arXiv subjects

Marc Ditzhaus

Publications and source records attributed to Marc Ditzhaus.

At least 19 recordsLinked to original sources

arXiv2026

Inference for competing risks based on area between curves statistics

In competing risks models, cumulative incidence functions are commonly compared to infer differences between groups. Many existing inference methods, however, struggle when these functions cross during the time frame of interest. To address this problem, we investigate a test statistic based on the area between cumulative incidence functions. As the corresponding limiting distribution depends on quantities that are typically unknown, we propose a wild bootstrap approach to obtain a feasible and asymptotically valid two-sample test. The finite sample performance of the proposed method, in comparison with existing methods, is examined in an extensive simulation study.

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arXiv2025

Effect measures for comparing paired event times

The progression-free survival ratio (PFSr) is a widely used measure in personalized oncology trials. It evaluates the effectiveness of treatment by comparing two consecutive event times - one under standard therapy and one under an experimental treatment. However, most proposed tests based on the PFSr cannot control the nominal type I error rate, even under mild assumptions such as random right-censoring. Consequently the results of these tests are often unreliable. As a remedy, we propose to estimate the relevant probabilities related to the PFSr by adapting recently developed methodology for the relative treatment effect between paired event times. As an additional alternative, we develop inference procedures based on differences and ratios of restricted mean survival times. An extensive simulation study confirms that the proposed novel methodology provides reliable inference, whereas previously proposed techniques break down in many realistic settings. The utility of our methods is further illustrated through an analysis of real data from a molecularly aided tumor trial.

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arXiv2024

A Central Limit Theorem for the permutation importance measure

Random Forests have become a widely used tool in machine learning since their introduction in 2001, known for their strong performance in classification and regression tasks. One key feature of Random Forests is the Random Forest Permutation Importance Measure (RFPIM), an internal, non-parametric measure of variable importance. While widely used, theoretical work on RFPIM is sparse, and most research has focused on empirical findings. However, recent progress has been made, such as establishing consistency of the RFPIM, although a mathematical analysis of its asymptotic distribution is still missing. In this paper, we provide a formal proof of a Central Limit Theorem for RFPIM using U-Statistics theory. Our approach deviates from the conventional Random Forest model by assuming a random number of trees and imposing conditions on the regression functions and error terms, which must be bounded and additive, respectively. Our result aims at improving the theoretical understanding of RFPIM rather than conducting comprehensive hypothesis testing. However, our contributions provide a solid foundation and demonstrate the potential for future work to extend to practical applications which we also highlight with a small simulation study.

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arXiv2024

Single CASANOVA? Not in multiple comparisons

When comparing multiple groups in clinical trials, we are not only interested in whether there is a difference between any groups but rather the location. Such research questions lead to testing multiple individual hypotheses. To control the familywise error rate (FWER), we must apply some corrections or introduce tests that control the FWER by design. In the case of time-to-event data, a Bonferroni-corrected log-rank test is commonly used. This approach has two significant drawbacks: (i) it loses power when the proportional hazards assumption is violated [1] and (ii) the correction generally leads to a lower power, especially when the test statistics are not independent [2]. We propose two new tests based on combined weighted log-rank tests. One as a simple multiple contrast test of weighted log-rank tests and one as an extension of the so-called CASANOVA test [3]. The latter was introduced for factorial designs. We propose a new multiple contrast test based on the CASANOVA approach. Our test promises to be more powerful under crossing hazards and eliminates the need for additional p-value correction. We assess the performance of our tests through extensive Monte Carlo simulation studies covering both proportional and non-proportional hazard scenarios. Finally, we apply the new and reference methods to a real-world data example. The new approaches control the FWER and show reasonable power in all scenarios. They outperform the adjusted approaches in some non-proportional settings in terms of power.

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arXiv2024

Early and Late Buzzards: Comparing Different Approaches for Quantile-based Multiple Testing in Heavy-Tailed Wildlife Research Data

In medical, ecological and psychological research, there is a need for methods to handle multiple testing, for example to consider group comparisons with more than two groups. Typical approaches that deal with multiple testing are mean or variance based which can be less effective in the context of heavy-tailed and skewed data. Here, the median is the preferred measure of location and the interquartile range (IQR) is an adequate alternative to the variance. Therefore, it may be fruitful to formulate research questions of interest in terms of the median or the IQR. For this reason, we compare different inference approaches for two-sided and non-inferiority hypotheses formulated in terms of medians or IQRs in an extensive simulation study. We consider multiple contrast testing procedures combined with a bootstrap method as well as testing procedures with Bonferroni correction. As an example of a multiple testing problem based on heavy-tailed data we analyse an ecological trait variation in early and late breeding in a medium-sized bird of prey.

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arXiv2024

Multiple tests for restricted mean time lost with competing risks data

Easy-to-interpret effect estimands are highly desirable in survival analysis. In the competing risks framework, one good candidate is the restricted mean time lost (RMTL). It is defined as the area under the cumulative incidence function up to a prespecified time point and, thus, it summarizes the cumulative incidence function into a meaningful estimand. While existing RMTL-based tests are limited to two-sample comparisons and mostly to two event types, we aim to develop general contrast tests for factorial designs and an arbitrary number of event types based on a Wald-type test statistic. Furthermore, we avoid the often-made, rather restrictive continuity assumption on the event time distribution. This allows for ties in the data, which often occur in practical applications, e.g., when event times are measured in whole days. In addition, we develop more reliable tests for RMTL comparisons that are based on a permutation approach to improve the small sample performance. In a second step, multiple tests for RMTL comparisons are developed to test several null hypotheses simultaneously. Here, we incorporate the asymptotically exact dependence structure between the local test statistics to gain more power. The small sample performance of the proposed testing procedures is analyzed in simulations and finally illustrated by analyzing a real data example about leukemia patients who underwent bone marrow transplantation.

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arXiv2024

Multiple Comparison Procedures for Simultaneous Inference in Functional MANOVA

Functional data analysis is becoming increasingly popular to study data from real-valued random functions. Nevertheless, there is a lack of multiple testing procedures for such data. These are particularly important in factorial designs to compare different groups or to infer factor effects. We propose a new class of testing procedures for arbitrary linear hypotheses in general factorial designs with functional data. Our methods allow global as well as multiple inference of both, univariate and multivariate mean functions without assuming particular error distributions nor homoscedasticity. That is, we allow for different structures of the covariance functions between groups. To this end, we use point-wise quadratic-form-type test functions that take potential heteroscedasticity into account. Taking the supremum over each test function, we define a class of local test statistics. We analyse their (joint) asymptotic behaviour and propose a resampling approach to approximate the limit distributions. The resulting global and multiple testing procedures are asymptotic valid under weak conditions and applicable in general functional MANOVA settings. We evaluate their small-sample performance in extensive simulations and finally illustrate their applicability by analysing a multivariate functional air pollution data set.

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arXiv2024

Even naive trees are consistent

The last decade has shed some light on theoretical properties such as their consistency for regression tasks. In the current paper, we propose a new class of very simple learners based on so-called naive trees. These naive trees partition the feature space completely at random and independent of the data. Although counter-intuitive, we prove these naive trees and ensembles are consistent under fairly general assumptions. However, naive trees appear to be too simple for actual application. We therefore analyze their finite sample properties in a simulation and small benchmark study. We find a slow convergence speed and a rather poor predictive performance. Based on these results, we finally discuss to what extent consistency proofs help to justify the application of complex learning algorithms.

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arXiv2023

RMST-based multiple contrast tests in general factorial designs

Several methods in survival analysis are based on the proportional hazards assumption. However, this assumption is very restrictive and often not justifiable in practice. Therefore, effect estimands that do not rely on the proportional hazards assumption are highly desirable in practical applications. One popular example for this is the restricted mean survival time (RMST). It is defined as the area under the survival curve up to a prespecified time point and, thus, summarizes the survival curve into a meaningful estimand. For two-sample comparisons based on the RMST, previous research found the inflation of the type I error of the asymptotic test for small samples and, therefore, a two-sample permutation test has already been developed. The first goal of the present paper is to further extend the permutation test for general factorial designs and general contrast hypotheses by considering a Wald-type test statistic and its asymptotic behavior. Additionally, a groupwise bootstrap approach is considered. Moreover, when a global test detects a significant difference by comparing the RMSTs of more than two groups, it is of interest which specific RMST differences cause the result. However, global tests do not provide this information. Therefore, multiple tests for the RMST are developed in a second step to infer several null hypotheses simultaneously. Hereby, the asymptotically exact dependence structure between the local test statistics is incorporated to gain more power. Finally, the small sample performance of the proposed global and multiple testing procedures is analyzed in simulations and illustrated in a real data example.

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arXiv2023

How to Simulate Realistic Survival Data? A Simulation Study to Compare Realistic Simulation Models

In statistics, it is important to have realistic data sets available for a particular context to allow an appropriate and objective method comparison. For many use cases, benchmark data sets for method comparison are already available online. However, in most medical applications and especially for clinical trials in oncology, there is a lack of adequate benchmark data sets, as patient data can be sensitive and therefore cannot be published. A potential solution for this are simulation studies. However, it is sometimes not clear, which simulation models are suitable for generating realistic data. A challenge is that potentially unrealistic assumptions have to be made about the distributions. Our approach is to use reconstructed benchmark data sets %can be used as a basis for the simulations, which has the following advantages: the actual properties are known and more realistic data can be simulated. There are several possibilities to simulate realistic data from benchmark data sets. We investigate simulation models based upon kernel density estimation, fitted distributions, case resampling and conditional bootstrapping. In order to make recommendations on which models are best suited for a specific survival setting, we conducted a comparative simulation study. Since it is not possible to provide recommendations for all possible survival settings in a single paper, we focus on providing realistic simulation models for two-armed phase III lung cancer studies. To this end we reconstructed benchmark data sets from recent studies. We used the runtime and different accuracy measures (effect sizes and p-values) as criteria for comparison.

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arXiv2023

General multiple tests for functional data

While there exists several inferential methods for analyzing functional data in factorial designs, there is a lack of statistical tests that are valid (i) in general designs, (ii) under non-restrictive assumptions on the data generating process and (iii) allow for coherent post-hoc analyses. In particular, most existing methods assume Gaussianity or equal covariance functions across groups (homoscedasticity) and are only applicable for specific study designs that do not allow for evaluation of interactions. Moreover, all available strategies are only designed for testing global hypotheses and do not directly allow a more in-depth analysis of multiple local hypotheses. To address the first two problems (i)-(ii), we propose flexible integral-type test statistics that are applicable in general factorial designs under minimal assumptions on the data generating process. In particular, we neither postulate homoscedasticity nor Gaussianity. To approximate the statistics' null distribution, we adopt a resampling approach and validate it methodologically. Finally, we use our flexible testing framework to (iii) infer several local null hypotheses simultaneously. To allow for powerful data analysis, we thereby take the complex dependencies of the different local test statistics into account. In extensive simulations we confirm that the new methods are flexibly applicable. Two illustrate data analyses complete our study. The new testing procedures are implemented in the R package multiFANOVA, which will be available on CRAN soon.

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arXiv2023

Factorial survival analysis for treatment effects under dependent censoring

Factorial analyses offer a powerful nonparametric means to detect main or interaction effects among multiple treatments. For survival outcomes, e.g. from clinical trials, such techniques can be adopted for comparing reasonable quantifications of treatment effects. The key difficulty to solve in survival analysis concerns the proper handling of censoring. So far, all existing factorial analyses for survival data were developed under the independent censoring assumption, which is too strong for many applications. As a solution, the central aim of this article is to develop new methods in factorial survival analyses under quite general dependent censoring regimes. This will be accomplished by combining existing results for factorial survival analyses with techniques developed for survival copula models. As a result, we will present an appealing F-test that exhibits sound performance in our simulation study. The new methods are illustrated in real data analysis. We implement the proposed method in an R function surv.factorial(.) in the R package compound.Cox.

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arXiv2023

Inference for all variants of the multivariate coefficient of variation in factorial designs

The multivariate coefficient of variation (MCV) is an attractive and easy-to-interpret effect size for the dispersion in multivariate data. Recently, the first inference methods for the MCV were proposed by Ditzhaus and Smaga (2022) for general factorial designs covering k-sample settings but also complex higher-way layouts. However, two questions are still pending: (1) The theory on inference methods for MCV is primarily derived for one special MCV variant while there are several reasonable proposals. (2) When rejecting a global null hypothesis in factorial designs, a more in-depth analysis is typically of high interest to find the specific contrasts of MCV leading to the aforementioned rejection. In this paper, we tackle both by, first, extending the aforementioned nonparametric permutation procedure to the other MCV variants and, second, by proposing a max-type test for post hoc analysis. To improve the small sample performance of the latter, we suggest a novel studentized bootstrap strategy and prove its asymptotic validity. The actual performance of all proposed tests and post hoc procedures are compared in an extensive simulation study and illustrated by a real data analysis.

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arXiv2022

Quantile-based MANOVA: A new tool for inferring multivariate data in factorial designs

Multivariate analysis-of-variance (MANOVA) is a well established tool to examine multivariate endpoints. While classical approaches depend on restrictive assumptions like normality and homogeneity, there is a recent trend to more general and flexible proce dures. In this paper, we proceed on this path, but do not follow the typical mean-focused perspective. Instead we consider general quantiles, in particular the median, for a more robust multivariate analysis. The resulting methodology is applicable for all kind of factorial designs and shown to be asymptotically valid. Our theoretical results are complemented by an extensive simulation study for small and moderate sample sizes. An illustrative data analysis is also presented.

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arXiv2022

A comparative study to alternatives to the log-rank test

Studies to compare the survival of two or more groups using time-to-event data are of high importance in medical research. The gold standard is the log-rank test, which is optimal under proportional hazards. As the latter is no simple regularity assumption, we are interested in evaluating the power of various statistical tests under different settings including proportional and non-proportional hazards with a special emphasize on crossing hazards. This challenge has been going on for many years now and multiple methods have already been investigated in extensive simulation studies. However, in recent years new omnibus tests and methods based on the restricted mean survival time appeared that have been strongly recommended in biometric literature. Thus, to give updated recommendations, we perform a vast simulation study to compare tests that showed high power in previous studies with these more recent approaches. We thereby analyze various simulation settings with varying survival and censoring distributions, unequal censoring between groups, small sample sizes and unbalanced group sizes. Overall, omnibus tests are more robust in terms of power against deviations from the proportional hazards assumption.

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arXiv2022

A Multiple kernel testing procedure for non-proportional hazards in factorial designs

In this paper we propose a Multiple kernel testing procedure to infer survival data when several factors (e.g. different treatment groups, gender, medical history) and their interaction are of interest simultaneously. Our method is able to deal with complex data and can be seen as an alternative to the omnipresent Cox model when assumptions such as proportionality cannot be justified. Our methodology combines well-known concepts from Survival Analysis, Machine Learning and Multiple Testing: differently weighted log-rank tests, kernel methods and multiple contrast tests. By that, complex hazard alternatives beyond the classical proportional hazard set-up can be detected. Moreover, multiple comparisons are performed by fully exploiting the dependence structure of the single testing procedures to avoid a loss of power. In all, this leads to a flexible and powerful procedure for factorial survival designs whose theoretical validity is proven by martingale arguments and the theory for $V$-statistics. We evaluate the performance of our method in an extensive simulation study and illustrate it by a real data analysis.

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arXiv2022

Hypothesis testing for matched pairs with missing data by maximum mean discrepancy: An application to continuous glucose monitoring

A frequent problem in statistical science is how to properly handle missing data in matched paired observations. There is a large body of literature coping with the univariate case. Yet, the ongoing technological progress in measuring biological systems raises the need for addressing more complex data, e.g., graphs, strings and probability distributions, among others. In order to fill this gap, this paper proposes new estimators of the maximum mean discrepancy (MMD) to handle complex matched pairs with missing data. These estimators can detect differences in data distributions under different missingness mechanisms. The validity of this approach is proven and further studied in an extensive simulation study, and results of statistical consistency are provided. Data from continuous glucose monitoring in a longitudinal population-based diabetes study are used to illustrate the application of this approach. By employing the new distributional representations together with cluster analysis, new clinical criteria on how glucose changes vary at the distributional level over five years can be explored.

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arXiv2021

Studentized Permutation Method for Comparing Restricted Mean Survival Times with Small Sample from Randomized Trials

Recent observations, especially in cancer immunotherapy clinical trials with time-to-event outcomes, show that the commonly used proportial hazard assumption is often not justifiable, hampering an appropriate analyse of the data by hazard ratios. An attractive alternative advocated is given by the restricted mean survival time (RMST), which does not rely on any model assumption and can always be interpreted intuitively. As pointed out recently by Horiguchi and Uno (2020), methods for the RMST based on asymptotic theory suffer from inflated type-I error under small sample sizes. To overcome this problem, they suggested a permutation strategy leading to more convincing results in simulations. However, their proposal requires an exchangeable data set-up between comparison groups which may be limiting in practice. In addition, it is not possible to invert their testing procedure to obtain valid confidence intervals, which can provide more in-depth information. In this paper, we address these limitations by proposing a studentized permutation test as well as the corresponding permutation-based confidence intervals. In our extensive simulation study, we demonstrate the advantage of our new method, especially in situations with relative small sample sizes and unbalanced groups. Finally we illustrate the application of the proposed method by re-analysing data from a recent lung cancer clinical trial.

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