Brannath, Werner
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Brannath, Werner
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Brannath, Werner
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Item-typ:Veröffentlichung, Non-parametric Sequential and Adaptive Designs for Survival Trials(2014-10-01); ; ; This thesis deals with fixed samples size, sequential and adaptive survival trials and consists of two major parts. In the first part fixed sample size, sequential and adaptive testing methods are derived that utilize data from a survival as well as a categorical surrogate endpoint in a fully non-parametric way without the need to assume any type of proportional hazards. In the second part extensions to quality-adjusted survival endpoints are discussed. In existing adaptive methods for confirmatory survival trials with flexible adaptation rules strict type-I-error control is only ensured if the interim decisions are based solely on the primary endpoint. In trials with long-term follow-up it is often desirable to base interim decisions also on correlated short-term endpoints, such as a surrogate marker. Surrogate information available at the interim analysis may be used to predict future event times. If interim decisions, such as selection of a subgroup or changes to the recruitment process, depend on this information, control of the type-I-error is no longer formally guaranteed for methods assuming an independent increments structure. In this thesis the weighted Kaplan-Meier estimator, a modification of the classical Kaplan-Meier estimator incorporating discrete surrogate information, is used to construct a non-parametric test statistic for the comparison of survival distributions, a generalization of the average hazard ratio. It is shown in this thesis how this test statistic can be used in fixed design, group-sequential and adaptive trials, such that the type-I-error is controlled. Asymptotic normality of the multivariate average hazard ratio is first verified in the fixed sample size context and then applied to noninferiority testing in a three-arm trial with non-proportional hazards survival data. In the next step the independent increments property is shown to hold asymptotically for the weighted Kaplan-Meier estimator. Consequently, for all test statistics based on it. Standard methods for the calculation of group-sequential rejection boundaries are applicable. For adaptive designs the weighted Kaplan-Meier estimator is modified to support stage-wise left-truncated and right-censored data to ensure independence of the stage-wise test statistics, even when interim decisions are based on surrogate information. Standard combination test methodology can then be used to ensure strict type-I-error control. Quality-adjusted survival is an integrated measure of quality-of-life data, which has gained interest in recent years. In this thesis a novel non-parametric two-sample test for quality-adjusted survival distributions is developed, that allows adjustment for covariate-dependent censoring, whereby the censoring is assumed to follow a proportional hazards model. It is shown how this result can be used to design adaptive trials with a quality-adjusted survival endpoint.Dissertation297 126 - Some of the metrics are blocked by yourconsent settings
Item-typ:Veröffentlichung, Weighted Mean Impact Analysis(2015-11-16); ; ; Linear regression is a popular tool that is often applied to biometric and epidemiological data. It relies on strong model assumptions that are rarely satisfied. To overcome this difficulty, Brannath and Scharpenberg (2014) proposed a new population based interpretation of linear regression coefficients. The idea is to quantify how much the unconditional mean of the dependent variable Y can be changed by changing the distribution of the independent variable X. The maximum change is called "mean impact". They show that linear regression can be used to obtain a conservative estimator of the mean impact and other population association measures. This provides a clear interpretation of the linear regression coefficients also under miss-specifications of the mean structure. A disadvantage of the new association measure is its dependence on the distribution of the independent variables in the specific study population. Hence, it may be difficult to compare the results between different studies with differing covariate distributions. To overcome this difficulty we develop a method to transfer the "mean impact" from one study population to a reference population by reweighting the observations. Accordingly, we call the resulting estimator the "weighted mean impact". The weights are obtained by a simple transformation of the expectation of the covariates multiplied with the target variable. They are defined as the density of the covariables in the true population divided by the distribution of the covariables in a pseudopopulation. For the new developed weighted mean impact we show desirable asymptotic properties like consistency and asymptotic normality. Although the weights are unknown in practical applications we first consider the case of known weights to improve the understanding of the reweighting mechanisms. Subsequently, the approach is generalized to the case of unknown weights which need to be estimated. One application for the reweighting mechanisms is to solve the problem of confounding. In the context of the mean impact confounding arises if the covariates are dependent. To avoid confounding we transform the mean impact under dependent covariates into a mean impact under independent covariates by using the weighting factor. For this example the weights are the ratio of the marginal density of one of the covariates and the conditional density. For this reason Robins et al. (2000) proposed theseweights in the context ofmarginal structural models. For the weighted mean impact with unknown weights we show asymptotic properties, develop bootstrap confidence intervals and demonstrate the utility of the new method by examples and results from a simulation study.Dissertation388 188 - Some of the metrics are blocked by yourconsent settings
Item-typ:Veröffentlichung, Group Sequential and Adaptive Designs for Three-Arm 'Gold Standard' Non-Inferiority Trials(2014-06-24); ; ; This thesis deals with the application of group sequential and adaptive methodology in three-arm non-inferiority trials for the case of normally distributed outcomes. Whenever feasible, use of the three-arm design including a test treatment, an active control and a placebo, is recommended by the health authorities. Nevertheless, especially from an ethical point of view, it is desirable to keep the placebo group size as small as possible. After giving a short introduction to two-arm non-inferiority trials, we investigate a hierarchical single-stage testing procedure for three-arm trials which starts by assessing the superiority comparison between test and placebo and then proceeds to the test versus control non-inferiority comparison. Based on formulas for the overall power we derive optimal sample size allocations that minimise the overall sample size. Interestingly, the placebo group size turns out to be very low under the optimal allocation. The optimal fixed sample size designs will then serve both as a starting point and a benchmark for the designs determined later. Subsequently, a general group sequential design for three-arm non-inferiority trials is presented that aims at further minimising the required sample sizes. By choosing different rejection boundaries for the two comparisons we obtain designs with quite different properties. The influence of the boundaries on the operating characteristics such as the expected sample sizes is investigated by means of a comprehensive comparison to the optimal fixed design. Moreover, approximately optimal boundaries are derived for different optimisation criteria such as minimising the placebo group size. It turns out that the implementation of group sequential methodology can further improve the optimal fixed designs, where the potential early termination of the placebo arm is a key advantage that can make the trial more acceptable for patients. After this, the group sequential testing procedure is extended to adaptive designs that allow data-dependent design changes at the interim analysis. In this context, we discuss optimal mid-trial decision-making based on the observed interim data, with a special focus on sample size re-calculation. In doing so, we will make use of the conditional power and the Bayesian predictive power. Our investigations show the advantages of the proposed adaptive designs over the optimal fixed designs. In particular, the possibility to adapt the sample sizes at interim can help to deal with uncertainties regarding the treatment effects, that often exist in the planning stage of three-arm non-inferiority trials. We conclude with a discussion of the results and an outlook on possible future work.Dissertation339 219 - Some of the metrics are blocked by yourconsent settings
Item-typ:Veröffentlichung, Biomarker selection and cutoff estimation in drug development(2019-05-16); ; ; In this cumulative thesis we discuss topics in the area of biomarker selection and cutoff estimation, where both subjects are related to the usability and applicability of biomarkers in drug development. The growing role of targeted medicine has led to an increased focus on the development of actionable biomarkers. Current penalized selection methods that are used to identify biomarker panels for classification in high-dimensional data, however, often result in highly complex panels that need careful pruning for practical use. In the framework of regularization methods, a penalty that is a weighted sum of the L1 and L0 norm has been proposed to account for the complexity of the resulting model. In practice, the limitation of this penalty is that the objective function is non-convex, non-smooth, the optimization is computationally intensive and the application to high-dimensional settings is challenging. In the first part of the thesis, we propose a stepwise forward variable selection method which combines the L0 with L1 or L2 norms. The penalized likelihood criterion that is used in the stepwise selection procedure results in more parsimonious models, keeping only the most relevant features. Moreover in this thesis, we introduce a new approach to derive the distribution of the cutoff and predictive values of a biomarker assay. To enable targeted therapies and enhance medical decision-making, biomarkers are increasingly used as screening and diagnostic tests. When using quantitative biomarkers for classification purposes, this often implies that an appropriate cutoff for the biomarker has to be determined and its clinical utility must be assessed. In the context of drug development, it is of interest how the probability of response changes with increasing values of the biomarker. Unlike sensitivity and specificity, predictive values are functions of the accuracy of the test, depend on the prevalence of the disease and therefore are a useful tool in this setting. We propose a Bayesian method to not only estimate the cutoff value using the negative and positive predictive values, but also estimate the uncertainty around this estimate. We use a step function, which serves as an approximate model facilitating classification into two groups that have different response rates. The advantage of using the step function is that both the cutoff and the predictive values are parameters of the model. Using Bayesian inference allows us to incorporate prior information and obtain posterior estimates and credible intervals for the cut-off and associated predictive values. Lastly, we further discuss the simultaneous variable selection and cutoff estimation (of the selected variables) by controlling the clinical utility, which is expressed in terms of negative and positive predictive values. A Bayesian variable selection method is introduced, which incorporates information about the predictive values into the biomarker selection process and simultaneously estimates the cutoff value on the risk score of the selected markers. The selection of the predictors in the final model is done under the constraint that the predictive values can take values in prespecified interval. The choice of different prior distributions is discussed. We conclude with discussions at each chapter of the dissertation.Dissertation462 272 - Some of the metrics are blocked by yourconsent settings
Item-typ:Veröffentlichung, Two-Stage Adaptive Designs With Interim Treatment Selection(2015-04-30); ; ; This dissertation is about two-stage adaptive designs with interim treatment selection. It includes two articles entitled (1) Shrinkage estimation in two-stage adaptive designs with midtrial treatment selection and (2) Adaptive seamless designs with interim treatment selection: a case study in oncology. Both articles are published in the journal Statistics in Medicine. Adaptive designs for clinical trials allow interim data-driven design modifications while maintaining the rigor and validity of the statistical inference [1]. Design adaptations may include early stopping for efficacy, futility or safety, reassessment of the overall sample size, adjustments to the study population (e.g. restriction to a sub-population), changes to endpoints or hypothesis to be tested as well as dropping or adding treatment arms. Adaptive designs have gained considerable popularity in recent years among clinical trialists because of their potential to improve efficiency in drug development. There are also ethical considerations that support the use of adaptive designs; for example, adaptive designs can reduce the number of patients within the trial who are treated with non-effective treatments. Overall, adaptive designs provide the same scientific rigor that is required in more traditional study designs while potentially utilizing fewer resources. However, while the increase in flexibility of adaptive designs offers great opportunities, it also brings limitations and pitfalls which should be carefully assessed when adaptive designs are intended to be used in confirmatory trials [2], [3]. In the traditional drug development process, a phase II study typically compares several treatments (e.g. different doses of a new compound) to a control. The objective of the study is to determine whether the development of the compound should be continued and, if so, which treatment(s) or dose(s) should be further investigated. The phase II study also provides initial estimates of treatment effect, which are used to power the subsequent phase III study. The phase III study is then conducted as a stand-alone confirmatory study, disregarding all data collected on the phase II study. One of the most appealing applications of adaptive designs is to combine phase II and phase III studies of the traditional drug development process into a single seamless phase II/III confirmatory study (see [4] and [5] for comprehensive summaries). Bauer and Kieser [6] proposed two-stage adaptive designs that allow the integration of the treatment selection and the confirmatory testing of efficacy for the selected treatments within a single study. An important feature of these designs is the fact that the treatment selection rule does not need to be pre-specified, which gives considerable flexibility to the inherently complex interim decision process. Hommel [7] extended Bauer and Kieser's work to allow design modifications which include interim changes to the primary endpoint as well as addition of experimental treatments. All these adaptive designs (see also [8]) propose tests that control the family-wise type I error rate in the strong sense; that is, the probability that any treatment is erroneously declared significantly superior to the control is maintained below a pre-specified significance level under all possible configurations of effective and ineffective treatments. In the introduction of the dissertation, we discuss hypothesis testing and estimation in two-stage adaptive designs with interim treatment selection, which serve as a summary of the topics developed in the two articles.Dissertation348 187 - Some of the metrics are blocked by yourconsent settings
Item-typ:Veröffentlichung, Bias and precision in early phase adaptive oncology studies and its consequences for confirmatory trials(2018-10-08); ; ; The need for a more efficient drug development process led to migration from the traditional fixed-sample clinical trial designs to group-sequential and adaptive designs, especially in early phases of clinical drug development. This, however, came with challenges in inference, since many of these newly proposed designs come without respective methods for statistical inference. In this dissertation, we study the estimation methods for oncology phase II group-sequential and adaptive designs in terms of bias and precision, and we propose new estimation methods for a new class of adaptive designs. We then evaluate the consequences, in terms of power, of using estimates from these designs to plan phase III trial. We also study and propose new approaches to adjust these estimates, based on the observed data, before employing them in planning of phase III sample size, in order to reach the desired power. Literature review showed that many estimation methods have been proposed for the classical single-arm two-stage group-sequential designs with a binary endpoint, which are the most commonly used designs in oncology trials of phase II. Simulation studies showed that the uniformly minimum variance unbiased estimator is the best amongst them in terms of bias and mean square error. However, for the adaptive group-sequential designs, these estimation methods have poor performance. Our proposed estimation methods in oncology phase II adaptive designs showed better performance as compared to the naive maximum likelihood estimator. A direct use of estimates from phase II adaptive designs to plan phase III results in underpowered phase III trials. Therefore, adjusting (discounting) these estimates beforehand is necessary. The amount of discounting, however, depends on the estimator, with our proposed estimators requiring less discounting as compared to the naive maximum likelihood estimator. Our proposed adjustment approaches show power improvements, which are similar across different estimators and design scenarios.Dissertation389 201