Determining sample size in a personalized randomized controlled (PRACTical) trial.

In clinical settings with no commonly accepted standard-of-care, multiple treatment regimens are potentially useful, but some treatments may not be appropriate for some patients. A personalized randomized controlled trial (PRACTical) design has been proposed for this setting. For a network of treatments, each patient is randomized only among treatments which are appropriate for them. The aim is to produce treatment rankings that can inform clinical decisions about treatment choices for individual patients. Here we propose methods for determining sample size in a PRACTical design, since standard power-based methods are not applicable. We derive a sample size by evaluating information gained from trials of varying sizes. For a binary outcome, we quantify how many adverse outcomes would be prevented by choosing the top-ranked treatment for each patient based on trial results rather than choosing a random treatment from the appropriate personalized randomization list. In simulations, we evaluate three performance measures: mean reduction in adverse outcomes using sample information, proportion of simulated patients for whom the top-ranked treatment performed as well or almost as well as the best appropriate treatment, and proportion of simulated trials in which the top-ranked treatment performed better than a randomly chosen treatment. We apply the methods to a trial evaluating eight different combination antibiotic regimens for neonatal sepsis (NeoSep1), in which a PRACTical design addresses varying patterns of antibiotic choice based on disease characteristics and resistance. Our proposed approach produces results that are more relevant to complex decision making by clinicians and policy makers.

Sharing information across patient subgroups to draw conclusions from sparse treatment networks.

Network meta-analysis (NMA) usually provides estimates of the relative effects with the highest possible precision. However, sparse networks with few available studies and limited direct evidence can arise, threatening the robustness and reliability of NMA estimates. In these cases, the limited amount of available information can hamper the formal evaluation of the underlying NMA assumptions of transitivity and consistency. In addition, NMA estimates from sparse networks are expected to be imprecise and possibly biased as they rely on large-sample approximations that are invalid in the absence of sufficient data. We propose a Bayesian framework that allows sharing of information between two networks that pertain to different population subgroups. Specifically, we use the results from a subgroup with a lot of direct evidence (a dense network) to construct informative priors for the relative effects in the target subgroup (a sparse network). This is a two-stage approach where at the first stage, we extrapolate the results of the dense network to those expected from the sparse network. This takes place by using a modified hierarchical NMA model where we add a location parameter that shifts the distribution of the relative effects to make them applicable to the target population. At the second stage, these extrapolated results are used as prior information for the sparse network. We illustrate our approach through a motivating example of psychiatric patients. Our approach results in more precise and robust estimates of the relative effects and can adequately inform clinical practice in presence of sparse networks.

A new approach to evaluating loop inconsistency in network meta-analysis.

In network meta-analysis, studies evaluating multiple treatment comparisons are modeled simultaneously, and estimation is informed by a combination of direct and indirect evidence. Network meta-analysis relies on an assumption of consistency, meaning that direct and indirect evidence should agree for each treatment comparison. Here we propose new local and global tests for inconsistency and demonstrate their application to three example networks. Because inconsistency is a property of a loop of treatments in the network meta-analysis, we locate the local test in a loop. We define a model with one inconsistency parameter that can be interpreted as loop inconsistency. The model builds on the existing ideas of node-splitting and side-splitting in network meta-analysis. To provide a global test for inconsistency, we extend the model across multiple independent loops with one degree of freedom per loop. We develop a new algorithm for identifying independent loops within a network meta-analysis. Our proposed models handle treatments symmetrically, locate inconsistency in loops rather than in nodes or treatment comparisons, and are invariant to choice of reference treatment, making the results less dependent on model parameterization. For testing global inconsistency in network meta-analysis, our global model uses fewer degrees of freedom than the existing design-by-treatment interaction approach and has the potential to increase power. To illustrate our methods, we fit the models to three network meta-analyses varying in size and complexity. Local and global tests for inconsistency are performed and we demonstrate that the global model is invariant to choice of independent loops.

Historical plant introductions predict current insect invasions.

Thousands of insect species have been introduced outside of their native ranges, and some of them strongly impact ecosystems and human societies. Because a large fraction of insects feed on or are associated with plants, nonnative plants provide habitat and resources for invading insects, thereby facilitating their establishment. Furthermore, plant imports represent one of the main pathways for accidental nonnative insect introductions. Here, we tested the hypothesis that plant invasions precede and promote insect invasions. We found that geographical variation in current nonnative insect flows was best explained by nonnative plant flows dating back to 1900 rather than by more recent plant flows. Interestingly, nonnative plant flows were a better predictor of insect invasions than potentially confounding socioeconomic variables. Based on the observed time lag between plant and insect invasions, we estimated that the global insect invasion debt consists of 3,442 region-level introductions, representing a potential increase of 35% of insect invasions. This debt was most important in the Afrotropics, the Neotropics, and Indomalaya, where we expect a 10 to 20-fold increase in discoveries of new nonnative insect species. Overall, our results highlight the strong link between plant and insect invasions and show that limiting the spread of nonnative plants might be key to preventing future invasions of both plants and insects.

The Personalised Randomized Controlled Trial: Evaluation of a new trial design.

In some clinical scenarios, for example, severe sepsis caused by extensively drug resistant bacteria, there is uncertainty between many common treatments, but a conventional multiarm randomized trial is not possible because individual participants may not be eligible to receive certain treatments. The Personalised Randomized Controlled Trial design allows each participant to be randomized between a "personalised randomization list" of treatments that are suitable for them. The primary aim is to produce treatment rankings that can guide choice of treatment, rather than focusing on the estimates of relative treatment effects. Here we use simulation to assess several novel analysis approaches for this innovative trial design. One of the approaches is like a network meta-analysis, where participants with the same personalised randomization list are like a trial, and both direct and indirect evidence are used. We evaluate this proposed analysis and compare it with analyses making less use of indirect evidence. We also propose new performance measures including the expected improvement in outcome if the trial's rankings are used to inform future treatment rather than random choice. We conclude that analysis of a personalized randomized controlled trial can be performed by pooling data from different types of participants and is robust to moderate subgroup-by-intervention interactions based on the parameters of our simulation. The proposed approach performs well with respect to estimation bias and coverage. It provides an overall treatment ranking list with reasonable precision, and is likely to improve outcome on average if used to determine intervention policies and guide individual clinical decisions.

Practical approaches to Bayesian sample size determination in non-inferiority trials with binary outcomes.

Bayesian analysis of a non-inferiority trial is advantageous in allowing direct probability statements to be made about the relative treatment difference rather than relying on an arbitrary and often poorly justified non-inferiority margin. When the primary analysis will be Bayesian, a Bayesian approach to sample size determination will often be appropriate for consistency with the analysis. We demonstrate three Bayesian approaches to choosing sample size for non-inferiority trials with binary outcomes and review their advantages and disadvantages. First, we present a predictive power approach for determining sample size using the probability that the trial will produce a convincing result in the final analysis. Next, we determine sample size by considering the expected posterior probability of non-inferiority in the trial. Finally, we demonstrate a precision-based approach. We apply these methods to a non-inferiority trial in antiretroviral therapy for treatment of HIV-infected children. A predictive power approach would be most accessible in practical settings, because it is analogous to the standard frequentist approach. Sample sizes are larger than with frequentist calculations unless an informative analysis prior is specified, because appropriate allowance is made for uncertainty in the assumed design parameters, ignored in frequentist calculations. An expected posterior probability approach will lead to a smaller sample size and is appropriate when the focus is on estimating posterior probability rather than on testing. A precision-based approach would be useful when sample size is restricted by limits on recruitment or costs, but it would be difficult to decide on sample size using this approach alone.

Alien insect dispersal mediated by the global movement of commodities.

Globalization and economic growth are recognized as key drivers of biological invasions. Alien species have become a feature of almost every biological community worldwide, and rates of new introductions continue to rise as the movement of people and goods accelerates. Insects are among the most numerous and problematic alien organisms, and are mainly introduced unintentionally with imported cargo or arriving passengers. However, the processes occurring prior to insect introductions remain poorly understood. We used a unique dataset of 1,902,392 border interception records from inspections at air, land, and maritime ports in Australia, New Zealand, Europe, Japan, USA, and Canada to identify key commodities associated with insect movement through trade and travel. In total, 8939 species were intercepted, and commodity association data were available for 1242 species recorded between 1960 and 2019. We used rarefaction and extrapolation methods to estimate the total species richness and diversity associated with different commodity types. Plant and wood products were the main commodities associated with insect movement across cargo, passenger baggage, and international mail. Furthermore, certain species were mainly associated with specific commodities within these, and other broad categories. More closely related species tended to share similar commodity associations, but this occurred largely at the genus level rather than within orders or families. These similarities within genera can potentially inform pathway management of new alien species. Combining interception records across regions provides a unique window into the unintentional movement of insects, and provides valuable information on establishment risks associated with different commodity types and pathways.

Once-daily dolutegravir-based antiretroviral therapy in infants and children living with HIV from age 4 weeks: results from the below 14 kg cohort in the randomised ODYSSEY trial.

BACKGROUND: Young children living with HIV have few treatment options. We aimed to assess the efficacy and safety of dolutegravir-based antiretroviral therapy (ART) in children weighing between 3 kg and less than 14 kg. METHODS: ODYSSEY is an open-label, randomised, non-inferiority trial (10% margin) comparing dolutegravir-based ART with standard of care and comprises two cohorts (children weighing ≥14 kg and <14 kg). Children weighing less than 14 kg starting first-line or second-line ART were enrolled in seven HIV treatment centres in South Africa, Uganda, and Zimbabwe. Randomisation, which was computer generated by the trial statistician, was stratified by first-line or second-line ART and three weight bands. Dispersible 5 mg dolutegravir was dosed according to WHO weight bands. The primary outcome was the Kaplan-Meier estimated proportion of children with virological or clinical failure by 96 weeks, defined as: confirmed viral load of at least 400 copies per mL after week 36; absence of virological suppression by 24 weeks followed by a switch to second-line or third-line ART; all-cause death; or a new or recurrent WHO stage 4 or severe WHO stage 3 event. The primary outcome was assessed by intention to treat in all randomly assigned participants. A primary Bayesian analysis of the difference in the proportion of children meeting the primary outcome between treatment groups incorporated evidence from the higher weight cohort (≥14 kg) in a prior distribution. A frequentist analysis was also done of the lower weight cohort (<14 kg) alone. Safety analyses are presented for all randomly assigned children in this study (<14 kg cohort). ODYSSEY is registered with ClinicalTrials.gov, NCT02259127. FINDINGS: Between July 5, 2018, and Aug 26, 2019, 85 children weighing less than 14 kg were randomly assigned to receive dolutegravir (n=42) or standard of care (n=43; 32 [74%] receiving protease inhibitor-based ART). Median age was 1·4 years (IQR 0·6-2·0) and median weight 8·1 kg (5·4-10·0). 72 (85%) children started first-line ART and 13 (15%) started second-line ART. Median follow-up was 124 weeks (112-137). By 96 weeks, treatment failure occurred in 12 children in the dolutegravir group (Kaplan-Meier estimated proportion 31%) versus 21 (48%) in the standard-of-care group. The Bayesian estimated difference in treatment failure (dolutegravir minus standard of care) was -10% (95% CI -19% to -2%; p=0·020), demonstrating superiority of dolutegravir. The frequentist estimated difference was -18% (-36% to 2%; p=0·057). 15 serious adverse events were reported in 11 (26%) children in the dolutegravir group, including two deaths, and 19 were reported in 11 (26%) children in the standard-of-care group, including four deaths (hazard ratio [HR] 1·08 [95% CI 0·47-2·49]; p=0·86). 36 adverse events of grade 3 or higher were reported in 19 (45%) children in the dolutegravir group, versus 34 events in 21 (49%) children in the standard-of-care group (HR 0·93 [0·50-1·74]; p=0·83). No events were considered related to dolutegravir. INTERPRETATION: Dolutegravir-based ART was superior to standard of care (mainly protease inhibitor-based) with a lower risk of treatment failure in infants and young children, providing support for global dispersible dolutegravir roll-out for younger children and allowing alignment of adult and paediatric treatment. FUNDING: Paediatric European Network for Treatment of AIDS Foundation, ViiV Healthcare, UK Medical Research Council.

Implications of analysing time-to-event outcomes as binary in meta-analysis: empirical evidence from the Cochrane Database of Systematic Reviews.

BACKGROUND: Systematic reviews and meta-analysis of time-to-event outcomes are frequently published within the Cochrane Database of Systematic Reviews (CDSR). However, these outcomes are handled differently across meta-analyses. They can be analysed on the hazard ratio (HR) scale or can be dichotomized and analysed as binary outcomes using effect measures such as odds ratios (OR) or risk ratios (RR). We investigated the impact of reanalysing meta-analyses from the CDSR that used these different effect measures. METHODS: We extracted two types of meta-analysis data from the CDSR: either recorded in a binary form only ("binary"), or in binary form together with observed minus expected and variance statistics ("OEV"). We explored how results for time-to-event outcomes originally analysed as "binary" change when analysed using the complementary log-log (clog-log) link on a HR scale. For the data originally analysed as HRs ("OEV"), we compared these results to analysing them as binary on a HR scale using the clog-log link or using a logit link on an OR scale. RESULTS: The pooled HR estimates were closer to 1 than the OR estimates in the majority of meta-analyses. Important differences in between-study heterogeneity between the HR and OR analyses were also observed. These changes led to discrepant conclusions between the OR and HR scales in some meta-analyses. Situations under which the clog-log link performed better than logit link and vice versa were apparent, indicating that the correct choice of the method does matter. Differences between scales arise mainly when event probability is high and may occur via differences in between-study heterogeneity or via increased within-study standard error in the OR relative to the HR analyses. CONCLUSIONS: We identified that dichotomising time-to-event outcomes may be adequate for low event probabilities but not for high event probabilities. In meta-analyses where only binary data are available, the complementary log-log link may be a useful alternative when analysing time-to-event outcomes as binary, however the exact conditions need further exploration. These findings provide guidance on the appropriate methodology that should be used when conducting such meta-analyses.

Borrowing information across patient subgroups in clinical trials, with application to a paediatric trial.

BACKGROUND: Clinical trial investigators may need to evaluate treatment effects in a specific subgroup (or subgroups) of participants in addition to reporting results of the entire study population. Such subgroups lack power to detect a treatment effect, but there may be strong justification for borrowing information from a larger patient group within the same trial, while allowing for differences between populations. Our aim was to develop methods for eliciting expert opinions about differences in treatment effect between patient populations, and to incorporate these opinions into a Bayesian analysis. METHODS: We used an interaction parameter to model the relationship between underlying treatment effects in two subgroups. Elicitation was used to obtain clinical opinions on the likely values of the interaction parameter, since this parameter is poorly informed by the data. Feedback was provided to experts to communicate how uncertainty about the interaction parameter corresponds with relative weights allocated to subgroups in the Bayesian analysis. The impact on the planned analysis was then determined. RESULTS: The methods were applied to an ongoing non-inferiority trial designed to compare antiretroviral therapy regimens in 707 children living with HIV and weighing ≥ 14 kg, with an additional group of 85 younger children weighing < 14 kg in whom the treatment effect will be estimated separately. Expert clinical opinion was elicited and demonstrated that substantial borrowing is supported. Clinical experts chose on average to allocate a relative weight of 78% (reduced from 90% based on sample size) to data from children weighing ≥ 14 kg in a Bayesian analysis of the children weighing < 14 kg. The total effective sample size in the Bayesian analysis was 386 children, providing 84% predictive power to exclude a difference of more than 10% between arms, whereas the 85 younger children weighing < 14 kg provided only 20% power in a standalone frequentist analysis. CONCLUSIONS: Borrowing information from a larger subgroup or subgroups can facilitate estimation of treatment effects in small subgroups within a clinical trial, leading to improved power and precision. Informative prior distributions for interaction parameters are required to inform the degree of borrowing and can be informed by expert opinion. We demonstrated accessible methods for obtaining opinions.

Worldwide border interceptions provide a window into human-mediated global insect movement.

As part of national biosecurity programs, cargo imports, passenger baggage, and international mail are inspected at ports of entry to verify compliance with phytosanitary regulations and to intercept potentially damaging nonnative species to prevent their introduction. Detection of organisms during inspections may also provide crucial information about the species composition and relative arrival rates in invasion pathways that can inform the implementation of other biosecurity practices such as quarantines and surveillance. In most regions, insects are the main taxonomic group encountered during inspections. We gathered insect interception data from nine world regions collected from 1995 to 2019 to compare the composition of species arriving at ports in these regions. Collectively, 8,716 insect species were intercepted in these regions over the last 25 yr, with the combined international data set comprising 1,899,573 interception events, of which 863,972 were identified to species level. Rarefaction analysis indicated that interceptions comprise only a small fraction of species present in invasion pathways. Despite differences in inspection methodologies, as well as differences in the composition of import source regions and imported commodities, we found strong positive correlations in species interception frequencies between regions, particularly within the Hemiptera and Thysanoptera. There were also significant differences in species frequencies among insects intercepted in different regions. Nevertheless, integrating interception data among multiple regions would be valuable for estimating invasion risks for insect species with high likelihoods of introduction as well as for identifying rare but potentially damaging species.

Personalised randomised controlled trial designs-a new paradigm to define optimal treatments for carbapenem-resistant infections.

Antimicrobial resistance is impacting treatment decisions for, and patient outcomes from, bacterial infections worldwide, with particular threats from infections with carbapenem-resistant Enterobacteriaceae, Acinetobacter baumanii, or Pseudomonas aeruginosa. Numerous areas of clinical uncertainty surround the treatment of these highly resistant infections, yet substantial obstacles exist to the design and conduct of treatment trials for carbapenem-resistant bacterial infections. These include the lack of a widely acceptable optimised standard of care and control regimens, varying antimicrobial susceptibilities and clinical contraindications making specific intervention regimens infeasible, and diagnostic and recruitment challenges. The current single comparator trials are not designed to answer the urgent public health question, identified as a high priority by WHO, of what are the best regimens out of the available options that will significantly reduce morbidity, costs, and mortality. This scenario has an analogy in network meta-analysis, which compares multiple treatments in an evidence synthesis to rank the best of a set of available treatments. To address these obstacles, we propose extending the network meta-analysis approach to individual randomisation of patients. We refer to this approach as a Personalised RAndomised Controlled Trial (PRACTical) design that compares multiple treatments in an evidence synthesis, to identify, overall, which is the best treatment out of a set of available treatments to recommend, or how these different treatments rank against each other. In this Personal View, we summarise the design principles of personalised randomised controlled trial designs. Specifically, of a network of different potential regimens for life-threatening carbapenem-resistant infections, each patient would be randomly assigned only to regimens considered clinically reasonable for that patient at that time, incorporating antimicrobial susceptibility, toxicity profile, pharmacometric properties, availability, and physician assessment. Analysis can use both direct and indirect comparisons across the network, analogous to network meta-analysis. This new trial design will maximise the relevance of the findings to each individual patient, and enable the top-ranked regimens from any personalised randomisation list to be identified, in terms of both efficacy and safety.

MultiBUGS: A Parallel Implementation of the BUGS Modelling Framework for Faster Bayesian Inference.

MultiBUGS is a new version of the general-purpose Bayesian modelling software BUGS that implements a generic algorithm for parallelising Markov chain Monte Carlo (MCMC) algorithms to speed up posterior inference of Bayesian models. The algorithm parallelises evaluation of the product-form likelihoods formed when a parameter has many children in the directed acyclic graph (DAG) representation; and parallelises sampling of conditionally-independent sets of parameters. A heuristic algorithm is used to decide which approach to use for each parameter and to apportion computation across computational cores. This enables MultiBUGS to automatically parallelise the broad range of statistical models that can be fitted using BUGS-language software, making the dramatic speed-ups of modern multi-core computing accessible to applied statisticians, without requiring any experience of parallel programming. We demonstrate the use of MultiBUGS on simulated data designed to mimic a hierarchical e-health linked-data study of methadone prescriptions including 425,112 observations and 20,426 random effects. Posterior inference for the e-health model takes several hours in existing software, but MultiBUGS can perform inference in only 28 minutes using 48 computational cores.

Considering unseen arrivals in predictions of establishment risk based on border biosecurity interceptions.

Assessing species establishment risk is an important task used for informing biosecurity activities aimed at preventing biological invasions. Propagule pressure is a major contributor to the probability of invading species establishment; however, direct assessment of numbers of individuals arriving is virtually never possible. Inspections conducted at borders by biosecurity officials record counts of species (or higher-level taxa) intercepted during inspections, which can be used as proxies for arrival rates. Such data may therefore be useful for predicting species establishments, though some species may establish despite never being intercepted. We present a stochastic process-based model of the arrival-interception-establishment process to predict species establishment risk from interception count data. The model can be used to estimate the probability of establishment, both for species that were intercepted and species that had no interceptions during a given observation period. We fit the stochastic model to data on two insect families, Cerambycidae and Aphididae, that were intercepted and/or established in the United States or New Zealand. We also explore the effects of variation in model parameters and the inclusion of an Allee effect in the establishment probability. Although interception data sets contain much noise due to variation in inspection policy, interception effort and among-species differences in detectability, our study shows that it is possible to use such data for predicting establishments and distinguishing differences in establishment risk profile between taxonomic groups. Our model provides a method for predicting the number of species that have breached border biosecurity, including both species detected during inspections but also "unseen arrivals" that have never been intercepted, but have not yet established a viable population. These estimates could inform prioritization of different taxonomic groups, pathways or identification effort in biosecurity programs.

Agreement was moderate between data-based and opinion-based assessments of biases affecting randomized trials within meta-analyses.

BACKGROUND AND OBJECTIVE: Randomized trials included in meta-analyses are often affected by bias caused by methodological flaws or limitations, but the degree of bias is unknown. Two proposed methods adjust the trial results for bias using empirical evidence from published meta-epidemiological studies or expert opinion. METHODS: We investigated agreement between data-based and opinion-based approaches to assessing bias in each of four domains: sequence generation, allocation concealment, blinding, and incomplete outcome data. From each sampled meta-analysis, a pair of trials with the highest and lowest empirical model-based bias estimates was selected. Independent assessors were asked which trial within each pair was judged more biased on the basis of detailed trial design summaries. RESULTS: Assessors judged trials to be equally biased in 68% of pairs evaluated. When assessors judged one trial as more biased, the proportion of judgments agreeing with the model-based ranking was highest for allocation concealment (79%) and blinding (79%) and lower for sequence generation (59%) and incomplete outcome data (56%). CONCLUSION: Most trial pairs found to be discrepant empirically were judged to be equally biased by assessors. We found moderate agreement between opinion and data-based evidence in pairs where assessors ranked one trial as more biased.

Handling an uncertain control group event risk in non-inferiority trials: non-inferiority frontiers and the power-stabilising transformation.

BACKGROUND: Non-inferiority trials are increasingly used to evaluate new treatments that are expected to have secondary advantages over standard of care, but similar efficacy on the primary outcome. When designing a non-inferiority trial with a binary primary outcome, the choice of effect measure for the non-inferiority margin (e.g. risk ratio or risk difference) has an important effect on sample size calculations; furthermore, if the control event risk observed is markedly different from that assumed, the trial can quickly lose power or the results become difficult to interpret. METHODS: We propose a new way of designing non-inferiority trials to overcome the issues raised by unexpected control event risks. Our proposal involves using clinical judgement to specify a 'non-inferiority frontier', i.e. a curve defining the most appropriate non-inferiority margin for each possible value of control event risk. Existing trials implicitly use frontiers defined by a fixed risk ratio or a fixed risk difference. We discuss their limitations and propose a fixed arcsine difference frontier, using the power-stabilising transformation for binary outcomes, which may better represent clinical judgement. We propose and compare three ways of designing a trial using this frontier: testing and reporting on the arcsine scale; testing on the arcsine scale but reporting on the risk difference or risk ratio scale; and modifying the margin on the risk difference or risk ratio scale after observing the control event risk according to the power-stabilising frontier. RESULTS: Testing and reporting on the arcsine scale leads to results which are challenging to interpret clinically. For small values of control event risk, testing on the arcsine scale and reporting results on the risk difference scale produces confidence intervals at a higher level than the nominal one or non-inferiority margins that are slightly smaller than those back-calculated from the power-stabilising frontier alone. However, working on the arcsine scale generally requires a larger sample size compared to the risk difference scale. Therefore, working on the risk difference scale, modifying the margin after observing the control event risk, might be preferable, as it requires a smaller sample size. However, this approach tends to slightly inflate type I error rate; a solution is to use a slightly lower significance level for testing, although this modestly reduces power. When working on the risk ratio scale instead, the same approach based on the modification of the margin leads to power levels above the nominal one, maintaining type I error under control. CONCLUSIONS: Our proposed methods of designing non-inferiority trials using power-stabilising non-inferiority frontiers make trial design more resilient to unexpected values of the control event risk, at the only cost of requiring somewhat larger sample sizes when the goal is to report results on the risk difference scale.

A comparison of arm-based and contrast-based models for network meta-analysis.

Differences between arm-based (AB) and contrast-based (CB) models for network meta-analysis (NMA) are controversial. We compare the CB model of Lu and Ades (2006), the AB model of Hong et al(2016), and two intermediate models, using hypothetical data and a selected real data set. Differences between models arise primarily from study intercepts being fixed effects in the Lu-Ades model but random effects in the Hong model, and we identify four key difference. (1) If study intercepts are fixed effects then only within-study information is used, but if they are random effects then between-study information is also used and can cause important bias. (2) Models with random study intercepts are suitable for deriving a wider range of estimands, eg, the marginal risk difference, when underlying risk is derived from the NMA data; but underlying risk is usually best derived from external data, and then models with fixed intercepts are equally good. (3) The Hong model allows treatment effects to be related to study intercepts, but the Lu-Ades model does not. (4) The Hong model is valid under a more relaxed missing data assumption, that arms (rather than contrasts) are missing at random, but this does not appear to reduce bias. We also describe an AB model with fixed study intercepts and a CB model with random study intercepts. We conclude that both AB and CB models are suitable for the analysis of NMA data, but using random study intercepts requires a strong rationale such as relating treatment effects to study intercepts.