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Objective: We aimed to develop a meta-analytic model for evaluation of predictive biomarkers and targeted therapies, utilising data from digital sources when individual participant data (IPD) from randomised controlled trials (RCTs) are unavailable. Methods: A Bayesian network meta-regression model, combining aggregate data (AD) from RCTs and IPD, was developed for modelling time-to-event data to evaluate predictive biomarkers. IPD were sourced from electronic health records, using target trial emulation approach, or digitised Kaplan-Meier curves. The model is illustrated using two examples; breast cancer with a hormone receptor biomarker, and metastatic colorectal cancer with the Kirsten Rat Sarcoma (KRAS) biomarker. Results: The model developed allowed for estimation of treatment effects in two subgroups of patients defined by their biomarker status. Effectiveness of taxane did not differ in hormone receptor positive and negative breast cancer patients. Epidermal growth factor receptor (EGFR) inhibitors were more effective than chemotherapy in KRAS wild type colorectal cancer patients but not in patients with KRAS mutant status. Use of IPD reduced uncertainty of the sub-group specific treatment effect estimates by up to 49%. Conclusion: Utilisation of IPD allowed for more detailed evaluation of predictive biomarkers and cancer therapies and improved precision of the estimates compared to use of AD alone.

Objective: We aim to utilise real world data in evidence synthesis to optimise an evidence base for the effectiveness of biologic therapies in rheumatoid arthritis in order to allow for evidence on first-line therapies to inform second-line effectiveness estimates. Study design and setting: We use data from the British Society for Rheumatology Biologics Register for Rheumatoid Arthritis (BSRBR-RA) to supplement RCT evidence obtained from the literature, by emulating target trials of treatment sequences to estimate treatment effects in each line of therapy. Treatment effects estimates from the target trials inform a bivariate network meta-analysis (NMA) of first and second-line treatments. Results: Summary data were obtained from 21 trials of biologic therapies including 2 for second-line treatment and results from six emulated target trials of both treatment lines. Bivariate NMA resulted in a decrease in uncertainty around the effectiveness estimates of the second-line therapies, when compared to the results of univariate NMA, and allowed for predictions of treatment effects not evaluated in second-line RCTs. Conclusion: Bivariate NMA provides effectiveness estimates for all treatments in first- and second-line, including predicted effects in second-line where these estimates did not exist in the data. This novel methodology may have further applications, for example for bridging networks of trials in children and adults.

Bivariate meta-analysis provides a useful framework for combining information across related studies and has been utilised to combine evidence from clinical studies to evaluate treatment efficacy on two outcomes. It has also been used to investigate surrogacy patterns between treatment effects on the surrogate endpoint 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 outcome and to predict clinical benefit or harm. The standard bivariate meta-analytic approach models the observed treatment effects on the surrogate and the final outcome outcomes jointly, at both the within-study and between-studies levels, using a bivariate normal distribution. For binomial data, a normal approximation on log odds ratio scale can be used. 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, we explore modelling the two outcomes on the original binomial scale. Firstly, we present a method that uses independent binomial likelihoods to model the within-study variability avoiding to approximate the observed treatment effects. However, the method ignores the within-study association. To overcome this issue, we propose a method using a bivariate copula with binomial marginals, which allows the model to account for the within-study association. 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: 22 pages, 5 figures

Survival models incorporating random effects to account for unmeasured heterogeneity are being increasingly used in biostatistical and applied research. Specifically, unmeasured covariates whose lack of inclusion in the model would lead to biased, inefficient results are commonly modelled by including a subject-specific (or cluster-specific) frailty term that follows a given distribution (e.g. Gamma or log-Normal). Despite that, in the context of parametric frailty models little is known about the impact of misspecifying the baseline hazard, the frailty distribution, or both. Therefore, our aim is to quantify the impact of such misspecification in a wide variety of clinically plausible scenarios via Monte Carlo simulation, using open source software readily available to applied researchers. We generate clustered survival data assuming various baseline hazard functions, including mixture distributions with turning points, and assess the impact of sample size, variance of the frailty, baseline hazard function, and frailty distribution. Models compared include standard parametric distributions and more flexible spline-based approaches; we also included semiparametric Cox models. The resulting bias can be clinically relevant. In conclusion, we highlight the importance of fitting models that are flexible enough and the importance of assessing model fit. We illustrate our conclusions with two applications using data on diabetic retinopathy and bladder cancer. Our results show the importance of assessing model fit with respect to the baseline hazard function and the distribution of the frailty: misspecifying the former leads to biased relative and absolute risk estimates while misspecifying the latter affects absolute risk estimates and measures of heterogeneity.

Electronic health records are being increasingly used in medical research to answer more relevant and detailed clinical questions; however, they pose new and significant methodological challenges. For instance, observation times are likely correlated with the underlying disease severity: patients with worse conditions utilise health care more and may have worse biomarker values recorded. Traditional methods for analysing longitudinal data assume independence between observation times and disease severity; yet, with healthcare data such assumptions unlikely holds. Through Monte Carlo simulation, we compare different analytical approaches proposed to account for an informative visiting process to assess whether they lead to unbiased results. Furthermore, we formalise a joint model for the observation process and the longitudinal outcome within an extended joint modelling framework. We illustrate our results using data from a pragmatic trial on enhanced care for individuals with chronic kidney disease, and we introduce user-friendly software that can be used to fit the joint model for the observation process and a longitudinal outcome.

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.

Background: Network Meta-Analysis (NMA) is a key component of submissions to reimbursement agencies world-wide, especially when there is limited direct head-to-head evidence for multiple technologies from randomised controlled trials (RCTs). Many NMAs include only data from RCTs. However, real-world evidence (RWE) is also becoming widely recognised as a valuable source of clinical data. We investigate methods for the inclusion of RWE in NMA and its impact on the uncertainty around the effectiveness estimates. Methods: A range of methods for inclusion of RWE in evidence synthesis, including Bayesian hierarchical and power prior models, were investigated by applying them to an example in relapsing remitting multiple sclerosis. The effect of the inclusion of RWE was investigated by varying the degree of down weighting of this part of evidence by the use of a power prior. Results: Whilst the inclusion of the RWE led to an increase in the level of uncertainty surrounding effect estimates in this example, this depended on the method of inclusion adopted for the RWE. Power prior NMA model resulted in stable effect estimates for fingolimod yet increasing the width of the credible intervals with increasing weight given to RWE data. The hierarchical NMA models were effective in allowing for heterogeneity between study designs; however, this also increased the level of uncertainty. Conclusion: The power prior approach for the inclusion of RWE in NMAs indicates that the degree to which RWE is taken into account can have a significant impact on the overall level of uncertainty. The hierarchical modelling approach further allowed for accommodating differences between study types. Consequently, further work investigating both empirical evidence for biases associated with individual RWE studies and methods of elicitation from experts on the extent of such biases is warranted., Comment: 24 pages, 3 figures

In health technology assessment, decisions are based on complex cost-effectiveness models which, to be implemented, require numerous input parameters. When some of relevant estimates are not available the model may have to be simplified. Multi-parameter evidence synthesis allows to combine data from diverse sources of evidence resulting in obtaining estimates required in clinical decision-making that otherwise may not be available. We demonstrate how bivariate meta-analysis (BVMA) can be used to predict unreported estimate of a treatment effect enabling implementation of multi-state Markov model, which otherwise needs to be simplified. To illustrate this, we used an example of cost-effectiveness analysis for docetaxel in combination with prednisolone in metastatic hormone-refractory prostate cancer (mHRPC). BVMA was used to model jointly available data on treatment effects on overall survival (OS) and progression-free survival (PFS) to predict the unreported effect on PFS in a study evaluating docetaxel. Predicted treatment effect on PFS allowed implementation of a three-state Markov model comprising of stable disease, progressive disease and death states, whilst lack of the estimate restricted the model to two-state model (stable disease and death states). The two-state and three-state models were compared by calculating incremental cost-effectiveness ratios, which was much lower in the three-state model: {\pounds}21966 per QALY gained compared to {\pounds}30026 obtained from the two-state model. In contrast to the two-state model, the three-state model has the advantage of distinguishing patients who progressed from those who did not progress. The use of advanced meta-analytic technique helped to obtain relevant parameter estimate to populate a model which describes natural history more accurately, and at the same helped to prevent valuable clinical data from being discarded.