Harald Binder

Fabian Kabus, Julia Hindel, Jelena Bratulić et al. · amazon-science

Recessive dystrophic epidermolysis bullosa (RDEB) is a rare genetic skin disorder for which clinicians greatly benefit from finding similar cases using images and clinical text. However, off-the-shelf foundation models do not reliably capture clinically meaningful features for this heterogeneous, long-tail disease, and structured measurement of agreement with experts is challenging. To address these gaps, we propose evaluating embedding spaces with expert ordinal comparisons (triplet judgments), which are fast to collect and encode implicit clinical similarity knowledge. We further introduce TriDerm, a multimodal framework that learns interpretable wound representations from small cohorts by integrating wound imagery, boundary masks, and expert reports. On the vision side, TriDerm adapts visual foundation models to RDEB using wound-level attention pooling and non-contrastive representation learning. For text, we prompt large language models with comparison queries and recover medically meaningful representations via soft ordinal embeddings (SOE). We show that visual and textual modalities capture complementary aspects of wound phenotype, and that fusing both modalities yields 73.5% agreement with experts, outperforming the best off-the-shelf single-modality foundation model by over 5.6 percentage points. We make the expert annotation tool, model code and representative dataset samples publicly available.

Maren Hackenberg, Astrid Pechmann, Clemens Kreutz et al.

Ordinary differential equations (ODEs) can provide mechanistic models of temporally local changes of processes, where parameters are often informed by external knowledge. While ODEs are popular in systems modeling, they are less established for statistical modeling of longitudinal cohort data, e.g., in a clinical setting. Yet, modeling of local changes could also be attractive for assessing the trajectory of an individual in a cohort in the immediate future given its current status, where ODE parameters could be informed by further characteristics of the individual. However, several hurdles so far limit such use of ODEs, as compared to regression-based function fitting approaches. The potentially higher level of noise in cohort data might be detrimental to ODEs, as the shape of the ODE solution heavily depends on the initial value. In addition, larger numbers of variables multiply such problems and might be difficult to handle for ODEs. To address this, we propose to use each observation in the course of time as the initial value to obtain multiple local ODE solutions and build a combined estimator of the underlying dynamics. Neural networks are used for obtaining a low-dimensional latent space for dynamic modeling from a potentially large number of variables, and for obtaining patient-specific ODE parameters from baseline variables. Simultaneous identification of dynamic models and of a latent space is enabled by recently developed differentiable programming techniques. We illustrate the proposed approach in an application with spinal muscular atrophy patients and a corresponding simulation study. In particular, modeling of local changes in health status at any point in time is contrasted to the interpretation of functions obtained from a global regression. This more generally highlights how different application settings might demand different modeling strategies.

Fabian Kabus, Maren Hackenberg, Julia Hindel et al.

While artificial neural networks excel in unsupervised learning of non-sparse structure, classical statistical regression techniques offer better interpretability, in particular when sparseness is enforced by $\ell_1$ regularization, enabling identification of which factors drive observed dynamics. We investigate how these two types of approaches can be optimally combined, exemplarily considering two-photon calcium imaging data where sparse autoregressive dynamics are to be extracted. We propose embedding a vector autoregressive (VAR) model as an interpretable regression technique into a convolutional autoencoder, which provides dimension reduction for tractable temporal modeling. A skip connection separately addresses non-sparse static spatial information, selectively channeling sparse structure into the $\ell_1$-regularized VAR. $\ell_1$-estimation of regression parameters is enabled by differentiating through the piecewise linear solution path. This is contrasted with approaches where the autoencoder does not adapt to the VAR model. Having an embedded statistical model also enables a testing approach for comparing temporal sequences from the same observational unit. Additionally, contribution maps visualize which spatial regions drive the learned dynamics.

Kiana Farhadyar, Maren Hackenberg, Kira Ahrens et al.

Modeling of longitudinal cohort data typically involves complex temporal dependencies between multiple variables. There, the transformer architecture, which has been highly successful in language and vision applications, allows us to account for the fact that the most recently observed time points in an individual's history may not always be the most important for the immediate future. This is achieved by assigning attention weights to observations of an individual based on a transformation of their values. One reason why these ideas have not yet been fully leveraged for longitudinal cohort data is that typically, large datasets are required. Therefore, we present a simplified transformer architecture that retains the core attention mechanism while reducing the number of parameters to be estimated, to be more suitable for small datasets with few time points. Guided by a statistical perspective on transformers, we use an autoregressive model as a starting point and incorporate attention as a kernel-based operation with temporal decay, where aggregation of multiple transformer heads, i.e. different candidate weighting schemes, is expressed as accumulating evidence on different types of underlying characteristics of individuals. This also enables a permutation-based statistical testing procedure for identifying contextual patterns. In a simulation study, the approach is shown to recover contextual dependencies even with a small number of individuals and time points. In an application to data from a resilience study, we identify temporal patterns in the dynamics of stress and mental health. This indicates that properly adapted transformers can not only achieve competitive predictive performance, but also uncover complex context dependencies in small data settings.

Stefan Lenz, Maren Hackenberg, Harald Binder

Like many groups considering the new programming language Julia, we faced the challenge of accessing the algorithms that we develop in Julia from R. Therefore, we developed the R package JuliaConnectoR, available from the CRAN repository and GitHub (https://github.com/stefan-m-lenz/JuliaConnectoR), in particular for making advanced deep learning tools available. For maintainability and stability, we decided to base communication between R and Julia on TCP, using an optimized binary format for exchanging data. Our package also specifically contains features that allow for a convenient interactive use in R. This makes it easy to develop R extensions with Julia or to simply call functionality from Julia packages in R. Interacting with Julia objects and calling Julia functions becomes user-friendly, as Julia functions and variables are made directly available as objects in the R workspace. We illustrate the further features of our package with code examples, and also discuss advantages over the two alternative packages JuliaCall and XRJulia. Finally, we demonstrate the usage of the package with a more extensive example for employing neural ordinary differential equations, a recent deep learning technique that has received much attention. This example also provides more general guidance for integrating deep learning techniques from Julia into R.

Fabian Kabus, Kian Kordtomeikel, Thomas Brox et al.

The training data of large language models (LLMs) comprises a wide range of biomedical literature, reflecting data from many different patient populations. We investigate how it might be possible to recover information on correlation and causal links between patient characteristics, as a key building block for medical decision making. To avoid the pitfalls of direct elicitation, we propose an approach based on structured comparison questions, specifically patient comparison triplet questions. This is combined with a statistical model for the LLM representation that provides estimates of correlations without access to activations or model internals. Intuitively, we consider how similarity decisions of LLMs based on a first variable are affected by providing information on a second variable for one of the patients being assessed. We then induce prompt-level environment shifts to obtain correlation estimates for different subpopulations, which enables an invariant causal prediction (ICP) approach to obtain conservative candidate parent links. We demonstrate the method in two clinical domains, chronic obstructive pulmonary disease (COPD) and multiple sclerosis (MS). Across prompted environments, the elicited correlations are smooth, stable, and clinically interpretable, yet vary in a statistically significant way that supports downstream invariance testing, such that ICP provides a small set of candidate invariant parent links. These results show that indirect elicitation via triplet comparisons can recover meaningful association structure from LLMs and offer a cautious route from implicit correlations to causal statements that are congruent with LLM answering patterns.

Kiana Farhadyar, Federico Bonofiglio, Maren Hackenberg et al.

In settings requiring synthetic data generation based on a clinical cohort, e.g., due to data protection regulations, heterogeneity across individuals might be a nuisance that we need to control or faithfully preserve. The sources of such heterogeneity might be known, e.g., as indicated by sub-groups labels, or might be unknown and thus reflected only in properties of distributions, such as bimodality or skewness. We investigate how such heterogeneity can be preserved and controlled when obtaining synthetic data from variational autoencoders (VAEs), i.e., a generative deep learning technique that utilizes a low-dimensional latent representation. To faithfully reproduce unknown heterogeneity reflected in marginal distributions, we propose to combine VAEs with pre-transformations. For dealing with known heterogeneity due to sub-groups, we complement VAEs with models for group membership, specifically from propensity score regression. The evaluation is performed with a realistic simulation design that features sub-groups and challenging marginal distributions. The proposed approach faithfully recovers the latter, compared to synthetic data approaches that focus purely on marginal distributions. Propensity scores add complementary information, e.g., when visualized in the latent space, and enable sampling of synthetic data with or without sub-group specific characteristics. We also illustrate the proposed approach with real data from an international stroke trial that exhibits considerable distribution differences between study sites, in addition to bimodality. These results indicate that describing heterogeneity by statistical approaches, such as propensity score regression, might be more generally useful for complementing generative deep learning for obtaining synthetic data that faithfully reflects structure from clinical cohorts.

Maryam Farhadizadeh, Maria Weymann, Michael Blaß et al.

Multimodal data modeling has emerged as a powerful approach in clinical research, enabling the integration of diverse data types such as imaging, genomics, wearable sensors, and electronic health records. Despite its potential to improve diagnostic accuracy and support personalized care, modeling such heterogeneous data presents significant technical challenges. This systematic review synthesizes findings from 69 studies to identify common obstacles, including missing modalities, limited sample sizes, dimensionality imbalance, interpretability issues, and finding the optimal fusion techniques. We highlight recent methodological advances, such as transfer learning, generative models, attention mechanisms, and neural architecture search that offer promising solutions. By mapping current trends and innovations, this review provides a comprehensive overview of the field and offers practical insights to guide future research and development in multimodal modeling for medical applications.

Clemens Schächter, Maren Hackenberg, Michelle Pfaffenlehner et al.

Many rare diseases offer limited established treatment options, leading patients to switch therapies when new medications emerge. To analyze the impact of such treatment switches within the low sample size limitations of rare disease trials, it is important to use all available data sources. This, however, is complicated when usage of measurement instruments change during the observation period, for example when instruments are adapted to specific age ranges. The resulting disjoint longitudinal data trajectories, complicate the application of traditional modeling approaches like mixed-effects regression. We tackle this by mapping observations of each instrument to a aligned low-dimensional temporal trajectory, enabling longitudinal modeling across instruments. Specifically, we employ a set of variational autoencoder architectures to embed item values into a shared latent space for each time point. Temporal disease dynamics and treatment switch effects are then captured through a mixed-effects regression model applied to latent representations. To enable statistical inference, we present a novel statistical testing approach that accounts for the joint parameter estimation of mixed-effects regression and variational autoencoders. The methodology is applied to quantify the impact of treatment switches for patients with spinal muscular atrophy. Here, our approach aligns motor performance items from different measurement instruments for mixed-effects regression and maps estimated effects back to the observed item level to quantify the treatment switch effect. Our approach allows for model selection as well as for assessing effects of treatment switching. The results highlight the potential of modeling in joint latent representations for addressing small data challenges.

Maren Hackenberg, Sophia G. Connor, Fabian Kabus et al.

The emergence of breakthrough artificial intelligence (AI) techniques has led to a renewed focus on how small data settings, i.e., settings with limited information, can benefit from such developments. This includes societal issues such as how best to include under-represented groups in data-driven policy and decision making, or the health benefits of assistive technologies such as wearables. We provide a conceptual overview, in particular contrasting small data with big data, and identify common themes from exemplary case studies and application areas. Potential solutions are described in a more detailed technical overview of current data analysis and modelling techniques, highlighting contributions from different disciplines, such as knowledge-driven modelling from statistics and data-driven modelling from computer science. By linking application settings, conceptual contributions and specific techniques, we highlight what is already feasible and suggest what an agenda for fully leveraging small data might look like.

Göran Köber, Raffael Kalisch, Lara Puhlmann et al.

When modeling longitudinal biomedical data, often dimensionality reduction as well as dynamic modeling in the resulting latent representation is needed. This can be achieved by artificial neural networks for dimension reduction, and differential equations for dynamic modeling of individual-level trajectories. However, such approaches so far assume that parameters of individual-level dynamics are constant throughout the observation period. Motivated by an application from psychological resilience research, we propose an extension where different sets of differential equation parameters are allowed for observation sub-periods. Still, estimation for intra-individual sub-periods is coupled for being able to fit the model also with a relatively small dataset. We subsequently derive prediction targets from individual dynamic models of resilience in the application. These serve as interpretable resilience-related outcomes, to be predicted from characteristics of individuals, measured at baseline and a follow-up time point, and selecting a small set of important predictors. Our approach is seen to successfully identify individual-level parameters of dynamic models that allows us to stably select predictors, i.e., resilience factors. Furthermore, we can identify those characteristics of individuals that are the most promising for updates at follow-up, which might inform future study design. This underlines the usefulness of our proposed deep dynamic modeling approach with changes in parameters between observation sub-periods.

Kiana Farhadyar, Federico Bonofiglio, Daniela Zoeller et al.

Synthetic data generation is of great interest in diverse applications, such as for privacy protection. Deep generative models, such as variational autoencoders (VAEs), are a popular approach for creating such synthetic datasets from original data. Despite the success of VAEs, there are limitations when it comes to the bimodal and skewed marginal distributions. These deviate from the unimodal symmetric distributions that are encouraged by the normality assumption typically used for the latent representations in VAEs. While there are extensions that assume other distributions for the latent space, this does not generally increase flexibility for data with many different distributions. Therefore, we propose a novel method, pre-transformation variational autoencoders (PTVAEs), to specifically address bimodal and skewed data, by employing pre-transformations at the level of original variables. Two types of transformations are used to bring the data close to a normal distribution by a separate parameter optimization for each variable in a dataset. We compare the performance of our method with other state-of-the-art methods for synthetic data generation. In addition to the visual comparison, we use a utility measurement for a quantitative evaluation. The results show that the PTVAE approach can outperform others in both bimodal and skewed data generation. Furthermore, the simplicity of the approach makes it usable in combination with other extensions of VAE.

Maren Hackenberg, Marlon Grodd, Clemens Kreutz et al.

Differentiable programming has recently received much interest as a paradigm that facilitates taking gradients of computer programs. While the corresponding flexible gradient-based optimization approaches so far have been used predominantly for deep learning or enriching the latter with modeling components, we want to demonstrate that they can also be useful for statistical modeling per se, e.g., for quick prototyping when classical maximum likelihood approaches are challenging or not feasible. In an application from a COVID-19 setting, we utilize differentiable programming to quickly build and optimize a flexible prediction model adapted to the data quality challenges at hand. Specifically, we develop a regression model, inspired by delay differential equations, that can bridge temporal gaps of observations in the central German registry of COVID-19 intensive care cases for predicting future demand. With this exemplary modeling challenge, we illustrate how differentiable programming can enable simple gradient-based optimization of the model by automatic differentiation. This allowed us to quickly prototype a model under time pressure that outperforms simpler benchmark models. We thus exemplify the potential of differentiable programming also outside deep learning applications, to provide more options for flexible applied statistical modeling.

Maren Hackenberg, Philipp Harms, Michelle Pfaffenlehner et al.

Longitudinal biomedical data are often characterized by a sparse time grid and individual-specific development patterns. Specifically, in epidemiological cohort studies and clinical registries we are facing the question of what can be learned from the data in an early phase of the study, when only a baseline characterization and one follow-up measurement are available. Inspired by recent advances that allow to combine deep learning with dynamic modeling, we investigate whether such approaches can be useful for uncovering complex structure, in particular for an extreme small data setting with only two observations time points for each individual. Irregular spacing in time could then be used to gain more information on individual dynamics by leveraging similarity of individuals. We provide a brief overview of how variational autoencoders (VAEs), as a deep learning approach, can be linked to ordinary differential equations (ODEs) for dynamic modeling, and then specifically investigate the feasibility of such an approach that infers individual-specific latent trajectories by including regularity assumptions and individuals' similarity. We also provide a description of this deep learning approach as a filtering task to give a statistical perspective. Using simulated data, we show to what extent the approach can recover individual trajectories from ODE systems with two and four unknown parameters and infer groups of individuals with similar trajectories, and where it breaks down. The results show that such dynamic deep learning approaches can be useful even in extreme small data settings, but need to be carefully adapted.

Sarah Friedrich, Gerd Antes, Sigrid Behr et al.

The research on and application of artificial intelligence (AI) has triggered a comprehensive scientific, economic, social and political discussion. Here we argue that statistics, as an interdisciplinary scientific field, plays a substantial role both for the theoretical and practical understanding of AI and for its future development. Statistics might even be considered a core element of AI. With its specialist knowledge of data evaluation, starting with the precise formulation of the research question and passing through a study design stage on to analysis and interpretation of the results, statistics is a natural partner for other disciplines in teaching, research and practice. This paper aims at contributing to the current discussion by highlighting the relevance of statistical methodology in the context of AI development. In particular, we discuss contributions of statistics to the field of artificial intelligence concerning methodological development, planning and design of studies, assessment of data quality and data collection, differentiation of causality and associations and assessment of uncertainty in results. Moreover, the paper also deals with the equally necessary and meaningful extension of curricula in schools and universities.

Stefan Lenz, Harald Binder

The best way to calculate statistics from medical data is to use the data of individual patients. In some settings, this data is difficult to obtain due to privacy restrictions. In Germany, for example, it is not possible to pool routine data from different hospitals for research purposes without the consent of the patients. The DataSHIELD software provides an infrastructure and a set of statistical methods for joint analyses of distributed data. The contained algorithms are reformulated to work with aggregated data from the participating sites instead of the individual data. If a desired algorithm is not implemented in DataSHIELD or cannot be reformulated in such a way, using artificial data is an alternative. We present a methodology together with a software implementation that builds on DataSHIELD to create artificial data that preserve complex patterns from distributed individual patient data. Such data sets of artificial patients, which are not linked to real patients, can then be used for joint analyses. We use deep Boltzmann machines (DBMs) as generative models for capturing the distribution of data. For the implementation, we employ the package "BoltzmannMachines" from the Julia programming language and wrap it for use with DataSHIELD, which is based on R. As an exemplary application, we conduct a distributed analysis with DBMs on a synthetic data set, which simulates genetic variant data. Patterns from the original data can be recovered in the artificial data using hierarchical clustering of the virtual patients, demonstrating the feasibility of the approach. Our implementation adds to DataSHIELD the ability to generate artificial data that can be used for various analyses, e. g. for pattern recognition with deep learning. This also demonstrates more generally how DataSHIELD can be flexibly extended with advanced algorithms from languages other than R.

Daniela Zöller, Harald Binder

The discovery of clinical biomarkers requires large patient cohorts and is aided by a pooled data approach across institutions. In many countries, data protection constraints, especially in the clinical environment, forbid the exchange of individual-level data between different research institutes, impeding the conduct of a joint analyses. To circumvent this problem, only non-disclosive aggregated data is exchanged, which is often done manually and requires explicit permission before transfer, i.e., the number of data calls and the amount of data should be limited. This does not allow for more complex tasks such as variable selection, as only simple aggregated summary statistics are typically transferred. Other methods have been proposed that require more complex aggregated data or use input data perturbation, but these methods can either not deal with a high number of biomarkers or lose information. Here, we propose a multivariable regression approach for identifying biomarkers by automatic variable selection based on aggregated data in iterative calls, which can be implemented under data protection constraints. The approach can be used to jointly analyze data distributed across several locations. To minimize the amount of transferred data and the number of calls, we also provide a heuristic variant of the approach. When performing global data standardization, the proposed method yields the same results as pooled individual-level data analysis. In a simulation study, the information loss introduced by local standardization is seen to be minimal. In a typical scenario, the heuristic decreases the number of data calls from more than 10 to 3, rendering manual data releases feasible. To make our approach widely available for application, we provide an implementation of the heuristic version incorporated in the DataSHIELD framework.\

Martin Treppner, Stefan Lenz, Harald Binder et al.

Commercial activity trackers are set to become an essential tool in health research, due to increasing availability in the general population. The corresponding vast amounts of mostly unlabeled data pose a challenge to statistical modeling approaches. To investigate the feasibility of deep learning approaches for unsupervised learning with such data, we examine weekly usage patterns of Fitbit activity trackers with deep Boltzmann machines (DBMs). This method is particularly suitable for modeling complex joint distributions via latent variables. We also chose this specific procedure because it is a generative approach, i.e., artificial samples can be generated to explore the learned structure. We describe how the data can be preprocessed to be compatible with binary DBMs. The results reveal two distinct usage patterns in which one group frequently uses trackers on Mondays and Tuesdays, whereas the other uses trackers during the entire week. This exemplary result shows that DBMs are feasible and can be useful for modeling activity tracker data.