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  • 1
    Abstract: In recent years, numerous approaches for biomarker-based clinical trials have been developed. One of these developments are multiple-biomarker trials, which aim to investigate multiple biomarkers simultaneously in independent subtrials. For low-prevalence biomarkers, small sample sizes within the subtrials have to be expected, as well as many biomarker-negative patients at the screening stage. The small sample sizes may make it unfeasible to analyze the subtrials individually. This imposes the need to develop new approaches for the analysis of such trials. With an expected large group of biomarker-negative patients, it seems reasonable to explore options to benefit from including them in such trials. We consider advantages and disadvantages of the inclusion of biomarker-negative patients in a multiple-biomarker trial with a survival endpoint. We discuss design options that include biomarker-negative patients in the study and address the issue of small sample size bias in such trials. We carry out a simulation study for a design where biomarker-negative patients are kept in the study and are treated with standard of care. We compare three different analysis approaches based on the Cox model to examine if the inclusion of biomarker-negative patients can provide a benefit with respect to bias and variance of the treatment effect estimates. We apply the Firth correction to reduce the small sample size bias. The results of the simulation study suggest that for small sample situations, the Firth correction should be applied to adjust for the small sample size bias. Additional to the Firth penalty, the inclusion of biomarker-negative patients in the analysis can lead to further but small improvements in bias and standard deviation of the estimates.
    Type of Publication: Journal article published
    PubMed ID: 28762532
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  • 2
    Abstract: We consider modeling competing risks data in high dimensions using a penalized cause-specific hazards (CSHs) approach. CSHs have conceptual advantages that are useful for analyzing molecular data. First, working on hazards level can further understanding of the underlying biological mechanisms that drive transition hazards. Second, CSH models can be used to extend the multistate framework for high-dimensional data. The CSH approach is implemented by fitting separate proportional hazards models for each event type (iCS). In the high-dimensional setting, this might seem too complex and possibly prone to overfitting. Therefore, we consider an extension, namely "linking" the separate models by choosing penalty tuning parameters that in combination yield best prediction of the incidence of the event of interest (penCR). We investigate whether this extension is useful with respect to prediction accuracy and variable selection. The two approaches are compared to the subdistribution hazards (SDH) model, which is an established method that naturally achieves "linking" by working on incidence level, but loses interpretability of the covariate effects. Our simulation studies indicate that in many aspects, iCS is competitive to penCR and the SDH approach. There are some instances that speak in favor of linking the CSH models, for example, in the presence of opposing effects on the CSHs. We conclude that penalized CSH models are a viable solution for competing risks models in high dimensions. Linking the CSHs can be useful in some particular cases; however, simple models using separately penalized CSH are often justified.
    Type of Publication: Journal article published
    PubMed ID: 28762523
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  • 3
    Keywords: NETWORK ; neural networks ; SUPPORT ; PROTEIN ; SEQUENCE ; FREQUENCY ; IDENTIFICATION ; max ; confusion matrix ; protein fold class prediction ; statistical classification methods ; support vector machines ; three-dimensional structure
    Abstract: Knowledge of the three-dimensional structure of a protein is essential for describing and understanding its function. Today, a large number of known protein sequences faces a small number of identified structures. Thus, the need arises to predict structure from sequence without using time-consuming experimental identification. In this paper the performance of Support Vector Machines (SVMs) is compared to Neural Networks and to standard statistical classification methods as Discriminant Analysis and Nearest Neighbor Classification. We show that SVMs can beat the competing methods on a dataset of 268 protein sequences to be classified into a set of 42 fold classes. We discuss misclassification with respect to biological function and similarity. In a second step we examine the performance of SVMs if the embedding is varied from frequencies of single amino acids to frequencies of tripletts of amino acids. This work shows that SVMs provide a promising alternative to standard statistical classification and prediction methods in functional genomics
    Type of Publication: Journal article published
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  • 4
    Keywords: CANCER ; CANCER CELLS ; CELLS ; CELL ; COMBINATION ; Germany ; human ; MODEL ; MODELS ; PATHWAY ; PATHWAYS ; ALGORITHMS ; GENE ; GENES ; microarray ; RNA ; COMPLEX ; COMPLEXES ; DNA ; BIOLOGY ; BREAST ; breast cancer ; BREAST-CANCER ; microarrays ; SIGNALING PATHWAY ; SIGNALING PATHWAYS ; CANCER-CELLS ; signaling ; review ; INTERFERENCE ; SIGNALING NETWORK ; signaling networks ; Nested effects models ; Perturbation data ; Signaling pathway inference
    Abstract: Targeted gene perturbations have become a major tool to gain insight into complex cellular processes. In combination with the measurement of downstream effects via DNA microarrays, this approach can be used to gain insight into signaling pathways. Nested Effects Models were first introduced by Markowetz et al. as a probabilistic method to reverse engineer signaling cascades based on the nested structure of downstream perturbation effects. The basic framework was substantially extended later on by Frohlich et al., Markowetz et al., and Tresch and Markowetz. In this paper, we present a review of the complete methodology with a detailed comparison of so far proposed algorithms on a qualitative and quantitative level. As an application, we present results on estimating the signaling network between 13 genes in the ER-a pathway of human MCF-7 breast cancer cells. Comparison with the literature shows a substantial overlap
    Type of Publication: Journal article published
    PubMed ID: 19358219
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  • 5
    Keywords: DISTRIBUTIONS ; leukemia ; PREDICTION ; REGRESSION ; PROPORTIONAL HAZARDS MODEL ; VARIABLE SELECTION ; LIKELIHOOD ; COORDINATE DESCENT ; SURVIVAL-TIME DATA ; REGULARIZATION PATHS
    Abstract: One important task in translational cancer research is the search for new prognostic biomarkers to improve survival prognosis for patients. The use of high-throughput technologies allows simultaneous measurement of genome-wide gene expression or other genomic data for all patients in a clinical trial. Penalized likelihood methods such as lasso regression can be applied to such high-dimensional data, where the number of (genomic) covariables is usually much larger than the sample size. There is a connection between the lasso and the Bayesian regression model with independent Laplace priors on the regression parameters, and understanding this connection has been useful for understanding the properties of lasso estimates in linear models (e.g. Park and Casella, ). In this paper, we study the lasso in the frequentist and Bayesian frameworks in the context of Cox models. For the Bayesian lasso we extend the approach by Lee et al. (). In particular, we impose the lasso penalty only on the genome features, but not on relevant clinical covariates, to allow the mandatory inclusion of important established factors. We investigate the models in high- and low-dimensional simulation settings and in an application to chronic lymphocytic leukemia.
    Type of Publication: Journal article published
    PubMed ID: 26417963
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  • 6
    Keywords: CANCER ; MICROARRAY DATA ; DATABASE ; support vector machines ; REGRESSION ; DRUG DISCOVERY ; GENE ONTOLOGY ; VARIABLE SELECTION ; pathway analysis ; GENOMIC DATA
    Abstract: Classification of patients based on molecular markers, for example into different risk groups, is a modern field in medical research. The aim of this classification is often a better diagnosis or individualized therapy. The search for molecular markers often utilizes extremely high-dimensional data sets (e.g. gene-expression microarrays). However, in situations where the number of measured markers (genes) is intrinsically higher than the number of available patients, standard methods from statistical learning fail to deal correctly with this so-called "curse of dimensionality''. Also feature or dimension reduction techniques based on statistical models promise only limited success. Several recent methods explore ideas of how to quantify and incorporate biological prior knowledge of molecular interactions and known cellular processes into the feature selection process. This article aims to give an overview of such current methods as well as the databases, where this external knowledge can be obtained from. For illustration, two recent methods are compared in detail, a feature selection approach for support vector machines as well as a boosting approach for regression models. As a practical example, data on patients with acute lymphoblastic leukemia are considered, where the binary endpoint "relapse within first year'' should be predicted.
    Type of Publication: Journal article published
    PubMed ID: 21328603
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  • 7
    Keywords: CLINICAL-TRIALS ; CORRELATED TEST STATISTICS ; GROUP SEQUENTIAL TRIALS ; BOUNDS
    Abstract: Adaptive designs were originally developed for independent and uniformly distributed p-values. There are trial settings where independence is not satisfied or where it may not be possible to check whether it is satisfied. In these cases, the test statistics and p-values of each stage may be dependent. Since the probability of a type I error for a fixed adaptive design depends on the true dependence structure between the p-values of the stages, control of the type I error rate might be endangered if the dependence structure is not taken into account adequately. In this paper, we address the problem of controlling the type I error rate in two-stage adaptive designs if any dependence structure between the test statistics of the stages is admitted (worst case scenario). For this purpose, we pursue a copula approach to adaptive designs. For two-stage adaptive designs without futility stop, we derive the probability of a type I error in the worst case, that is for the most adverse dependence structure between the p-values of the stages. Explicit analytical considerations are performed for the class of inverse normal designs. A comparison with the significance level for independent and uniformly distributed p-values is performed. For inverse normal designs without futility stop and equally weighted stages, it turns out that correcting for the worst case is too conservative as compared to a simple Bonferroni design.
    Type of Publication: Journal article published
    PubMed ID: 24395207
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  • 8
    Abstract: A multistage single arm phase II trial with binary endpoint is considered. Bayesian posterior probabilities are used to monitor futility in interim analyses and efficacy in the final analysis. For a beta-binomial model, decision rules based on Bayesian posterior probabilities are converted to "traditional" decision rules in terms of number of responders among patients observed so far. Analytical derivations are given for the probability of stopping for futility and for the probability to declare efficacy. A workflow is presented on how to select the parameters specifying the Bayesian design, and the operating characteristics of the design are investigated. It is outlined how the presented approach can be transferred to statistical models other than the beta-binomial model.
    Type of Publication: Journal article epub ahead of print
    PubMed ID: 30175405
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  • 9
    Keywords: SURVIVAL ; Germany ; MODEL ; MODELS ; INFORMATION ; RISK ; GENE ; microarray ; prognosis ; BIOLOGY ; ASSOCIATION ; VARIANTS ; BREAST-CANCER ; MICROARRAY DATA ; NUMBER ; REQUIRES ; PREDICTION ; REGRESSION ; VARIANT ; model selection ; development ; survival analysis ; GENE-EXPRESSION SIGNATURE ; SURVIVAL PREDICTION ; ADAPTIVE LASSO ; High dimensions ; NONCONCAVE PENALIZED LIKELIHOOD ; ORACLE PROPERTIES ; Penalized proportional hazards ; Predictive accuracy ; PROBABILITIES ; PROPORTIONAL HAZARDS MODEL ; VARIABLE SELECTION
    Abstract: The Cox proportional hazards regression model is the most popular approach to model covariate information for survival times. In this context, the development of high-dimensional models where the number of covariates is much larger than the number of observations (p 〉〉 n) is an ongoing challenge. A practicable approach is to use ridge penalized Cox regression in such situations. Beside focussing on finding the best prediction rule, one is often interested in determining a subset of covariates that are the most important ones for prognosis. This could be a gene set in the biostatistical analysis of microarray data. Covariate selection can then, for example, be done by L-1-penalized Cox regression using the lasso (Tibshirani (1997). Statistics in Medicine 16, 385-395). Several approaches beyond the lasso, that incorporate covariate selection, have been developed in recent years. This includes modifications of the lasso as well as nonconvex variants such as smoothly clipped absolute deviation (SCAD) (Fan and Li (2001). Journal of the American Statistical Association 96, 1348-1360; Fan and Li (2002). The Annals of Statistics 30, 74-99). The purpose of this article is to implement them practically into the model building process when analyzing high-dimensional data with the Cox proportional hazards model. To evaluate penalized regression models beyond the lasso, we included SCAD variants and the adaptive lasso (Zou (2006). Journal of the American Statistical Association 101, 1418-1429). We compare them with "standard" applications such as ridge regression, the lasso, and the elastic net. Predictive accuracy, features of variable selection, and estimation bias will be studied to assess the practical use of these methods. We observed that the performance of SCAD and adaptive lasso is highly dependent on nontrivial preselection procedures. A practical solution to this problem does not yet exist. Since there is high risk of missing relevant covariates when using SCAD or adaptive lasso applied after an inappropriate initial selection step, we recommend to stay with lasso or the elastic net in actual data applications. But with respect to the promising results for truly sparse models, we see some advantage of SCAD and adaptive lasso, if better preselection procedures would be available. This requires further methodological research
    Type of Publication: Journal article published
    PubMed ID: 20166132
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  • 10
    Abstract: When analyzing clinical trials with a stratified population, homogeneity of treatment effects is a common assumption in survival analysis. However, in the context of recent developments in clinical trial design, which aim to test multiple targeted therapies in corresponding subpopulations simultaneously, the assumption that there is no treatment-by-stratum interaction seems inappropriate. It becomes an issue if the expected sample size of the strata makes it unfeasible to analyze the trial arms individually. Alternatively, one might choose as primary aim to prove efficacy of the overall (targeted) treatment strategy. When testing for the overall treatment effect, a violation of the no-interaction assumption renders it necessary to deviate from standard methods that rely on this assumption. We investigate the performance of different methods for sample size calculation and data analysis under heterogeneous treatment effects. The commonly used sample size formula by Schoenfeld is compared to another formula by Lachin and Foulkes, and to an extension of Schoenfeld's formula allowing for stratification. Beyond the widely used (stratified) Cox model, we explore the lognormal shared frailty model, and a two-step analysis approach as potential alternatives that attempt to adjust for interstrata heterogeneity. We carry out a simulation study for a trial with three strata and violations of the no-interaction assumption. The extension of Schoenfeld's formula to heterogeneous strata effects provides the most reliable sample size with respect to desired versus actual power. The two-step analysis and frailty model prove to be more robust against loss of power caused by heterogeneous treatment effects than the stratified Cox model and should be preferred in such situations.
    Type of Publication: Journal article published
    PubMed ID: 28263395
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