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Franz König

Publications and source records attributed to Franz König.

17 recordsLinked to original sources

Clustering-Based Outcome Models for Clinical Studies: A Scoping Review

This review provides a systematic overview of methods that combine covariate-based clustering of observational units (patients) with outcome models for clinical studies. We distinguish between informed-cluster models, where the outcome contributes to cluster formation, and agnostic-cluster models, where clustering is performed solely on covariates in a separate first step. Informed-cluster models include product partition models with covariates (PPMx), finite mixtures of regression models (FMR), and cluster-aware supervised learning (CluSL). Agnostic-cluster models encompass two-step procedures using either model-based or algorithmic clustering followed by cluster-specific regression models. Following a systematic search of Web of Science and PubMed, 55 records were identified that propose or evaluate such models. We describe the key models, summarise study characteristics, and present applications from biomedical and public health research. Clustering-based outcome models are particularly relevant for settings with high-dimensional covariates (e.g., biomarker panels and "omics") and heterogeneous patient populations. These models can support risk stratification and we discuss extensions to estimate subgroup-specific treatment effects. They are most valuable when the population is clustered in distinct regions of the covariate space that correspond to different outcome distributions. We discuss applications to rare disease research, covariate adjustment and borrowing from historical data, and subgroup-specific treatment effect estimation in clinical trials.

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Stratification in Randomised Clinical Trials for Rare Diseases and Analysis of Covariance: Some Simple Theory and Recommendations

A simple device for balancing for a continuous covariate in clinical trials is to stratify by whether the covariate is above or below some target value, typically the predicted median. This raises an issue as to which model should be used for modelling the effect of treatment on the outcome variable, $Y$. Should one fit, the stratum indicator, $S$, the continuous covariate, $X$, both or neither? When a covariate is added to a linear model there are three consequences for inference: 1) the mean square error effect, 2) the variance inflation factor and 3) second order precision. We consider that it is valuable to consider these three factors separately, even if, ultimately, it is their joint effect that matters. We present some simple theory, concentrating in particular on the variance inflation factor, that may be used to guide trialists in their choice of model. We also consider the case where the precise form of the relationship between the outcome and the covariate is not known. We conclude by recommending that the continuous covariate should always be in the model but that, depending on circumstances, there may be some justification in fitting the stratum indicator also.

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Selection Bias in Hybrid Randomized Controlled Trials using External Controls: A Simulation Study

Hybrid randomized controlled trials (hybrid RCTs) integrate external control data, such as historical or concurrent data, with data from randomized trials. While numerous frequentist and Bayesian methods, such as the test-then-pool and Meta-Analytic-Predictive prior, have been developed to account for potential disagreement between the external control and randomized data, they cannot ensure strict type I error rate control. However, these methods can reduce biases stemming from systematic differences between external controls and trial data. A critical yet underexplored issue in hybrid RCTs is the prespecification of external data to be used in analysis. The validity of statistical conclusions in hybrid RCTs depends on the assumption that external control selection is independent of historical trials outcomes. In practice, historical data may be accessible during the planning stage, potentially influencing important decisions, such as which historical datasets to include or the sample size of the prospective part of the hybrid trial, thus introducing bias. Such data-driven design choices can be an additional source of bias, which can occur even when historical and prospective controls are exchangeable. Through a simulation study, we quantify the biases introduced by outcome-dependent selection of historical controls in hybrid RCTs using both Bayesian and frequentist approaches, and discuss potential strategies to mitigate this bias. Our scenarios consider variability and time trends in the historical studies, distributional shifts between historical and prospective control groups, sample sizes and allocation ratios, as well as the number of studies included. The impact of different rules for selecting external controls is demonstrated using a clinical trial example.

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Covariate adjustment for linear models in estimating treatment effects in randomised clinical trials. Some useful theory to guide simulation

Building on key papers that were published in special issues of Biometrics in 1957 and 1982 we propose and develop a three-aspect system for evaluating the effect of fitting covariates in the analysis of designed experiments, in particular randomised clinical trials. The three aspects are: first the effect on residual mean square error, second the effect on the variance inflation factor (VIF) and third the effect on second order precision. We concentrate, in particular, on the VIF and highlight not only an existing formula for its expected value based on assuming covariates have a Normal distribution but also develop a formula for its variance. We show how VIFs for categorical variable are related to the chi-square contingency table with rows as treatment and columns as categories. We illustrate the value of these formulae using a randomised clinical trial with five covariates, one of which is binary, and show that both mean and variance formulae predict results well for all $2^5=32$ possible models for each of three forms of simulation, random permutation, sampling from a Normal distribution and bootstrap resampling. Finally, we illustrate how the three-aspect system may be used to address various questions of interest when considering covariate adjustment.

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A two-step approach for analyzing time to event data under non-proportional hazards

The log-rank test and the Cox proportional hazards model are commonly used to compare time-to-event data in clinical trials, as they are most powerful under proportional hazards. But there is a loss of power if this assumption is violated, which is the case for some new oncology drugs like immunotherapies. We consider a two-stage test procedure, in which the weighting of the log-rank test statistic depends on a pre-test of the proportional hazards assumption. I.e., depending on the pre-test either the log-rank or an alternative test is used to compare the survival probabilities. We show that if naively implemented this can lead to a substantial inflation of the type-I error rate. To address this, we embed the two-stage test in a permutation test framework to keep the nominal level alpha. We compare the operating characteristics of the two-stage test with the log-rank test and other tests by clinical trial simulations.

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Methods for non-proportional hazards in clinical trials: A systematic review

For the analysis of time-to-event data, frequently used methods such as the log-rank test or the Cox proportional hazards model are based on the proportional hazards assumption, which is often debatable. Although a wide range of parametric and non-parametric methods for non-proportional hazards (NPH) has been proposed, there is no consensus on the best approaches. To close this gap, we conducted a systematic literature search to identify statistical methods and software appropriate under NPH. Our literature search identified 907 abstracts, out of which we included 211 articles, mostly methodological ones. Review articles and applications were less frequently identified. The articles discuss effect measures, effect estimation and regression approaches, hypothesis tests, and sample size calculation approaches, which are often tailored to specific NPH situations. Using a unified notation, we provide an overview of methods available. Furthermore, we derive some guidance from the identified articles. We summarized the contents from the literature review in a concise way in the main text and provide more detailed explanations in the supplement.

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Efficiency of Multivariate Tests in Trials in Progressive Supranuclear Palsy

Measuring disease progression in clinical trials for testing novel treatments for multifaceted diseases as Progressive Supranuclear Palsy (PSP), remains challenging. In this study we assess a range of statistical approaches to compare outcomes measured by the items of the Progressive Supranuclear Palsy Rating Scale (PSPRS). We consider several statistical approaches, including sum scores, as an FDA-recommended version of the PSPRS, multivariate tests, and analysis approaches based on multiple comparisons of the individual items. We propose two novel approaches which measure disease status based on Item Response Theory models. We assess the performance of these tests in an extensive simulation study and illustrate their use with a re-analysis of the ABBV-8E12 clinical trial. Furthermore, we discuss the impact of the FDA-recommended scoring of item scores on the power of the statistical tests. We find that classical approaches as the PSPRS sum score demonstrate moderate to high power when treatment effects are consistent across the individual items. The tests based on Item Response Theory models yield the highest power when the simulated data are generated from an IRT model. The multiple testing based approaches have a higher power in settings where the treatment effect is limited to certain domains or items. The FDA-recommended item rescoring tends to decrease the simulated power. The study shows that there is no one-size-fits-all testing procedure for evaluating treatment effects using PSPRS items; the optimal method varies based on the specific effect size patterns. The efficiency of the PSPRS sum score, while generally robust and straightforward to apply, varies depending on the effect sizes' patterns encountered and more powerful alternatives are available in specific settings. These findings can have important implications for the design of future clinical trials in PSP.

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A neutral comparison of statistical methods for time-to-event analyses under non-proportional hazards

While well-established methods for time-to-event data are available when the proportional hazards assumption holds, there is no consensus on the best inferential approach under non-proportional hazards (NPH). However, a wide range of parametric and non-parametric methods for testing and estimation in this scenario have been proposed. To provide recommendations on the statistical analysis of clinical trials where non proportional hazards are expected, we conducted a comprehensive simulation study under different scenarios of non-proportional hazards, including delayed onset of treatment effect, crossing hazard curves, subgroups with different treatment effect and changing hazards after disease progression. We assessed type I error rate control, power and confidence interval coverage, where applicable, for a wide range of methods including weighted log-rank tests, the MaxCombo test, summary measures such as the restricted mean survival time (RMST), average hazard ratios, and milestone survival probabilities as well as accelerated failure time regression models. We found a trade-off between interpretability and power when choosing an analysis strategy under NPH scenarios. While analysis methods based on weighted logrank tests typically were favorable in terms of power, they do not provide an easily interpretable treatment effect estimate. Also, depending on the weight function, they test a narrow null hypothesis of equal hazard functions and rejection of this null hypothesis may not allow for a direct conclusion of treatment benefit in terms of the survival function. In contrast, non-parametric procedures based on well interpretable measures as the RMST difference had lower power in most scenarios. Model based methods based on specific survival distributions had larger power, however often gave biased estimates and lower than nominal confidence interval coverage.

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Simultaneous inference procedures for the comparison of multiple characteristics of two survival functions

Survival time is the primary endpoint of many randomized controlled trials, and a treatment effect is typically quantified by the hazard ratio under the assumption of proportional hazards. Awareness is increasing that in many settings this assumption is a-priori violated, e.g. due to delayed onset of drug effect. In these cases, interpretation of the hazard ratio estimate is ambiguous and statistical inference for alternative parameters to quantify a treatment effect is warranted. We consider differences or ratios of milestone survival probabilities or quantiles, differences in restricted mean survival times and an average hazard ratio to be of interest. Typically, more than one such parameter needs to be reported to assess possible treatment benefits, and in confirmatory trials the according inferential procedures need to be adjusted for multiplicity. By using the counting process representation of the mentioned parameters, we show that their estimates are asymptotically multivariate normal and we propose according parametric multiple testing procedures and simultaneous confidence intervals. Also, the logrank test may be included in the framework. Finite sample type I error rate and power are studied by simulation. The methods are illustrated with an example from oncology. A software implementation is provided in the R package nph.

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Design Considerations for a Phase II platform trial in Major Depressive Disorder

Major Depressive Disorder (MDD) is one of the most common causes of disability worldwide. Unfortunately, about one-third of patients do not benefit sufficiently from available treatments and not many new drugs have been developed in this area in recent years. We thus need better and faster ways to evaluate many different treatment options quickly. Platform trials are a possible remedy - they facilitate the evaluation of more investigational treatments in a shorter period of time by sharing controls, as well as reducing clinical trial activation and recruitment times. We discuss design considerations for a platform trial in MDD, taking into account the unique disease characteristics, and present the results of extensive simulations to investigate the operating characteristics under various realistic scenarios. To allow the testing of more treatments, interim futility analyses should be performed to eliminate treatments that have either no or negligible treatment effect. Furthermore, we investigate different randomisation and allocation strategies as well as the impact of the per-treatment arm sample size. We compare the operating characteristics of such platform trials to those of traditional randomised controlled trials and highlight the potential advantages of platform trials.

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Designing an exploratory phase 2b platform trial in NASH with correlated, co-primary binary endpoints

Non-alcoholic steatohepatitis (NASH) is the progressive form of nonalcoholic fatty liver disease (NAFLD) and a disease with high unmet medical need. Platform trials provide great benefits for sponsors and trial participants in terms of accelerating drug development programs. In this article, we describe some of the activities of the EU-PEARL consortium (EU Patient-cEntric clinicAl tRial pLatforms) regarding the use of platform trials in NASH, in particular the proposed trial design, decision rules and simulation results. For a set of assumptions, we present the results of a simulation study recently discussed with two health authorities and the learnings from these meetings from a trial design perspective. Since the proposed design uses co-primary binary endpoints, we furthermore discuss the different options and practical considerations for simulating correlated binary endpoints.

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Online error control for platform trials

Platform trials evaluate multiple experimental treatments under a single master protocol, where new treatment arms are added to the trial over time. Given the multiple treatment comparisons, there is the potential for inflation of the overall type I error rate, which is complicated by the fact that the hypotheses are tested at different times and are not all necessarily pre-specified. Online error control methodology provides a possible solution to the problem of multiplicity for platform trials where a relatively large number of hypotheses are expected to be tested over time. In the online testing framework, hypotheses are tested in a sequential manner, where at each time-step an analyst decides whether to reject the current null hypothesis without knowledge of future tests but based solely on past decisions. Methodology has recently been developed for online control of the false discovery rate as well as the familywise error rate (FWER). In this paper, we describe how to apply online error control to the platform trial setting, present extensive simulation results, and give some recommendations for the use of this new methodology in practice. We show that the algorithms for online error rate control can have a substantially lower FWER than uncorrected testing, while still achieving noticeable gains in power when compared with the use of a Bonferroni procedure. We also illustrate how online error control would have impacted a currently ongoing platform trial.

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CohortPlat: Simulation of cohort platform trials investigating combination therapies

Platform trials have gained a lot of attention recently as a possible remedy for time-consuming classical two-arm randomized controlled trials, especially in early phase drug development. This short article illustrates how to use the CohortPlat R package to simulate a cohort platform trial, where each cohort consists of a combination treatment and the respective monotherapies and standard-of-care. The endpoint is always assumed to be binary. The package offers extensive flexibility with respect to both platform trial trajectories, as well as treatment effect scenarios and decision rules. As a special feature, the package provides a designated function for running multiple such simulations efficiently in parallel and saving the results in a concise manner. Many illustrations of code usage are provided.

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Decision rules for identifying combination therapies in open-entry, randomized controlled platform trials

Platform trials have become increasingly popular for drug development programs, attracting interest from statisticians, clinicians and regulatory agencies. Many statistical questions related to designing platform trials - such as the impact of decision rules, sharing of information across cohorts, and allocation ratios on operating characteristics and error rates - remain unanswered. In many platform trials, the definition of error rates is not straightforward as classical error rate concepts are not applicable. For an open-entry, exploratory platform trial design comparing combination therapies to the respective monotherapies and standard-of-care, we define a set of error rates and operating characteristics and then use these to compare a set of design parameters under a range of simulation assumptions. When setting up the simulations, we aimed for realistic trial trajectories, such that e.g. a priori we do not know the exact number of treatments that will be included over time in a specific simulation run as this follows a stochastic mechanism. Our results indicate that the method of data sharing, exact specification of decision rules and a priori assumptions regarding the treatment efficacy all strongly contribute to the operating characteristics of the platform trial. Furthermore, different operating characteristics might be of importance to different stakeholders. Together with the potential flexibility and complexity of a platform trial, which also impact the achieved operating characteristics via e.g. the degree of efficiency of data sharing, this implies that utmost care needs to be given to evaluation of different assumptions and design parameters at the design stage.

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Adding experimental treatment arms to Multi-Arm Multi-Stage platform trials in progress

Multi-Arm Multi-Stage (MAMS) platform trials are an efficient tool for the comparison of several treatments. Suppose we wish to add a treatment to a trial already in progress, to access the benefits of a MAMS design. How should this be done? The MAMS framework requires pre-planned options for how the trial proceeds at each stage in order to control the family-wise error rate. Thus, it is difficult to make both planned and unplanned design modifications. The conditional error approach is a tool that allows unplanned design modifications while maintaining the overall error rate. In this work, we use the conditional error approach to allow adding new arms to a MAMS trial in progress. We demonstrate the principles of incorporating additional hypotheses into the testing structure. Using this framework, we show how to update the testing procedure for a MAMS trial in progress to incorporate additional treatment arms. Simulations illustrate the possible operating characteristics of such procedures using a fixed rule for how and when the design modification is made.

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A multiple comparison procedure for dose-finding trials with subpopulations

Identifying subgroups of patients with an enhanced response to a new treatment has become an area of increased interest in the last few years. When there is knowledge about possible subpopulations with an enhanced treatment effect before the start of a trial it might be beneficial to set up a testing strategy, which tests for a significant treatment effect not only in the full population, but also in these prespecified subpopulations. In this paper we present a parametric multiple testing approach for tests in multiple populations for dose-finding trials. Our approach is based on the MCP-Mod methodology, which uses multiple comparison procedures to test for a dose-response signal, while considering multiple possible candidate dose-response shapes. Our proposed methods allow for heteroscedasticity between populations and control the FWER over tests in multiple populations and for multiple candidate models. We show in simulations, that the proposed multi-population testing approaches can increase the power to detect a significant dose-response signal over the standard single-population MCP-Mod, when the considered subpopulation has an enhanced treatment effect.

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Optimizing Trial Designs for Targeted Therapies

An important objective in the development of targeted therapies is to identify the populations where the treatment under consideration has positive benefit risk balance. We consider pivotal clinical trials, where the efficacy of a treatment is tested in an overall population and/or in a pre-specified subpopulation. Based on a decision theoretic framework we derive optimized trial designs by maximizing utility functions. Features to be optimized include the sample size and the population in which the trial is performed (the full population or the targeted subgroup only) as well as the underlying multiple test procedure. The approach accounts for prior knowledge of the efficacy of the drug in the considered populations using a two dimensional prior distribution. The considered utility functions account for the costs of the clinical trial as well as the expected benefit when demonstrating efficacy in the different subpopulations. We model utility functions from a sponsor's as well as from a public health perspective, reflecting actual civil interests. Examples of optimized trial designs obtained by numerical optimization are presented for both perspectives.

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