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Tim Friede

Publications and source records attributed to Tim Friede.

At least 73 records · Page 4Linked to original sources
arXiv2020

Shrinkage estimation for dose-response modeling in phase II trials with multiple schedules

Recently, phase II trials with multiple schedules (frequency of administrations) have become more popular, for instance in the development of treatments for atopic dermatitis. If the relationship of the dose and response is described by a parametric model, a simplistic approach is to pool doses from different schedules. However, this approach ignores the potential heterogeneity in dose-response curves between schedules. A more reasonable approach is the partial pooling, i.e. certain parameters of the dose-response curves are shared, while others are allowed to vary. Rather than using schedule-specific fixed-effects, we propose a Bayesian hierarchical model with random-effects to model the between-schedule heterogeneity with regard to certain parameters. Schedule-specific dose-response relationships can then be estimated using shrinkage estimation. Considering Emax models, the proposed method displayed desirable performance in terms of the mean absolute error and the coverage probabilities for the dose-response curve compared to the complete pooling. Furthermore, it outperformed the partial pooling with schedule-specific fixed-effects by producing lower mean absolute error and shorter credible intervals. The methods are illustrated using simulations and a phase II trial example in atopic dermatitis. A publicly available R package, \texttt{ModStan}, is developed to automate the implementation of the proposed method (\href{https://github.com/gunhanb/ModStan}{https://github.com/gunhanb/ModStan}).

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arXiv2020

A Bayesian time-to-event pharmacokinetic model for phase I dose-escalation trials with multiple schedules

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 paper, 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 to an existing method in terms of recommending acceptable dose-schedule combinations, yet reduces the number of patients enrolled in most of scenarios. The \texttt{R} and \texttt{Stan} code to implement the proposed method is publicly available from Github (\url{https://github.com/gunhanb/TITEPK_code}).

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arXiv2020

Estimating and comparing adverse event probabilities in the presence of varying follow-up times and competing events

Safety analyses in terms of adverse events (AEs) are an important aspect of benefit-risk assessments of therapies. Compared to efficacy analyses AE analyses are often rather simplistic. The probability of an AE of a specific type is typically estimated by the incidence proportion, sometimes the incidence density or the Kaplan-Meier estimator are proposed. But these analyses either do not account for censoring, rely on a too restrictive parametric model, or ignore competing events. With the non-parametric Aalen-Johansen estimator as the gold-standard, these potential sources of bias are investigated in a data example from oncology and in simulations, both in the one-sample and in the two-sample case. As the estimators may have large variances at the end of follow-up, the estimators are not only compared at the maximal event time but also at two quantiles of the observed times. To date, consequences for safety comparisons have hardly been investigated in the literature. The impact of using different estimators for group comparisons is unclear, as, for example, the ratio of two both underestimating or overestimating estimators may or may not be comparable to the ratio of the gold-standard estimator. Therefore, the ratio of the AE probabilities is also calculated based on different approaches. By simulations investigating constant and non-constant hazards, different censoring mechanisms and event frequencies, we show that ignoring competing events is more of a problem than falsely assuming constant hazards by use of the incidence density and that the choice of the AE probability estimator is crucial for group comparisons.

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arXiv2019

Survival analysis for AdVerse events with VarYing follow-up times (SAVVY): Rationale and statistical concept of a meta-analytic study

The assessment of safety is an important aspect of the evaluation of new therapies in clinical trials, with analyses of adverse events being an essential part of this. Standard methods for the analysis of adverse events such as the incidence proportion, i.e. the number of patients with a specific adverse event out of all patients in the treatment groups, do not account for both varying follow-up times and competing risks. Alternative approaches such as the Aalen-Johansen estimator of the cumulative incidence function have been suggested. Theoretical arguments and numerical evaluations support the application of these more advanced methodology, but as yet there is to our knowledge only insufficient empirical evidence whether these methods would lead to different conclusions in safety evaluations. The Survival analysis for AdVerse events with VarYing follow-up times (SAVVY) project strives to close this gap in evidence by conducting a meta-analytical study to assess the impact of the methodology on the conclusion of the safety assessment empirically. Here we present the rationale and statistical concept of the empirical study conducted as part of the SAVVY project. The statistical methods are presented in unified notation and examples of their implementation in R and SAS are provided.

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arXiv2019

Decline of COPD exacerbations in clinical trials over two decades -- a systematic review and meta-regression

BACKGROUND: An important goal of chronic obstructive pulmonary disease (COPD) treatment is to reduce the frequency of exacerbations. Some observations suggest a decline in exacerbation rates in clinical trials over time. A more systematic understanding would help to improve the design and interpretation of COPD trials. METHODS: We performed a systematic review and meta-regression of the placebo groups in published randomized controlled trials reporting exacerbations as an outcome. A Bayesian negative binomial model was developed to accommodate results that are reported in different formats; results are reported with credible intervals (CI) and posterior tail probabilities ($p_B$). RESULTS: Of 1114 studies identified by our search, 55 were ultimately included. Exacerbation rates decreased by 6.7% (95% CI (4.4, 9.0); $p_B$ < 0.001) per year, or 50% (95% CI (36, 61)) per decade. Adjusting for available study and baseline characteristics such as forced expiratory volume in 1 s (FEV1) did not alter the observed trend considerably. Two subsets of studies, one using a true placebo group and the other allowing inhaled corticosteroids in the "placebo" group, also yielded consistent results. CONCLUSIONS: In conclusion, this meta-regression indicates that the rate of COPD exacerbations decreased over the past two decades to a clinically relevant extent independent of important prognostic factors. This suggests that care is needed in the design of new trials or when comparing results from older trials with more recent ones. Also a considerable effect of adjunct therapy on COPD exacerbations can be assumed.

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arXiv2019

Random-effects meta-analysis of phase I dose-finding studies using stochastic process priors

Phase I dose-finding studies aim at identifying the maximal tolerated dose (MTD). It is not uncommon that several dose-finding studies are conducted, although often with some variation in the administration mode or dose panel. For instance, sorafenib (BAY 43-900) was used as monotherapy in at least 29 phase I trials according to a recent search in clinicaltrials.gov. Since the toxicity may not be directly related to the specific indication, synthesizing the information from several studies might be worthwhile. However, this is rarely done in practice and only a fixed-effect meta-analysis framework was proposed to date. We developed a Bayesian random-effects meta-analysis methodology to pool several phase I trials and suggest the MTD. A curve free hierarchical model on the logistic scale with random effects, accounting for between-trial heterogeneity, is used to model the probability of toxicity across the investigated doses. An Ornstein-Uhlenbeck Gaussian process is adopted for the random effects structure. Prior distributions for the curve free model are based on a latent Gamma process. An extensive simulation study showed good performance of the proposed method also under model deviations. Sharing information between phase I studies can improve the precision of MTD selection, at least when the number of trials is reasonably large.

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arXiv2019

Blinded continuous information monitoring of recurrent event endpoints with time trends in clinical trials

Blinded sample size re-estimation and information monitoring based on blinded data has been suggested to mitigate risks due to planning uncertainties regarding nuisance parameters. Motivated by a randomized controlled trial in pediatric multiple sclerosis (MS), a continuous monitoring procedure for overdispersed count data was proposed recently. However, this procedure assumed constant event rates, an assumption often not met in practice. Here we extend the procedure to accommodate time trends in the event rates considering two blinded approaches: (a) the mixture approach modeling the number of events by a mixture of two negative binomial distributions, and (b) the lumping approach approximating the marginal distribution of the event counts by a negative binomial distribution. Through simulations the operating characteristics of the proposed procedures are investigated under decreasing event rates. We find that the type I error rate is not inflated relevantly by either of the monitoring procedures, with the exception of strong time dependencies where the procedure assuming constant rates exhibits some inflation. Furthermore, the procedure accommodating time trends has generally favorable power properties compared to the procedure based on constant rates which stops often too late. The proposed method is illustrated by the clinical trial in pediatric MS.

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arXiv2019

Sample size re-estimation incorporating prior information on a nuisance parameter

Prior information is often incorporated informally when planning a clinical trial. Here, we present an approach on how to incorporate prior information, such as data from historical clinical trials, into the nuisance parameter based sample size re-estimation in a design with an internal pilot study. We focus on trials with continuous endpoints in which the outcome variance is the nuisance parameter. For planning and analyzing the trial frequentist methods are considered. Moreover, the external information on the variance is summarized by the Bayesian meta-analytic-predictive (MAP) approach. To incorporate external information into the sample size re-estimation, we propose to update the MAP prior based on the results of the internal pilot study and to re-estimate the sample size using an estimator from the posterior. By means of a simulation study, we compare the operating characteristics such as power and sample size distribution of the proposed procedure with the traditional sample size re-estimation approach which uses the pooled variance estimator. The simulation study shows that, if no prior-data conflict is present, incorporating external information into the sample size re-estimation improves the operating characteristics compared to the traditional approach. In the case of a prior-data conflict, that is when the variance of the ongoing clinical trial is unequal to the prior location, the performance of the traditional sample size re-estimation procedure is in general superior, even when the prior information is robustified. When considering to include prior information in sample size re-estimation, the potential gains should be balanced against the risks.

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arXiv2019

Group sequential designs for negative binomial outcomes

Count data and recurrent events in clinical trials, such as the number of lesions in magnetic resonance imaging in multiple sclerosis, the number of relapses in multiple sclerosis, the number of hospitalizations in heart failure, and the number of exacerbations in asthma or in chronic obstructive pulmonary disease (COPD) are often modeled by negative binomial distributions. In this manuscript we study planning and analyzing clinical trials with group sequential designs for negative binomial outcomes. We propose a group sequential testing procedure for negative binomial outcomes based on Wald statistics using maximum likelihood estimators. The asymptotic distribution of the proposed group sequential tests statistics are derived. The finite sample size properties of the proposed group sequential test for negative binomial outcomes and the methods for planning the respective clinical trials are assessed in a simulation study. The simulation scenarios are motivated by clinical trials in chronic heart failure and relapsing multiple sclerosis, which cover a wide range of practically relevant settings. Our research assures that the asymptotic normal theory of group sequential designs can be applied to negative binomial outcomes when the hypotheses are tested using Wald statistics and maximum likelihood estimators. We also propose two methods, one based on Student's t-distribution and one based on resampling, to improve type I error rate control in small samples. The statistical methods studied in this manuscript are implemented in the R package \textit{gscounts}, which is available for download on the Comprehensive R Archive Network (CRAN).

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arXiv2019

Seamless phase II/III clinical trials using early outcomes for treatment or subgroup selection: Methods and aspects of their implementation

Adaptive seamless designs combine confirmatory testing, a domain of phase III trials, with features such as treatment or subgroup selection, typically associated with phase II trials. They promise to increase the efficiency of development programmes of new drugs, e.g. in terms of sample size and / or development time. It is well acknowledged that adaptive designs are more involved from a logistical perspective and require more upfront planning, often in form of extensive simulation studies, than conventional approaches. Here we present a framework for adaptive treatment and subgroup selection using the same notation, which links the somewhat disparate literature on treatment selection on one side and on subgroup selection on the other. Furthermore, we introduce a flexible and yet efficient simulation model that serves both designs. As primary endpoints often take a long time to observe, interim analyses are frequently informed by early outcomes. Therefore, all methods presented accommodate both, interim analyses informed by the primary outcome or an early outcome. The R package asd, previously developed to simulate designs with treatment selection, was extended to include subpopulation selection (so-called adaptive enrichment designs). Here we describe the functionality of the R package asd and use it to present some worked-up examples motivated by clinical trials in chronic obstructive pulmonary disease and oncology. The examples illustrate various features of the R package providing at the same time insights into the operating characteristics of adaptive seamless studies.

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arXiv2018

Dynamically borrowing strength from another study through shrinkage estimation

Meta-analytic methods may be used to combine evidence from different sources of information. Quite commonly, the normal-normal hierarchical model (NNHM) including a random-effect to account for between-study heterogeneity is utilized for such analyses. The same modeling framework may also be used to not only derive a combined estimate, but also to borrow strength for a particular study from another by deriving a shrinkage estimate. For instance, a small-scale randomized controlled trial could be supported by a non-randomized study, e.g. a clinical registry. This would be particularly attractive in the context of rare diseases. We demonstrate that a meta-analysis still makes sense in this extreme two-study setup, as illustrated using a recent trial and a clinical registry in Creutzfeld-Jakob disease. Derivation of a shrinkage estimate within a Bayesian random-effects meta-analysis may substantially improve a given estimate even based on only a single additional estimate while accounting for potential effect heterogeneity between the studies. Alternatively, inference may equivalently be motivated via a model specification that does not require a common overall mean parameter but considers the treatment effect in one study, and the difference in effects between the studies. The proposed approach is quite generally applicable to combine different types of evidence originating e.g. from meta-analyses or individual studies. An application of this more general setup is provided in immunosuppression following liver transplantation in children.

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arXiv2018

Likelihood-based meta-analysis with few studies: Empirical and simulation studies

Standard random-effects meta-analysis methods perform poorly when applied to few studies only. Such settings however are commonly encountered in practice. It is unclear, whether or to what extent small-sample-size behaviour can be improved by more sophisticated modeling. We consider several likelihood-based inference methods. Confidence intervals are based on normal or Student-t approximations. We extract an empirical data set of 40 meta-analyses from recent reviews published by the German Institute for Quality and Efficiency in Health Care (IQWiG). Methods are then compared empirically as well as in a simulation study, considering odds-ratio and risk ratio effect sizes. Empirically, a majority of the identified meta-analyses include only 2 studies. In the simulation study, coverage probability is, in the presence of heterogeneity and few studies, below the nominal level for all frequentist methods based on normal approximation, in particular when sizes in meta-analyses are not balanced, but improve when confidence intervals are adjusted. Bayesian methods result in better coverage than the frequentist methods with normal approximation in all scenarios. Credible intervals are empirically and in the simulation study wider than unadjusted confidence intervals, but considerably narrower than adjusted ones. Confidence intervals based on the generalized linear mixed models are in general, slightly narrower than those from other frequentist methods. Certain methods turned out impractical due to frequent numerical problems. In the presence of between-study heterogeneity, especially with unbalanced study sizes, caution is needed in applying meta-analytical methods to few studies, as either coverage probabilities might be compromised, or intervals are inconclusively wide. Bayesian estimation with a sensibly chosen prior for between-trial heterogeneity may offer a promising compromise.

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arXiv2018

On estimands and the analysis of adverse events in the presence of varying follow-up times within the benefit assessment of therapies

The analysis of adverse events (AEs) is a key component in the assessment of a drug's safety profile. Inappropriate analysis methods may result in misleading conclusions about a therapy's safety and consequently its benefit-risk ratio. The statistical analysis of AEs is complicated by the fact that the follow-up times can vary between the patients included in a clinical trial. This paper takes as its focus the analysis of AE data in the presence of varying follow-up times within the benefit assessment of therapeutic interventions. Instead of approaching this issue directly and solely from an analysis point of view, we first discuss what should be estimated in the context of safety data, leading to the concept of estimands. Although the current discussion on estimands is mainly related to efficacy evaluation, the concept is applicable to safety endpoints as well. Within the framework of estimands, we present statistical methods for analysing AEs with the focus being on the time to the occurrence of the first AE of a specific type. We give recommendations which estimators should be used for the estimands described. Furthermore, we state practical implications of the analysis of AEs in clinical trials and give an overview of examples across different indications. We also provide a review of current practices of health technology assessment (HTA) agencies with respect to the evaluation of safety data. Finally, we describe problems with meta-analyses of AE data and sketch possible solutions.

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arXiv2018

Model averaging for robust extrapolation in evidence synthesis

Extrapolation from a source to a target, e.g., from adults to children, is a promising approach to utilizing external information when data are sparse. In the context of meta-analysis, one is commonly faced with a small number of studies, while potentially relevant additional information may also be available. Here we describe a simple extrapolation strategy using heavy-tailed mixture priors for effect estimation in meta-analysis, which effectively results in a model-averaging technique. The described method is robust in the sense that a potential prior-data conflict, i.e., a discrepancy between source and target data, is explicitly anticipated. The aim of this paper to develop a solution for this particular application, to showcase the ease of implementation by providing R code, and to demonstrate the robustness of the general approach in simulations.

stat.ME↗
arXiv2018

Meta-analysis of few studies involving rare events

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 meta-analysis methods can lead to serious distortions because of such data sparsity. To overcome this, we suggest the use of weakly informative priors (WIP) 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) which 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 (1) as a symmetric prior centred around unity and constraining the odds ratio to within a range from 1/250 to 250 with 95 % probability, and (2) as consistent with empirically observed effect estimates from a set of $\mbox{$37\,773$}$ 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 paediatric transplantation. A publicly available $\textbf{R}$ package, $\texttt{MetaStan}$, is developed to automate the $\textbf{Stan}$ implementation of meta-analysis models using WIPs.

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arXiv2017

Blinded sample size re-estimation in three-arm trials with 'gold standard' design

The sample size of a clinical trial relies on information about nuisance parameters such as the outcome variance. When no or only limited information is available, it has been proposed to include an internal pilot study in the design of the trial. Based on the results of the internal pilot study, the initially planned sample size can be adjusted. In this paper, we study blinded sample size re-estimation in the 'gold standard' design for normally distributed outcomes. The 'gold standard' design is a three-arm clinical trial design which includes an active and a placebo control in addition to an experimental treatment. We compare several sample size re-estimation procedures in a simulation study assessing operating characteristics including power and type I error. We find that sample size re-estimation based on the popular one-sample variance estimator results in overpowered trials. Moreover, sample size re-estimation based on unbiased variance estimators such as the Xing-Ganju variance estimator results in underpowered trials, as it is expected since an overestimation of the variance and thus the sample size is in general required for the re-estimation procedure to eventually meet the target power. Moreover, we propose an inflation factor for the sample size re-estimation with the Xing-Ganju variance estimator and show that this approach results in adequately powered trials. Due to favorable features of Xing-Ganju variance estimator such as unbiasedness and a distribution independent of the group means, the inflation factor does not depend on the nuisance parameter and, therefore, can be calculated prior to a trial.

stat.AP↗
arXiv2017

Discrete approximation of a mixture distribution via restricted divergence

Mixture distributions arise in many application areas, for example as marginal distributions or convolutions of distributions. We present a method of constructing an easily tractable discrete mixture distribution as an approximation to a mixture distribution with a large to infinite number, discrete or continuous, of components. The proposed DIRECT (Divergence Restricting Conditional Tesselation) algorithm is set up such that a pre-specified precision, defined in terms of Kullback-Leibler divergence between true distribution and approximation, is guaranteed. Application of the algorithm is demonstrated in two examples.

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