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Randomised controlled trials of cancer treatments typically report progression free survival (PFS) and overall survival (OS) outcomes. Existing methods to synthesise evidence on PFS and OS either rely on the proportional hazards assumption or make parametric assumptions which may not capture the diverse survival curve shapes across studies and treatments. Furthermore, PFS and OS are not independent; OS is the sum of PFS and post-progression survival (PPS). Our aim was to develop a non-parametric approach for jointly synthesising evidence from published Kaplan-Meier survival curves of PFS and OS without assuming proportional hazards. Restricted mean survival times (RMST) are estimated by the area under the survival curves (AUCs) up to a restricted follow-up time. The correlation between AUCs due to the constraint that OS > PFS is estimated using bootstrap re-sampling. Network meta-analysis models are given for RMST for PFS and PPS and ensure that OS = PFS + PPS. Both additive and multiplicative network meta-analysis models are presented to obtain relative treatment effects as either differences or ratios of RMST. The methods are illustrated with a network meta-analysis of treatments for stage IIIA-N2 non-small cell lung cancer. The approach has implications for health economic models of cancer treatments, which require estimates of the mean time spent in the PFS and PPS health-states. The methods can be applied to a single time-to-event outcome, and so have wide applicability in any field where time-to-event outcomes are reported, the proportional hazards assumption is in doubt, and survival curve shapes differ across studies and interventions.

We respond to discussant comments on our paper “Twenty years of network meta‐analysis: Continuing controversies and recent developments” (https://doi.org/10.1002/jrsm.1700) and raise some additional points for consideration, including: the way in which methodological guidance is generated; integration of the estimand framework with evidence synthesis; and implications of the European Joint Clinical Assessment. We ask: what properties are required of population adjustment methods to enable transparent and consistent decision‐making? We also ask why individual patient data is not routinely made available to re‐imbursement authorities and clinical guideline developers. [ABSTRACT FROM AUTHOR]

Background People with comorbidities are underrepresented in clinical trials. Empirical estimates of treatment effect modification by comorbidity are lacking, leading to uncertainty in treatment recommendations. We aimed to produce estimates of treatment effect modification by comorbidity using individual participant data (IPD). Methods and findings We obtained IPD for 120 industry-sponsored phase 3/4 trials across 22 index conditions (n = 128,331). Trials had to be registered between 1990 and 2017 and have recruited [greater than or equal to]300 people. Included trials were multicentre and international. For each index condition, we analysed the outcome most frequently reported in the included trials. We performed a two-stage IPD meta-analysis to estimate modification of treatment effect by comorbidity. First, for each trial, we modelled the interaction between comorbidity and treatment arm adjusted for age and sex. Second, for each treatment within each index condition, we meta-analysed the comorbidity-treatment interaction terms from each trial. We estimated the effect of comorbidity measured in 3 ways: (i) the number of comorbidities (in addition to the index condition); (ii) presence or absence of the 6 commonest comorbid diseases for each index condition; and (iii) using continuous markers of underlying conditions (e.g., estimated glomerular filtration rate (eGFR)). Treatment effects were modelled on the usual scale for the type of outcome (absolute scale for numerical outcomes, relative scale for binary outcomes). Mean age in the trials ranged from 37.1 (allergic rhinitis trials) to 73.0 (dementia trials) and percentage of male participants range from 4.4% (osteoporosis trials) to 100% (benign prostatic hypertrophy trials). The percentage of participants with 3 or more comorbidities ranged from 2.3% (allergic rhinitis trials) to 57% (systemic lupus erythematosus trials). We found no evidence of modification of treatment efficacy by comorbidity, for any of the 3 measures of comorbidity. This was the case for 20 conditions for which the outcome variable was continuous (e.g., change in glycosylated haemoglobin in diabetes) and for 3 conditions in which the outcomes were discrete events (e.g., number of headaches in migraine). Although all were null, estimates of treatment effect modification were more precise in some cases (e.g., sodium-glucose co-transporter-2 (SGLT2) inhibitors for type 2 diabetes-interaction term for comorbidity count 0.004, 95% CI -0.01 to 0.02) while for others credible intervals were wide (e.g., corticosteroids for asthma-interaction term -0.22, 95% CI -1.07 to 0.54). The main limitation is that these trials were not designed or powered to assess variation in treatment effect by comorbidity, and relatively few trial participants had >3 comorbidities. Conclusions Assessments of treatment effect modification rarely consider comorbidity. Our findings demonstrate that for trials included in this analysis, there was no empirical evidence of treatment effect modification by comorbidity. The standard assumption used in evidence syntheses is that efficacy is constant across subgroups, although this is often criticised. Our findings suggest that for modest levels of comorbidities, this assumption is reasonable. Thus, trial efficacy findings can be combined with data on natural history and competing risks to assess the likely overall benefit of treatments in the context of comorbidity., Author(s): Peter Hanlon 1, Elaine W. Butterly 1, Anoop SV Shah 2, Laurie J. Hannigan 3,4,5, Jim Lewsey 1, Frances S. Mair 1, David M. Kent 6, Bruce Guthrie 7, [...]

Time-course model-based network meta-analysis (MBNMA) has been proposed as a framework to combine treatment comparisons from a network of randomized controlled trials reporting outcomes at multiple time-points. This can explain heterogeneity/inconsistency that arises by pooling studies with different follow-up times and allow inclusion of studies from earlier in drug development. The aim of this study is to explore using simulation: (a) how MBNMA model parameters are affected by the quantity/location of observed time-points across studies/comparisons, (b) how reliably an appropriate MBNMA model can be identified, (c) the robustness of model estimates and predictions under different dataset characteristics. Our results indicate that model parameters for a given treatment comparison are estimated with low mean bias even when no direct evidence was available, provided there was sufficient indirect evidence to estimate the time-course. A staged model selection strategy that selects time-course function, then heterogeneity, then covariance structure, identified the true model most reliably and efficiently. Predictions and parameter estimates from selected models had low mean bias even in the presence of high heterogeneity/correlation between time-points. However, failure to properly account for heterogeneity/correlation could lead to high error in precision of the estimates. Time-course MBNMA provides a statistically robust framework for synthesizing direct and indirect evidence to estimate relative effects and predicted mean responses whilst accounting for time-course and incorporating correlation and heterogeneity. This supports the use of MBNMA in evidence synthesis, particularly when additional studies are available with follow-up times that would otherwise prohibit their inclusion by conventional meta-analysis.

Indirect comparisons are used to obtain estimates of relative effectiveness between two treatments that have not been compared in the same randomized controlled trial, but have instead been compared against a common comparator in separate trials. Standard indirect comparisons use only aggregate data, under the assumption that there are no differences in effect-modifying variables between the trial populations. Population-adjusted indirect comparisons aim to relax this assumption by using individual patient data (IPD) from one trial to adjust for differences in effect modifiers between populations. At present, the most commonly used approach is matching-adjusted indirect comparison (MAIC), where weights are estimated that match the covariate distributions of the reweighted IPD to the aggregate trial. MAIC was originally proposed using the method of moments to estimate the weights, but more recently entropy balancing has been proposed as an alternative. Entropy balancing has an additional "optimality" property ensuring that the weights are as uniform as possible, reducing the standard error of the estimates. In this brief method note, we show that MAIC weights are mathematically identical whether estimated using entropy balancing or the method of moments. Importantly, this means that the standard MAIC (based on the method of moments) also enjoys the "optimality" property. Moreover, the additional flexibility of entropy balancing suggests several interesting avenues for further research, such as combining population adjustment via MAIC with adjustments for treatment switching or nonparametric covariate adjustment.

This paper considers the problem in aggregate data meta-analysis of studies reporting multiple competing binary outcomes and of studies using different summary formats for those outcomes. For example, some may report numbers of patients with at least one of each outcome while others may report the total number of such outcomes. We develop a shared parameter model on hazard ratio scale accounting for different data summaries and competing risks. We adapt theoretical arguments from the literature to demonstrate that the models are equivalent if events are rare. We use constructed data examples and a simulation study to find an event rate threshold of approximately 0.2 above which competing risks and different data summaries may bias results if no adjustments are made. Below this threshold, simpler models may be sufficient. We recommend analysts to consider the absolute event rates and only use a simple model ignoring data types and competing risks if all of underlying events are rare (below our threshold of approximately 0.2). If one or more of the absolute event rates approaches or exceeds our informal threshold, it may be necessary to account for data types and competing risks through a shared parameter model in order to avoid biased estimates.

Background Health-related quality of life metrics evaluate treatments in ways that matter to patients, so are often included in randomised clinical trials (hereafter trials). Multimorbidity, where individuals have 2 or more conditions, is negatively associated with quality of life. However, whether multimorbidity predicts change over time or modifies treatment effects for quality of life is unknown. Therefore, clinicians and guideline developers are uncertain about the applicability of trial findings to people with multimorbidity. We examined whether comorbidity count (higher counts indicating greater multimorbidity) (i) is associated with quality of life at baseline; (ii) predicts change in quality of life over time; and/or (iii) modifies treatment effects on quality of life. Methods and findings Included trials were registered on the United States trials registry for selected index medical conditions and drug classes, phase 2/3, 3 or 4, had [greater than or equal to]300 participants, a nonrestrictive upper age limit, and were available on 1 of 2 trial repositories on 21 November 2016 and 18 May 2018, respectively. Of 124 meeting these criteria, 56 trials (33,421 participants, 16 index conditions, and 23 drug classes) collected a generic quality of life outcome measure (35 EuroQol-5 dimension (EQ-5D), 31 36-item short form survey (SF-36) with 10 collecting both). Blinding and completeness of follow up were examined for each trial. Using trials where individual participant data (IPD) was available from 2 repositories, a comorbidity count was calculated from medical history and/or prescriptions data. Linear regressions were fitted for the association between comorbidity count and (i) quality of life at baseline; (ii) change in quality of life during trial follow up; and (iii) treatment effects on quality of life. These results were then combined in Bayesian linear models. Posterior samples were summarised via the mean, 2.5th and 97.5th percentiles as credible intervals (95% CI) and via the proportion with values less than 0 as the probability (P.sub.Bayes) of a negative association. All results are in standardised units (obtained by dividing the EQ-5D/SF-36 estimates by published population standard deviations). Per additional comorbidity, adjusting for age and sex, across all index conditions and treatment comparisons, comorbidity count was associated with lower quality of life at baseline and with a decline in quality of life over time (EQ-5D -0.02 [95% CI -0.03 to -0.01], P.sub.Bayes > 0.999). Associations were similar, but with wider 95% CIs crossing the null for SF-36-PCS and SF-36-MCS (-0.05 [-0.10 to 0.01], P.sub.Bayes = 0.956 and -0.05 [-0.10 to 0.01], P.sub.Bayes = 0.966, respectively). Importantly, there was no evidence of any interaction between comorbidity count and treatment efficacy for either EQ-5D or SF-36 (EQ-5D -0.0035 [95% CI -0.0153 to -0.0065], P.sub.Bayes = 0.746; SF-36-MCS (-0.0111 [95% CI -0.0647 to 0.0416], P.sub.Bayes = 0.70 and SF-36-PCS -0.0092 [95% CI -0.0758 to 0.0476], P.sub.Bayes = 0.631. Conclusions Treatment effects on quality of life did not differ by multimorbidity (measured via a comorbidity count) at baseline-for the medical conditions studied, types and severity of comorbidities and level of quality of life at baseline, suggesting that evidence from clinical trials is likely to be applicable to settings with (at least modestly) higher levels of comorbidity. Trial registration A prespecified protocol was registered on PROSPERO (CRD42018048202)., Author(s): Elaine W. Butterly 1, Peter Hanlon 1, Anoop S. V. Shah 2, Laurie J. Hannigan 3,4,5, Emma McIntosh 1, Jim Lewsey 1, Sarah H. Wild 6, Bruce Guthrie 6, [...]

When numerous treatments exist for a disease (Treatments 1, 2, 3, etc), network meta-regression (NMR) examines whether each relative treatment effect (eg, mean difference for 2 vs 1, 3 vs 1, and 3 vs 2) differs according to a covariate (eg, disease severity). Two consistency assumptions underlie NMR: consistency of the treatment effects at the covariate value 0 and consistency of the regression coefficients for the treatment by covariate interaction. The NMR results may be unreliable when the assumptions do not hold. Furthermore, interactions may exist but are not found because inconsistency of the coefficients is masking them, for example, when the treatment effect increases as the covariate increases using direct evidence but the effect decreases with the increasing covariate using indirect evidence. We outline existing NMR models that incorporate different types of treatment by covariate interaction. We then introduce models that can be used to assess the consistency assumptions underlying NMR for aggregate data. We extend existing node-splitting models, the unrelated mean effects inconsistency model, and the design by treatment inconsistency model to incorporate covariate interactions. We propose models for assessing both consistency assumptions simultaneously and models for assessing each of the assumptions in turn to gain a more thorough understanding of consistency. We apply the methods in a Bayesian framework to trial-level data comparing antimalarial treatments using the covariate average age and to four fabricated data sets to demonstrate key scenarios. We discuss the pros and cons of the methods and important considerations when applying models to aggregated data.

Background: Model-based meta-analysis (MBMA) is increasingly used to inform drug-development decisions by synthesising results from multiple studies to estimate treatment, dose-response, and time-course characteristics. Network meta-analysis (NMA) is used in Health Technology Appraisals for simultaneously comparing effects of multiple treatments, to inform reimbursement decisions. Recently, a framework for dose-response model-based network meta-analysis (MBNMA) has been proposed that combines, often nonlinear, MBMA modelling with the statistically robust properties of NMA. Here, we aim to extend this framework to time-course models. Methods: We propose a Bayesian time-course MBNMA modelling framework for continuous summary outcomes that allows for nonlinear modelling of multiparameter time-course functions, accounts for residual correlation between observations, preserves randomisation by modelling relative effects, and allows for testing of inconsistency between direct and indirect evidence on the time-course parameters. We demonstrate our modelling framework using an illustrative dataset of 23 trials investigating treatments for pain in osteoarthritis. Results: Of the time-course functions that we explored, the Emax model gave the best fit to the data and has biological plausibility. Some simplifying assumptions were needed to identify the ET50, due to few observations at early follow-up times. Treatment estimates were robust to the inclusion of correlations in the likelihood. Conclusions: Time-course MBNMA provides a statistically robust framework for synthesising evidence on multiple treatments at multiple time points. The use of placebo-controlled studies in drug-development means there is limited potential for inconsistency. The methods can inform drug-development decisions and provide the rigour needed in the reimbursement decision-making process.

Network meta-analysis compares multiple treatments from studies that form a connected network of evidence. However, for complex networks, it is not easy to see if the network is connected. We use simple techniques from graph theory to test the connectedness of evidence networks in network meta-analysis. The method is to build the adjacency matrix for a network, with rows and columns corresponding to the treatments in the network and entries being one or zero depending on whether the treatments have been compared or not, and with zeros along the diagonal. Manipulation of this matrix gives the indirect connection matrix. The entries of this matrix determine whether two treatments can be compared, directly or indirectly. We also describe the distance matrix, which gives the minimum number of steps in the network required to compare a pair of treatments. This is a useful assessment of an indirect comparison as each additional step requires further assumptions of homogeneity in, for example, design and target populations of included trials. If there are no loops in the network, the distance is a measure of the degree of assumptions needed; it is approximately this with loops. We illustrate our methods using several constructed examples and giving R code for computation. We have also implemented the techniques in the Stata package "network." The methods provide a fast way to ensure comparisons are only made between connected treatments and to assess the degree of indirectness of a comparison.

Objective To generate global and regional estimates for the prevalence and incidence of herpes simplex virus (HSV) type 1 and type 2 infection for 2016. Methods To obtain data, we undertook a systematic review to identify studies up to August 2018. Adjustments were made to account for HSV test sensitivity and specificity. For each World Health Organization (WHO) region, we applied a constant incidence model to pooled prevalence by age and sex to estimate the prevalence and incidence of HSV types 1 and 2 infections. For HSV type 1, we apportioned infection by anatomical site using pooled estimates of the proportions that were oral and genital. Findings In 2016, an estimated 491.5 million people (95% uncertainty interval, UI: 430.4 million-610.6 million) were living with HSV type 2 infection, equivalent to 13.2% of the world's population aged 15-49 years. An estimated 3752.0 million people (95% UI: 3555.5 million-3854.6 million) had HSV type 1 infection at any site, equivalent to a global prevalence of 66.6% in 0-49-year-olds. Differing patterns were observed by age, sex and geographical region, with HSV type 2 prevalence being highest among women and in the WHO African Region. Conclusion An estimated half a billion people had genital infection with HSV type 2 or type 1, and several billion had oral HSV type 1 infection. Millions of people may also be at higher risk of acquiring human immunodeficiency virus (HIV), particularly women in the WHO African Region who have the highest HSV type 2 prevalence and exposure to HIV. [phrase omitted] [phrase omitted] Objectif Estimer la prevalence et l'incidence, au niveau regional et mondial, des infections au virus Herpes simplex (HSV) de type 1 et de type 2 en 2016. Methodes Pour nous procurer les donnees necessaires, nous avons entrepris une revue systematique afin d'identifier des etudes publiees en aout 2018 au plus tard. Des ajustements ont ete effectues pour tenir compte de la sensibilite et de la specificite du depistage HSV. Pour chaque region definie par l'Organisation mondiale de la Sante (OMS), nous avons applique un modele d'incidence constante par groupe de prevalence en fonction de l'age et du sexe. Notre but etait d'estimer la prevalence et l'incidence des infections a HSV de type 1 et 2. Pour le HSV de type 1, nous avons reparti les infections selon le site anatomique, en utilisant des estimations groupees de la proportion d'atteintes orales et genitales. Resultats En 2016, environ 491,5 millions de personnes (intervalle d'incertitude de 95%: 430,4 millions--610,6 millions) vivaient avec une infection a HSV de type 2, l'equivalent de 13,2 % de la population mondiale entre 15 et 49 ans. Nous estimons que 3752,0 millions de personnes (intervalle d'incertitude de 95%: 3555,5 millions-3854,6 millions) souffraient d'une infection a HSV de type 1 a un site quelconque, ce qui represente une prevalence globale de 66,6% chez les 0-49 ans. Differentes tendances ont ete constatees en fonction de l'age, du sexe et de la zone geographique, le plus fort taux de prevalence de HSV de type 2 etant observe chez les femmes de la region Afrique de l'OMS. Conclusion Pres d'un demi-milliard de personnes presentaient une infection genitale a HSV de type 2 ou type 1, et plusieurs milliards avaient une infection orale a HSV de type 1. Des millions de personnes pourraient egalement etre plus susceptibles de contracter le virus de l'immunodeficience humaine (VIH), en particulier les femmes de la region Afrique de l'OMS qui possedent la plus grande prevalence de HSV de type 2 et sont davantage exposees au VIH. [phrase omitted] Objetivo Calcular las estimaciones mundiales y regionales de la prevalencia y la incidencia de la infeccion por el virus del herpes simple (VHS) tipo 1 y tipo 2 para 2016. Metodos Se realizo una revision sistematica para identificar los estudios hasta agosto de 2018 con el fin de obtener datos. Se hicieron ajustes para tener en cuenta la sensibilidad y la especificidad de la prueba de VHS. Se aplico un modelo de incidencia constante para cada region de la Organizacion Mundial de la Salud (OMS) con el fin de agrupar la prevalencia por edad y sexo para estimar la prevalencia y la incidencia de las infecciones por VHS de los tipos 1 y 2. Para el VHS tipo 1, se repartio la infeccion por sitio anatomico utilizando estimaciones agrupadas de los porcentajes que eran orales y genitales. Resultados En 2016, se estima que 491,5 millones de personas (95 % de intervalo de incertidumbre, UI: 430,4 millones a 610,6 millones) vivian con la infeccion por el VHS tipo 2, equivalente al 13,2 % de la poblacion mundial de 15 a 49 anos. Se estima que 3752,0 millones de personas (95 % UI: 3555,5 millones a 3854,6 millones) tenian la infeccion por VHS tipo 1 sin importar el lugar, lo que equivale a una prevalencia mundial del 66,6 % en las personas de 0 a 49 anos. Se observaron patrones diferentes segun la edad, el sexo y la region geografica, siendo la mayor prevalencia del VHS tipo 2 entre las mujeres y en la region de Africa de la OMS. Conclusion Se estima que 500 millones de personas tienen una infeccion genital con VHS tipo 2 o tipo 1, y varios miles de millones tienen una infeccion oral de VHS tipo 1. Millones de personas tambien pueden correr un mayor riesgo de contraer el virus de la inmunodeficiencia humana (VIH), en particular las mujeres de la Region de Africa de la OMS que tienen la mayor prevalencia del VHS tipo 2 y la mayor exposicion al VIH., Introduction Herpes simplex virus (HSV) infections are widespread among humans globally. (1,2) The infection is lifelong and characterized by periodic reactivations at the infection site. HSV type 1 is primarily [...]

Background: Meta-regression results must be interpreted taking into account the range of covariate values of the contributing studies. Results based on interpolation or extrapolation may be unreliable. In network meta-regression (NMR) models, which include covariates in network meta-analyses, results are estimated using direct and indirect evidence; therefore, it may be unclear which studies and covariate values contribute to which result. We propose graphs to help understand which trials and covariate values contribute to each NMR result and to highlight extrapolation or interpolation. Methods: We introduce methods to calculate the contribution that each trial and covariate value makes to each result and compare them with existing methods. We show how to construct graphs including a network covariate distribution diagram, covariate-contribution plot, heat plot, contribution-NMR plot, and heat-NMR plot. We demonstrate the methods using a dataset with treatments for malaria using the covariate "average age" and a dataset of topical fluoride interventions for preventing dental caries using the covariate "randomisation year." Results: For the malaria dataset, no contributing trials had an average age between 7-25 years and therefore results were interpolated within this range. For the fluoride dataset, there are no contributing trials randomised between 1954-1959 for most comparisons therefore, within this range, results would be extrapolated. Conclusions: Even in a fully connected network, an NMR result may be estimated from trials with a narrower covariate range than the range of the whole dataset. Calculating contributions and graphically displaying them aids interpretation of NMR result by highlighting extrapolated or interpolated results.

Background: Many reviews aim to compare numerous treatments and report results stratified by subgroups (eg, by disease severity). In such cases, a network meta-analysis model including treatment by covariate interactions can estimate the relative effects of all treatment pairings for each subgroup of patients. Two key assumptions underlie such models: consistency of treatment effects and consistency of the regression coefficients for the interactions. Consistency may differ depending on the covariate value at which consistency is assessed. For valid inference, we need to be confident of consistency for the relevant range of covariate values. In this paper, we demonstrate how to assess consistency of treatment effects from direct and indirect evidence at various covariate values. Methods: Consistency is assessed using visual inspection, inconsistency estimates, and probabilities. The method is applied to an individual patient dataset comparing artemisinin combination therapies for treating uncomplicated malaria in children using the covariate age. Results: The magnitude of the inconsistency appears to be decreasing with increasing age for each comparison. For one comparison, direct and indirect evidence differ for age 1 (P = 0.05), and this brings results for age 1 for all comparisons into question. Conclusion: When fitting models including interactions, the consistency of direct and indirect evidence must be assessed across the range of covariates included in the trials. Clinical inferences are only valid for covariate values for which results are consistent.