Meta-analyses of clinical trials targeting rare events face particular challenges when the data lack adequate numbers of events for all treatment arms. Especially when the number of studies is low, standard random-effects meta-analysis methods can lead to serious distortions because of such data sparsity. To overcome this, we suggest the use of weakly informative priors (WIPs) for the treatment effect parameter of a Bayesian meta-analysis model, which may also be seen as a form of penalization. As a data model, we use a binomial-normal hierarchical model (BNHM) that does not require continuity corrections in case of zero counts in one or both arms. We suggest a normal prior for the log-odds ratio with mean 0 and standard deviation 2.82, which is motivated (a) as a symmetric prior centered around unity and constraining the odds ratio within a range from 1/250 to 250 with 95% probability and (b) as consistent with empirically observed effect estimates from a set of 37 773 meta-analyses from the Cochrane Database of Systematic Reviews. In a simulation study with rare events and few studies, our BNHM with a WIP outperformed a Bayesian method without a WIP and a maximum likelihood estimator in terms of smaller bias and shorter interval estimates with similar coverage. Furthermore, the methods are illustrated by a systematic review in immunosuppression of rare safety events following pediatric transplantation. A publicly available R package, MetaStan, is developed to automate a Bayesian implementation of meta-analysis models using WIPs. KEYWORDS Bayes, few studies, random-effects meta-analysis, rare events, weakly informative priorsThis is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. HIGHLIGHTSWhat is already known: Standard random-effects meta-analysis methods are not suitable for meta-analysis of few studies with rare events. What is new: To deal with data sparsity present in the random-effects meta-analysis of few studies with rare events, we suggest the use of weakly informative priors as penalization for the treatment effect parameter. 85 ET AL. Ü G NHAN 87 ET AL. Ü G NHAN FIGURE A1 Traceplots for the estimated parameters and ⊤ including burn-in for death outcomes [Colour figure can be viewed at wileyonlinelibrary.com] FIGURE A2 Traceplots for the estimated parameters and⊤including burn-in for posttransplant lymphoproliferative disease (PTLD) outcomes [Colour figure can be viewed at wileyonlinelibrary.com] 88 ET AL. Ü G NHAN 89 ET AL. Ü G NHAN FIGURE D1 Simulations with high baseline risks: The bias for the mean treatment effect , coverage probabilities, and log mean length of the interval estimates for obtained by three methods (maximum likelihood estimate [MLE], Vague, and weakly informative prior [WIP]) are shown [Colour figure can be viewed at wileyonlinelibrary.com] 90 ET AL. Ü G NHAN

Where there are a limited number of patients, such as in a rare disease, clinical trials in these small populations present several challenges, including statistical issues. This led to an EU FP7 call for proposals in 2013. One of the three projects funded was the Innovative Methodology for Small Populations Research (InSPiRe) project. This paper summarizes the main results of the project, which was completed in 2017.The InSPiRe project has led to development of novel statistical methodology for clinical trials in small populations in four areas. We have explored new decision-making methods for small population clinical trials using a Bayesian decision-theoretic framework to compare costs with potential benefits, developed approaches for targeted treatment trials, enabling simultaneous identification of subgroups and confirmation of treatment effect for these patients, worked on early phase clinical trial design and on extrapolation from adult to pediatric studies, developing methods to enable use of pharmacokinetics and pharmacodynamics data, and also developed improved robust meta-analysis methods for a small number of trials to support the planning, analysis and interpretation of a trial as well as enabling extrapolation between patient groups. In addition to scientific publications, we have contributed to regulatory guidance and produced free software in order to facilitate implementation of the novel methods.

Network meta‐analysis (NMA) is gaining popularity for comparing multiple treatments in a single analysis. Generalized linear mixed models provide a unifying framework for NMA, allow us to analyze datasets with dichotomous, continuous or count endpoints, and take into account multiarm trials, potential heterogeneity between trials and network inconsistency. To perform inference within such NMA models, the use of Bayesian methods is often advocated. The standard inference tool is Markov chain Monte Carlo (MCMC), which is computationally expensive and requires convergence diagnostics. A deterministic approach to do fully Bayesian inference for latent Gaussian models can be achieved by integrated nested Laplace approximations (INLA), which is a fast and accurate alternative to MCMC. We show how NMA models fit in the class of latent Gaussian models and how NMA models are implemented using INLA and demonstrate that the estimates obtained by INLA are in close agreement with the ones obtained by MCMC. Specifically, we emphasize the design‐by‐treatment interaction model with random inconsistency parameters (also known as the Jackson model). Also, we have proposed a network meta‐regression model, which is constructed by incorporating trial‐level covariates to the Jackson model to explain possible sources of heterogeneity and/or inconsistency in the network. A publicly available package, , is developed to automate the INLA implementation of NMA models, which are considered in this paper. Three applications illustrate the use of INLA for a NMA.

Phase I dose‐escalation trials must be guided by a safety model in order to avoid exposing patients to unacceptably high risk of toxicities. Traditionally, these trials are based on one type of schedule. In more recent practice, however, there is often a need to consider more than one schedule, which means that in addition to the dose itself, the schedule needs to be varied in the trial. Hence, the aim is finding an acceptable dose‐schedule combination. However, most established methods for dose‐escalation trials are designed to escalate the dose only and ad hoc choices must be made to adapt these to the more complicated setting of finding an acceptable dose‐schedule combination. In this article, we introduce a Bayesian time‐to‐event model which takes explicitly the dose amount and schedule into account through the use of pharmacokinetic principles. The model uses a time‐varying exposure measure to account for the risk of a dose‐limiting toxicity over time. The dose‐schedule decisions are informed by an escalation with overdose control criterion. The model is formulated using interpretable parameters which facilitates the specification of priors. In a simulation study, we compared the proposed method with an existing method. The simulation study demonstrates that the proposed method yields similar or better results compared with an existing method in terms of recommending acceptable dose‐schedule combinations, yet reduces the number of patients enrolled in most of scenarios. The R and Stan code to implement the proposed method is publicly available from Github ( https://github.com/gunhanb/TITEPK_code).

Background Conventional methods for phase I dose-escalation trials in oncology are based on a single treatment schedule only. More recently, however, multiple schedules are more frequently investigated in the same trial. Methods Here, we consider sequential phase I trials, where the trial proceeds with a new schedule (e.g. daily or weekly dosing) once the dose escalation with another schedule has been completed. The aim is to utilize the information from both the completed and the ongoing schedules to inform decisions on the dose level for the next dose cohort. For this purpose, we adapted the time-to-event pharmacokinetics (TITE-PK) model, which were originally developed for simultaneous investigation of multiple schedules. TITE-PK integrates information from multiple schedules using a pharmacokinetics (PK) model. Results In a simulation study, the developed approach is compared to the bridging continual reassessment method and the Bayesian logistic regression model using a meta-analytic-predictive prior. TITE-PK results in better performance than comparators in terms of recommending acceptable dose and avoiding overly toxic doses for sequential phase I trials in most of the scenarios considered. Furthermore, better performance of TITE-PK is achieved while requiring similar number of patients in the simulated trials. For the scenarios involving one schedule, TITE-PK displays similar performance with alternatives in terms of acceptable dose recommendations. The and code for the implementation of an illustrative sequential phase I trial example in oncology is publicly available (https://github.com/gunhanb/TITEPK_sequential). Conclusion In phase I oncology trials with sequential multiple schedules, the use of all relevant information is of great importance. For these trials, the adapted TITE-PK which combines information using PK principles is recommended.