Diminishing returns drive altruists to help extended family.

Altruism between close relatives can be easily explained. However, paradoxes arise when organisms divert altruism towards more distantly related recipients. In some social insects, workers drift extensively between colonies and help raise less related foreign brood, seemingly reducing inclusive fitness. Since being highlighted by W. D. Hamilton, three hypotheses (bet hedging, indirect reciprocity and diminishing returns to cooperation) have been proposed for this surprising behaviour. Here, using inclusive fitness theory, we show that bet hedging and indirect reciprocity could only drive cooperative drifting under improbable conditions. However, diminishing returns to cooperation create a simple context in which sharing workers is adaptive. Using a longitudinal dataset comprising over a quarter of a million nest cell observations, we quantify cooperative payoffs in the Neotropical wasp Polistes canadensis, for which drifting occurs at high levels. As the worker-to-brood ratio rises in a worker's home colony, the predicted marginal benefit of a worker for expected colony productivity diminishes. Helping related colonies can allow effort to be focused on related brood that are more in need of care. Finally, we use simulations to show that cooperative drifting evolves under diminishing returns when dispersal is local, allowing altruists to focus their efforts on related recipients. Our results indicate the power of nonlinear fitness effects to shape social organization, and suggest that models of eusocial evolution should be extended to include neglected social interactions within colony networks.

Adjusting trial results for biases in meta-analysis: combining data-based evidence on bias with detailed trial assessment.

Flaws in the conduct of randomized trials can lead to biased estimation of the intervention effect. Methods for adjustment of within-trial biases in meta-analysis include the use of empirical evidence from an external collection of meta-analyses, and the use of expert opinion informed by the assessment of detailed trial information. Our aim is to present methods to combine these two approaches to gain the advantages of both. We make use of the risk of bias information that is routinely available in Cochrane reviews, by obtaining empirical distributions for the bias associated with particular bias profiles (combinations of risk of bias judgements). We propose three methods: a formal combination of empirical evidence and opinion in a Bayesian analysis; asking experts to give an opinion on bias informed by both summary trial information and a bias distribution from the empirical evidence, either numerically or by selecting areas of the empirical distribution. The methods are demonstrated through application to two example binary outcome meta-analyses. Bias distributions based on opinion informed by trial information alone were most dispersed on average, and those based on opinions obtained by selecting areas of the empirical distribution were narrowest. Although the three methods for combining empirical evidence with opinion vary in ease and speed of implementation, they yielded similar results in the two examples.

Has Chlamydia trachomatis prevalence in young women in England, Scotland and Wales changed? Evidence from national probability surveys.

We evaluate the utility of the National Surveys of Attitudes and Sexual Lifestyles (Natsal) undertaken in 2000 and 2010, before and after the introduction of the National Chlamydia Screening Programme, as an evidence source for estimating the change in prevalence of Chlamydia trachomatis (CT) in England, Scotland and Wales. Both the 2000 and 2010 surveys tested urine samples for CT by Nucleic Acid Amplification Tests (NAATs). We examined the sources of uncertainty in estimates of CT prevalence change, including sample size and adjustments for test sensitivity and specificity, survey non-response and informative non-response. In 2000, the unadjusted CT prevalence was 4.22% in women aged 18-24 years; in 2010, CT prevalence was 3.92%, a non-significant absolute difference of 0.30 percentage points (95% credible interval -2.8 to 2.0). In addition to uncertainty due to small sample size, estimates were sensitive to specificity, survey non-response or informative non-response, such that plausible changes in any one of these would be enough to either reverse or double any likely change in prevalence. Alternative ways of monitoring changes in CT incidence and prevalence over time are discussed.

Network meta-analysis in health psychology and behavioural medicine: a primer.

Progress in the science and practice of health psychology depends on the systematic synthesis of quantitative psychological evidence. Meta-analyses of experimental studies have led to important advances in understanding health-related behaviour change interventions. Fundamental questions regarding such interventions have been systematically investigated through synthesising relevant experimental evidence using standard pairwise meta-analytic procedures that provide reliable estimates of the magnitude, homogeneity and potential biases in effects observed. However, these syntheses only provide information about whether particular types of interventions work better than a control condition or specific alternative approaches. To increase the impact of health psychology on health-related policy-making, evidence regarding the comparative efficacy of all relevant intervention approaches - which may include biomedical approaches - is necessary. With the development of network meta-analysis (NMA), such evidence can be synthesised, even when direct head-to-head trials do not exist. However, care must be taken in its application to ensure reliable estimates of the effect sizes between interventions are revealed. This review paper describes the potential importance of NMA to health psychology, how the technique works and important considerations for its appropriate application within health psychology.

Pelvic inflammatory disease and salpingitis: incidence of primary and repeat episodes in England.

Pelvic inflammatory disease (PID) and more specifically salpingitis (visually confirmed inflammation) is the primary cause of tubal factor infertility and is an important risk factor for ectopic pregnancy. The risk of these outcomes increases following repeated episodes of PID. We developed a homogenous discrete-time Markov model for the distribution of PID history in the UK. We used a Bayesian framework to fully propagate parameter uncertainty into the model outputs. We estimated the model parameters from routine data, prospective studies, and other sources. We estimated that for women aged 35-44 years, 33·6% and 16·1% have experienced at least one episode of PID and salpingitis, respectively (diagnosed or not) and 10·7% have experienced one salpingitis and no further PID episodes, 3·7% one salpingitis and one further PID episode, and 1·7% one salpingitis and ⩾2 further PID episodes. Results are consistent with numerous external data sources, but not all. Studies of the proportion of PID that is diagnosed, and the proportion of PIDs that are salpingitis together with the severity distribution in different diagnostic settings and of overlap between routine data sources of PID would be valuable.

Model-Based Network Meta-Analysis: A Framework for Evidence Synthesis of Clinical Trial Data.

Model-based meta-analysis (MBMA) is increasingly used in drug development to inform decision-making and future trial designs, through the use of complex dose and/or time course models. Network meta-analysis (NMA) is increasingly being used by reimbursement agencies to estimate a set of coherent relative treatment effects for multiple treatments that respect the randomization within the trials. However, NMAs typically either consider different doses completely independently or lump them together, with few examples of models for dose. We propose a framework, model-based network meta-analysis (MBNMA), that combines both approaches, that respects randomization, and allows estimation and prediction for multiple agents and a range of doses, using plausible physiological dose-response models. We illustrate our approach with an example comparing the efficacies of triptans for migraine relief. This uses a binary endpoint, although we note that the model can be easily modified for other outcome types.

Methods to induce labour: a systematic review, network meta-analysis and cost-effectiveness analysis.

OBJECTIVES: To compare the clinical effectiveness and cost-effectiveness of labour induction methods. METHODS: We conducted a systematic review of randomised trials comparing interventions for third-trimester labour induction (search date: March 2014). Network meta-analysis was possible for six of nine prespecified key outcomes: vaginal delivery within 24 hours (VD24), caesarean section, uterine hyperstimulation, neonatal intensive care unit (NICU) admissions, instrumental delivery and infant Apgar scores. We developed a decision-tree model from a UK NHS perspective and calculated incremental cost-effectiveness ratios, expected costs, utilities and net benefit, and cost-effectiveness acceptability curves. MAIN RESULTS: In all, 611 studies comparing 31 active interventions were included. Intravenous oxytocin with amniotomy and vaginal misoprostol (≥50 µg) were most likely to achieve VD24. Titrated low-dose oral misoprostol achieved the lowest odds of caesarean section, but there was considerable uncertainty in ranking estimates. Vaginal (≥50 µg) and buccal/sublingual misoprostol were most likely to increase uterine hyperstimulation with high uncertainty in ranking estimates. Compared with placebo, extra-amniotic prostaglandin E2 reduced NICU admissions. There were insufficient data to conduct analyses for maternal and neonatal mortality and serious morbidity or maternal satisfaction. Conclusions were robust after exclusion of studies at high risk of bias. Due to poor reporting of VD24, the cost-effectiveness analysis compared a subset of 20 interventions. There was considerable uncertainty in estimates, but buccal/sublingual and titrated (low-dose) misoprostol showed the highest probability of being most cost-effective. CONCLUSIONS: Future trials should be designed and powered to detect a method that is more cost-effective than low-dose titrated oral misoprostol. TWEETABLE ABSTRACT: New study ranks methods to induce labour in pregnant women on effectiveness and cost.

Minimal clinically important difference on the Beck Depression Inventory--II according to the patient's perspective.

BACKGROUND: The Beck Depression Inventory, 2nd edition (BDI-II) is widely used in research on depression. However, the minimal clinically important difference (MCID) is unknown. MCID can be estimated in several ways. Here we take a patient-centred approach, anchoring the change on the BDI-II to the patient's global report of improvement. METHOD: We used data collected (n = 1039) from three randomized controlled trials for the management of depression. Improvement on a 'global rating of change' question was compared with changes in BDI-II scores using general linear modelling to explore baseline dependency, assessing whether MCID is best measured in absolute terms (i.e. difference) or as percent reduction in scores from baseline (i.e. ratio), and receiver operator characteristics (ROC) to estimate MCID according to the optimal threshold above which individuals report feeling 'better'. RESULTS: Improvement in BDI-II scores associated with reporting feeling 'better' depended on initial depression severity, and statistical modelling indicated that MCID is best measured on a ratio scale as a percentage reduction of score. We estimated a MCID of a 17.5% reduction in scores from baseline from ROC analyses. The corresponding estimate for individuals with longer duration depression who had not responded to antidepressants was higher at 32%. CONCLUSIONS: MCID on the BDI-II is dependent on baseline severity, is best measured on a ratio scale, and the MCID for treatment-resistant depression is larger than that for more typical depression. This has important implications for clinical trials and practice.

A Bayesian framework to account for uncertainty due to missing binary outcome data in pairwise meta-analysis.

Missing outcome data are a common threat to the validity of the results from randomised controlled trials (RCTs), which, if not analysed appropriately, can lead to misleading treatment effect estimates. Studies with missing outcome data also threaten the validity of any meta-analysis that includes them. A conceptually simple Bayesian framework is proposed, to account for uncertainty due to missing binary outcome data in meta-analysis. A pattern-mixture model is fitted, which allows the incorporation of prior information on a parameter describing the missingness mechanism. We describe several alternative parameterisations, with the simplest being a prior on the probability of an event in the missing individuals. We describe a series of structural assumptions that can be made concerning the missingness parameters. We use some artificial data scenarios to demonstrate the ability of the model to produce a bias-adjusted estimate of treatment effect that accounts for uncertainty. A meta-analysis of haloperidol versus placebo for schizophrenia is used to illustrate the model. We end with a discussion of elicitation of priors, issues with poor reporting and potential extensions of the framework. Our framework allows one to make the best use of evidence produced from RCTs with missing outcome data in a meta-analysis, accounts for any uncertainty induced by missing data and fits easily into a wider evidence synthesis framework for medical decision making.

Incidence of Chlamydia trachomatis infection in women in England: two methods of estimation.

Information on the incidence of Chlamydia trachomatis (CT) is essential for models of the effectiveness and cost-effectiveness of screening programmes. We developed two independent estimates of CT incidence in women in England: one based on an incidence study, with estimates 'recalibrated' to the general population using data on setting-specific relative risks, and allowing for clearance and re-infection during follow-up; the second based on UK prevalence data, and information on the duration of CT infection. The consistency of independent sources of data on incidence, prevalence and duration, validates estimates of these parameters. Pooled estimates of the annual incidence rate in women aged 16-24 and 16-44 years for 2001-2005 using all these data were 0·05 [95% credible interval (CrI) 0·035-0·071] and 0·021 (95% CrI 0·015-0·028), respectively. Although, the estimates apply to England, similar methods could be used in other countries. The methods could be extended to dynamic models to synthesize, and assess the consistency of data on contact and transmission rates.

An evaluation of the feasibility, cost and value of information of a multicentre randomised controlled trial of intravenous immunoglobulin for sepsis (severe sepsis and septic shock): incorporating a systematic review, meta-analysis and value of information analysis.

BACKGROUND: Sepsis is a syndrome characterised by a systemic inflammatory response to infection that leads to rapid acute organ failure and potentially rapid decline to death. Intravenous immunoglobulin (IVIG), a blood product derived from human donor blood, has been proposed as an adjuvant therapy for sepsis. OBJECTIVES: To describe current practice in the management of adult patients severely ill with sepsis (severe sepsis or septic shock) in the UK; to assess the clinical effectiveness of IVIG for severe sepsis and septic shock and to obtain the appropriate inputs for the relative efficacy parameters, and the key uncertainties associated with these parameters, required to populate the decision model; to develop a decision-analytic model structure and identify key parameter inputs consistent with the decision problem and relevant to an NHS setting; and to populate the decision model and determine the cost-effectiveness of IVIG and to estimate the value of additional primary research. DATA SOURCES: Existing literature on IVIG and severe sepsis. Existing case-mix and outcome data on critical care admissions. Survey data on management of admissions with severe sepsis. Databases searched for clinical effectiveness were Cochrane Infectious Diseases Group Specialized Trials Register, the Cochrane Trials Register, MEDLINE and EMBASE. Dates searched were 1 January 2002 to 2 October 2009 to update previous Cochrane review. Databases searched for cost-effectiveness were NHS Economic Evaluation Database (NHS EED) to 2 October 2009, MEDLINE, MEDLINE In-Process & Other Non-Indexed Citations and EMBASE to 20 October 2009. REVIEW METHODS: Systematic literature searching with data extraction, descriptive analysis and clinical effectiveness and cost-effectiveness modelling of IVIG in severe sepsis. Additional primary data analysis. Expected value of information (EVI) analysis. RESULTS: Our meta-analysis, the first to simultaneously allow for type of IVIG (IVIG or immunoglobulin M-enriched polyclonal IVIG), choice of control (no treatment or albumin), study quality/publication bias and other potential covariates, indicated that the treatment effect of IVIG on mortality for patients with severe sepsis is borderline significant with a large degree of heterogeneity in treatment effect between individual studies. Modelling indicated that there were issues with bias associated with trial methodology, publication and small-study effects with the current evidence. The large degree of heterogeneity in treatment effects between studies, however, could be explained (best-fitting model) by a measure of study quality (i.e. use of albumin as control - as an indicator of proper blinding to treatment as a proxy for study quality - associated with decreased effect) and duration of IVIG therapy (longer duration associated with increased effect). In-depth discussion within the Expert Group on duration of IVIG therapy, with daily dose and total dose also clearly inter-related, indicated no clear clinical rationale for this association and exposed a lack of evidence on the understanding of the mechanism of action of IVIG in severe sepsis. Although the EVI analyses suggested substantial expected net benefit from a large, multicentre randomised controlled trial (RCT) evaluating the clinical effectiveness of IVIG, the remaining uncertainties around the design of such a study mean that we are unable to recommend it at this time. LIMITATIONS: As has been identified in previous meta-analyses, there are issues with the methodological quality of the available evidence. CONCLUSIONS: Although the results highlight the value for money obtained in conducting further primary research in this area, the biggest limitation for such research regards the uncertainties over the mechanism of action of IVIG and the heterogeneous nature of severe sepsis. Resolving these would allow for better definition of the plausibility of the effectiveness scenarios presented and, consequently, a better understanding of the cost-effectiveness of this treatment. This information would also inform the design of future, primary evaluative research. Our recommendations for future research focus on filling the knowledge gaps to inform a future multicentre RCT prior to recommending its immediate design and conduct. FUNDING: The National Institute for Health Research Health Technology Assessment programme.

Accounting for correlation in network meta-analysis with multi-arm trials.

Multi-arm trials (trials with more than two arms) are particularly valuable forms of evidence for network meta-analysis (NMA). Trial results are available either as arm-level summaries, where effect measures are reported for each arm, or as contrast-level summaries, where the differences in effect between arms compare with the control arm chosen for the trial. We show that likelihood-based inference in both contrast-level and arm-level formats is identical if there are only two-arm trials, but that if there are multi-arm trials, results from the contrast-level format will be incorrect unless correlations are accounted for in the likelihood. We review Bayesian and frequentist software for NMA with multi-arm trials that can account for this correlation and give an illustrative example of the difference in estimates that can be introduced if the correlations are not incorporated. We discuss methods of imputing correlations when they cannot be derived from the reported results and urge trialists to report the standard error for the control arm even if only contrast-level summaries are reported. Copyright © 2012 John Wiley & Sons, Ltd.

Checking consistency in mixed treatment comparison meta-analysis.

Pooling of direct and indirect evidence from randomized trials, known as mixed treatment comparisons (MTC), is becoming increasingly common in the clinical literature. MTC allows coherent judgements on which of the several treatments is the most effective and produces estimates of the relative effects of each treatment compared with every other treatment in a network.We introduce two methods for checking consistency of direct and indirect evidence. The first method (back-calculation) infers the contribution of indirect evidence from the direct evidence and the output of an MTC analysis and is useful when the only available data consist of pooled summaries of the pairwise contrasts. The second more general, but computationally intensive, method is based on 'node-splitting' which separates evidence on a particular comparison (node) into 'direct' and 'indirect' and can be applied to networks where trial-level data are available. Methods are illustrated with examples from the literature. We take a hierarchical Bayesian approach to MTC implemented using WinBUGS and R.We show that both methods are useful in identifying potential inconsistencies in different types of network and that they illustrate how the direct and indirect evidence combine to produce the posterior MTC estimates of relative treatment effects. This allows users to understand how MTC synthesis is pooling the data, and what is 'driving' the final estimates.We end with some considerations on the modelling assumptions being made, the problems with the extension of the back-calculation method to trial-level data and discuss our methods in the context of the existing literature.

Controlling ecological bias in evidence synthesis of trials reporting on collapsed and overlapping covariate categories.

Meta-analysis of randomized controlled trials based on aggregated data is vulnerable to ecological bias if trial results are pooled over covariates that influence the outcome variable, even when the covariate does not modify the treatment effect, or is not associated with the treatment. This paper shows how, when trial results are aggregated over different levels of covariates, the within-study covariate distribution, and the effects of both covariates and treatments can be simultaneously estimated, and ecological bias reduced. Bayesian Markov chain Monte Carlo methods are used. The method is applied to a mixed treatment comparison evidence synthesis of six alternative approaches to post-stroke inpatient care. Results are compared with a model using only the stratified covariate data available, where each stratum is treated as a separate trial, and a model using fully aggregated data, where no covariate data are used.

Synthesis of survival and disease progression outcomes for health technology assessment of cancer therapies.

Studies of clinical efficacy commonly report more than one clinical endpoint. For example, randomized controlled trials of treatments for cancer will normally report time to disease progression as well as overall survival. It is likely that disease progression will be associated with higher mortality rates. Disease progression rates will also have consequences for the societal economic burden of the disease. Economic evaluation of the cost-effectiveness of different treatment regimes therefore requires the joint estimation of both disease progression and mortality. We describe a model to combine evidence from studies reporting time to event summaries for disease progression and/or mortality, motivated by a systematic review of 1st-line treatment for advanced breast cancer to provide inputs for an economic evaluation as part of the National Institute for Health and Clinical Excellence (NICE) clinical guideline on treatment of advanced breast cancer in England and Wales. The review identified a network of treatment comparisons, which provides the basis for indirect comparison. A variety of outcomes were reported: overall survival, time to progression (overall and responders only), and the proportion of responder, stable, progressive disease, and non-assessable patients. There were only five trials, and not all trials reported all outcomes. The scarcity of the available evidence required us to make strong assumptions in order to identify model parameters. However, this evidence structure often occurs in health technology assessment (HTA) of treatments for cancer. We discuss the validity of the assumptions made, and the potential to assess their validity in other applications of HTA of cancer therapies. Copyright © 2011 John Wiley & Sons, Ltd.

Antiviral drugs for the treatment of influenza: a systematic review and economic evaluation.

OBJECTIVES: To evaluate the clinical effectiveness (including adverse events) and cost-effectiveness of antivirals for the treatment of naturally acquired influenza for 'at-risk' and otherwise healthy populations. DATA SOURCES: Eleven electronic databases (MEDLINE, EMBASE, Cumulative Index to Nursing and Allied Health Literature, Pascal, Science Citation Index, BIOSIS, Latin American and Caribbean Health Sciences, Cochrane Database of Systematic Reviews, Cochrane Central Register of Controlled Trials, Database of Abstracts of Reviews of Effects, and Health Technology Assessment Database) were searched from October 2001 to November 2007. A supplementary search was undertaken in June 2008 for information relating to drug resistance during the 2007-8 influenza season. REVIEW METHODS: Systematic reviews of the evidence on the clinical effectiveness and cost-effectiveness of antivirals for the treatment of influenza were undertaken. Twenty-nine randomised controlled trials comparing antivirals with each other, placebo, or best symptomatic care were included in the evaluation of clinical effectiveness in patients presenting with an influenza-like illness (ILI). Primary outcomes were measures of symptom duration (median time to alleviation of symptoms and median time to return to normal activity). Incidence of complications, mortality, hospitalisations, antibiotic use (as a surrogate for complications) and adverse events was also assessed. In addition, an independent decision model was developed to evaluate the cost-effectiveness of antiviral treatment from the perspective of the UK NHS. RESULTS: Amantadine was excluded at an early stage, owing to a lack of any new trials that met the inclusion criteria and the limitations of the existing evidence. The review therefore focused on the neuraminidase inhibitors (NIs) oseltamivir and zanamivir, both of which were found to be effective in reducing symptom duration (zanamavir by 0.5-1.0 days and oseltamivir by 0.5-1.5 days). However, the effect sizes were often small and unlikely to be clinically significant in many cases, particularly in healthy adults. For the at-risk subgroups, effect sizes for differences in symptom duration were generally larger, and potentially more clinically significant, than those seen in healthy adults (median duration of symptoms reduced by 1-2 days with zanamivir and 0.50-0.75 days with oseltamivir). However, there was greater uncertainty around these results, with estimates often failing to reach statistical significance. The most consistent data and strongest evidence related to antibiotic use, with both zanamivir and oseltamivir resulting in statistically significant reductions in antibiotic use. In general, the estimates from the cost-effectiveness model were more favourable in at-risk populations (including adults and children with comorbid conditions and the elderly) compared with otherwise healthy populations. Zanamivir was the optimal NI treatment in each of the at-risk populations considered, and oseltamivir was optimal for healthy populations (both adults and children). CONCLUSIONS: The clinical effectiveness data for population subgroups used to inform the multiparameter evidence synthesis and cost-effectiveness modelling were, in places, limited and this should be borne in mind when interpreting the findings of this review. Trials were often not designed to determine clinical effectiveness in population subgroups and hence, although the direction of effect was clear, estimates of differences in symptom duration tended to be subject to greater uncertainty in subgroups. Despite some concerns, the use of NIs in at-risk populations appeared to be a cost-effective approach for the treatment of influenza. Well-designed observational studies might also be considered to evaluate the clinical course of influenza in terms of complications, hospitalisation, mortality and quality of life, as well as the impact of NIs.

Mixed treatment comparison with multiple outcomes reported inconsistently across trials: evaluation of antivirals for treatment of influenza A and B.

We present a mixed treatment meta-analysis of antivirals for treatment of influenza, where some trials report summary measures on at least one of the two outcomes: time to alleviation of fever and time to alleviation of symptoms. The synthesis is further complicated by the variety of summary measures reported: mean time, median time and proportion symptom free at the end of follow-up. We compare several models using the deviance information criteria and the contribution of different evidence sources to the residual deviance to aid model selection. A Weibull model with exchangeable treatment effects that are independent for each outcome but have a common random effect mean for the two outcomes gives the best fit according to these criteria. This model allows us to summarize treatment effect on two outcomes in a single summary measure and draw conclusions as to the most effective treatment. Amantadine and Oseltamivir were the most effective treatments, with the probability of being most effective of 0.56 and 0.37, respectively. Amantadine reduces the duration of symptoms by an estimated 2.8 days, and Oseltamivir 2.6 days, compared with placebo. The models provide flexible methods for synthesis of evidence on multiple treatments in the absence of head-to-head trial data, when different summary measures are used and either different clinical outcomes are reported or where the same outcomes are reported at different or multiple time points.