climate) or a few drivers of change. In general, there is a bias in the set of nature and ecosystem service indicators assessed. In particular, cultural services and human well-being are greatly underrepresented in the literature. We argue that these shortfalls hamper our capacity to make the best use of predictive tools to inform decision-making in the context of global change.This work was supported by the Spanish Government through the INMODES project (grant number CGL2017-89999-C2-2-R), the ERA-NET FORESTERRA project INFORMED (grant number 29183), and the project Boscos Sans per a una Societat Saludable funded by Obra Social la Caixa (https://obrasociallacaixa.org/). AMO and AA were supported by Spanish Government through the “Juan de la Cierva” fellowship program (IJCI-2016-30349 and IJCI-2016-30049, respectively). JVRD was supported by the Government of Asturias and the FP7-Marie Curie-COFUND program of the European Commission (Grant “Clarín” ACA17-02)