Hierarchical network meta-analysis models to address sparsity of events and differing treatment classifications with regard to adverse outcomes

This is the accepted version of the article, which has been published in final form at DOI: 10.1002/sim.6131.Meta-analysis for adverse events resulting from medical interventions has many challenges, in part due to small numbers of such events within primary studies. Furthermore, variability in drug dose, potential differences between drugs within the same pharmaceutical class and multiple indications for a specific treatment can all add to the complexity of the evidence base. This paper explores the use of synthesis methods, incorporating mixed treatment comparisons, to estimate the risk of adverse events for a medical intervention, while acknowledging and modelling the complexity of the structure of the evidence base. The motivating example was the effect on malignancy of three anti-tumour necrosis factor (anti-TNF) drugs (etanercept, adalimumab and infliximab) indicated to treat rheumatoid arthritis. Using data derived from 13 primary studies, a series of meta-analysis models of increasing complexity were applied. Models ranged from a straightforward comparison of anti-TNF against non-anti-TNF controls, to more complex models in which a treatment was defined by individual drug and its dose. Hierarchical models to allow 'borrowing strength' across treatment classes and dose levels, and models involving constraints on the impact of dose level, are described. These models provide a flexible approach to estimating sparse, often adverse, outcomes associated with interventions. Each model makes its own set of assumptions, and approaches to assessing goodness of fit of the various models will usually be extremely limited in their effectiveness, due to the sparse nature of the data. Both methodological and clinical considerations are required to fit realistically complex models in this area and to evaluate their appropriateness.Partially supported by a National Institute for Health Research Senior Investigator Awar

Is primary angioplasty cost effective in the UK? Results of a comprehensive decision analysis

Objective: To assess the cost effectiveness of primary angioplasty, compared with medical management with thrombolytic drugs, to achieve reperfusion after acute myocardial infarction ( AMI) from the perspective of the UK NHS. Design: Bayesian evidence synthesis and decision analytic model. Methods: A systematic review was conducted and Bayesian statistical methods used to synthesise evidence from 22 randomised control trials. Resource utilisation was based on UK registry data, published literature and national databases, with unit costs taken from routine NHS sources and published literature. Main outcome measure: Costs from a health service perspective and outcomes measured as quality-adjusted life years (QALYs). Results: For the base case, the incremental cost-effectiveness ratio of primary angioplasty was pound 9241 for each additional QALY, with a probability of being cost effective of 0.90 for a cost-effectiveness threshold of pound 20 000. Results were sensitive to variations in the additional time required to initiate treatment with primary angioplasty. Conclusions: Primary angioplasty is cost effective for the treatment of AMI on the basis of threshold cost-effectiveness values used in the NHS and subject to a delay of up to about 80 minutes. These findings are mainly explained by the superior mortality benefit and the prevention of non-fatal outcomes associated with primary angioplasty for delays of up to this length

Assessing the effectiveness of primary angioplasty compared with thrombolysis and its relationship to time delay: a Bayesian evidence synthesis

Background: Meta-analyses of trials have shown greater benefits from angioplasty than thrombolysis after an acute myocardial infarction, but the time delay in initiating angioplasty needs to be considered. Objective: To extend earlier meta-analyses by considering 1- and 6-month outcome data for both forms of reperfusion. To use Bayesian statistical methods to quantify the uncertainty associated with the estimated relationships. Methods: A systematic review and meta-analysis published in 2003 was updated. Data on key clinical outcomes and the difference between time-to-balloon and time-to-needle were independently extracted by two researchers. Bayesian statistical methods were used to synthesise evidence despite differences between reported follow-up times and outcomes. Outcomes are presented as absolute probabilities of specific events and odds ratios (ORs; with 95% credible intervals (Crl)) as a function of the additional time delay associated with angioplasty. \ Results: 22 studies were included in the meta-analysis, with 3760 and 3758 patients randomised to primary angioplasty and thrombolysis, respectively. The mean ( SE) angioplasty-related time delay ( over and above time to thrombolysis) was 54.3 (2.2) minutes. For this delay, mean event probabilities were lower for primary angioplasty for all outcomes. Mortality within 1 month was 4.5% after angioplasty and 6.4% after thrombolysis ( OR = 0.68 ( 95% Crl 0.46 to 1.01)). For non-fatal reinfarction, OR = 0.32 ( 95% Crl 0.20 to 0.51); for non-fatal stroke OR = 0.24 ( 95% Crl 0.11 to 0.50). For all outcomes, the benefit of angioplasty decreased with longer delay from initiation. Conclusions: The benefit of primary angioplasty, over thrombolysis, depends on the former's additional time delay. For delays of 30-90 minutes, angioplasty is superior for 1- month fatal and non-fatal outcomes. For delays of around 90 minutes thrombolysis may be the preferred option as assessed by 6-month mortality; there is considerable uncertainty for longer time delays

Bayesian survival analysis.

In cancer research the efficacy of a new treatment is often assessed by means of a clinical trial. In such trials the outcome measure of interest is usually time to death from entry into the study. The time to intermediate events may also be of interest, for example time to the spread of the disease to other organs (metastases). Thus, cancer clinical trials can be seen to generate multi-state data, in which patients may be in anyone of a finite number of states at a particular time. The classical analysis of data from cancer clinical trials uses a survival regression model. This type of model allows for the fact that patients in the trial will have been observed for different lengths of time and for some patients the time to the event of interest will not be observed (censored). The regression structure means that a measure of treatment effect can be obtained after allowing for other important factors. Clinical trials are not conducted in isolation, but are part of an on-going learning process. In order to assess the current weight of evidence for the use of a particular treatment a Bayesian approach is necessary. Such an approach allows for the formal inclusion of prior information, either in the form of clinical expertise or the results from previous studies, into the statistical analysis. An initial Bayesian analysis, for a single non-recurrent event, can be performed using non-temporal models that consider the occurrence of events up to a specific time from entry into the study. Although these models are conceptually simple, they do not explicitly allow for censoring or covariates. In order to address both of these deficiencies a Bayesian fully parametric multiplicative intensity regression model is developed. The extra complexity of this model means that approximate integration techniques are required. Asymptotic Laplace approximations and the more computer intensive Gauss-Hermite quadrature are shown to perform well and yield virtually identical results. By adopting counting process notation the multiplicative intensity model is extended to the multi-state scenario quite easily. These models are used in the analysis of a cancer clinical trial to assess the efficacy of neutron therapy compared to standard photon therapy for patients with cancer of the pelvic region. In this trial there is prior information both in the form of clinical prior beliefs and results from previous studies. The usefulness of multi-state models is also demonstrated in the analysis of a pilot quality of life study. Bayesian multi-state models are shown to provide a coherent framework for the analysis of clinical studies, both interventionist and observational, yielding clinically meaningful summaries about the current state of knowledge concerning the disease/treatment process

A novel approach to bivariate meta-analysis of binary outcomes and its application in the context of surrogate endpoints

Bivariate meta-analysis provides a useful framework for combining information across related studies and has been widely utilised to combine evidence from clinical studies in order to evaluate treatment efficacy. Bivariate meta-analysis has also been used to investigate surrogacy patterns between treatment effects on the surrogate and the final outcome. Surrogate endpoints play an important role in drug development when they can be used to measure treatment effect early compared to the final clinical outcome and to predict clinical benefit or harm. The standard bivariate meta-analytic approach models the observed treatment effects on the surrogate and final outcomes jointly, at both the within-study and between-studies levels, using a bivariate normal distribution. For binomial data a normal approximation can be used on log odds ratio scale, however, this method may lead to biased results when the proportions of events are close to one or zero, affecting the validation of surrogate endpoints. In this paper, two Bayesian meta-analytic approaches are introduced which allow for modelling the within-study variability using binomial data directly. The first uses independent binomial likelihoods to model the within-study variability avoiding to approximate the observed treatment effects, however, ignores the within-study association. The second, models the summarised events in each arm jointly using a bivariate copula with binomial marginals. This allows the model to take into account the within-study association through the copula dependence parameter. We applied the methods to an illustrative example in chronic myeloid leukemia to investigate the surrogate relationship between complete cytogenetic response (CCyR) and event-free-survival (EFS).Comment: 20 pages, 6 figure

Bivariate network meta-analysis for surrogate endpoint evaluation

Surrogate endpoints are very important in regulatory decision-making in healthcare, in particular if they can be measured early compared to the long-term final clinical outcome and act as good predictors of clinical benefit. Bivariate meta-analysis methods can be used to evaluate surrogate endpoints and to predict the treatment effect on the final outcome from the treatment effect measured on a surrogate endpoint. However, candidate surrogate endpoints are often imperfect, and the level of association between the treatment effects on the surrogate and final outcomes may vary between treatments. This imposes a limitation on the pairwise methods which do not differentiate between the treatments. We develop bivariate network meta-analysis (bvNMA) methods which combine data on treatment effects on the surrogate and final outcomes, from trials investigating heterogeneous treatment contrasts. The bvNMA methods estimate the effects on both outcomes for all treatment contrasts individually in a single analysis. At the same time, they allow us to model the surrogacy patterns across multiple trials (different populations) within a treatment contrast and across treatment contrasts, thus enabling predictions of the treatment effect on the final outcome for a new study in a new population or investigating a new treatment. Modelling assumptions about the between-studies heterogeneity and the network consistency, and their impact on predictions, are investigated using simulated data and an illustrative example in advanced colorectal cancer. When the strength of the surrogate relationships varies across treatment contrasts, bvNMA has the advantage of identifying treatments for which surrogacy holds, thus leading to better predictions