Biometrisches Kolloquium 2021

Chairs: Matthias Schmid and Thomas Welchowski

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Interpretable Machine Learning
Bernd Bischl
Ludwig-Maximilians-Universität München

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Adapting Variational Autoencoders for Realistic Synthetic Data with Skewed and Bimodal Distributions
Kiana Farhadyar, Harald Binder
Faculty of Medicine and Medical Center – University of Freiburg, Germany

Background: Passing synthetic data instead of original data to the other researchers is an option when data protection restrictions exist. Such data should preserve the statistical relationships between the variables while protecting privacy. In recent years, deep generative models have allowed for significant progress in the field of synthetic data generation. In particular, variational autoencoders (VAEs) are a popular class of deep generative models. Standard VAEs are typically built around a latent space with a Gaussian distribution and this is a key challenge for VAEs when they encounter more complex data distributions like bimodal or skewed data.

Methods: In this work, we propose a novel method for synthetic data generation that handles bimodal and skewed data as well, while keeping the overall VAE framework. Moreover, this method can generate synthetic data for datasets consisting of both continuous and binary variables. We apply two transformations to convert the data into a form that is more compliant with VAEs. First, we use Box-Cox transformations to transform the skewed distribution to something closer to a symmetric distribution. Then, dealing with potential bimodal data, we employ a power function sgn(x)|x|^p that can transform the data in a way that it has closer peaks and lighter tails. For the evaluation, we use a simulation design data, which is based on a large breast cancer study and The International Stroke Trial (IST) dataset as a real data example.

Results: We show that the pre-transformations can make a considerable improvement in the utility of synthetic data for skewed and bimodal distributions. We investigate this in comparison with standard VAEs and a VAE with an autoregressive implicit quantile network approach (AIQN) and also Generative Adversarial Networks (GAN). We see that our method is the only method that can generate bimodality and the other methods typically generate unimodal distributions. For skewed data, these methods decrease the skewness of synthetic data and make the data closer to a symmetric distribution while our method produces similar skewness to original data and honors the value range of original data better.

Conclusion: In conclusion, we developed a simple method, which adapts VAEs by transformations to handle skewed and bimodal data. Due to its simplicity, it is possible to combine it with many extensions of VAEs. Thus, it becomes feasible to generate high-quality synthetic clinical data for research under data protection constraints.

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Statistical power for cell identity detection in deep generative models
Martin Treppner^1,2, Harald Binder^1,2
1Institute of Medical Biometry and Statistics, Faculty of Medicine and Medical Center – University of Freiburg, Germany; ²Freiburg Center of Data Analysis and Modelling, Mathematical Institute – Faculty of Mathematics and Physics, University of Freiburg, Germany

One of the most common applications of single-cell RNA-sequencing experiments is to discover groups of cells with a similar expression profile in an attempt to define cell identities. The similarity of these expression profiles is typically examined in a low-dimensional latent space, which can be learned by deep generative models such as variational autoencoders (VAEs). However, the quality of representations in VAEs varies greatly depending on the number of cells under study, which is also reflected in the assignment to specific cell identities. We propose a strategy to answer what number of cells is needed so that a pre-specified percentage of the cells in the latent space is well represented.

We train VAEs on a varying number of cells and evaluate the learned representations‘ quality by use of the estimated log-likelihood lower bound of each cell. The distribution arising from the values of the log-likelihoods are then compared to a permutation-based distribution of log-likelihoods. We generate the permutation-based distribution by randomly drawing a small subset of cells before training the VAE and permuting each gene’s expression values among these randomly drawn cells. By doing so, we ensure that the latent representation’s overall structure is preserved, and at the same time, we obtain a null distribution for the log-likelihoods. We then compare log-likelihood distributions for different numbers of cells. We also harness the properties of VAEs by artificially increasing the number of samples in small datasets by generating synthetic data and combining them with the original pilot datasets.

We demonstrate performance on varying sizes of subsamples of the Tabula Muris scRNA-seq dataset from the brain of seven mice processed with the SMART-Seq2 protocol. We show that our approach can be used to plan cell numbers for single-cell RNA-seq experiments, which might improve the reliability of downstream analyses such as cell identity detection and inference of developmental trajectories.

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Individualizing deep dynamic models for psychological resilience data
Göran Köber^1,2, Shakoor Pooseh^2,3, Haakon Engen⁴, Andrea Chmitorz^5,6,7, Miriam Kampa^5,8,9, Anita Schick^4,10, Alexandra Sebastian⁶, Oliver Tüscher^5,6, Michèle Wessa^5,11, Kenneth S.L. Yuen^4,5, Henrik Walter^12,13, Raffael Kalisch^4,5, Jens Timmer^2,3,14, Harald Binder^1,2
1Institute of Medical Biometry and Statistics, Faculty of Medicine and Medical Center, University of Freiburg, Germany; ²Freiburg Center of Data Analysis and Modelling (FDM), University of Freiburg, Freiburg, 79104, Germany; ³Institute of Physics, University of Freiburg, 79104, Germany; ⁴Neuroimaging Center (NIC), Focus Program Translational Neuroscience (FTN), Johannes Gutenberg University Medical Center, Mainz, 55131, Germany; ⁵Leibniz Institute for Resilience Research (LIR), Mainz, 55122, Germany; ⁶Department of Psychiatry and Psychotherapy, Johannes Gutenberg University Medical Center, Mainz, 55131, Germany; ⁷Faculty of Social Work, Health and Nursing, University of Applied Sciences Esslingen, Esslingen, 73728, Germany; ⁸Department of Clinical Psychology, University of Siegen, 57076, Germany; ⁹Bender Institute of Neuroimaging (BION), Department of Psychology, Justus Liebig University, Gießen, 35394, Germany; ¹⁰Department of Public Mental Health, Central Institute of Mental Health, Medical Faculty Mannheim, Heidelberg University, Germany; ¹¹Department of Clinical Psychology and Neuropsychology, Institute of Psychology, Johannes Gutenberg University, Mainz, 55131, Germany; ¹²Research Division of Mind and Brain, Charité–Universitätsmedizin Berlin, Corporate Member of Freie Universität Berlin, Humboldt-Universität zu Berlin, and Berlin Institute of Health, Germany; ¹³Berlin School of Mind and Brain, Humboldt-Universität zu Berlin, Germany; ¹⁴CIBSS—Centre for Integrative Biological Signaling Studies, University of Freiburg, 79104, Germany

Deep learning approaches can uncover complex patterns in data. In particular, variational autoencoders (VAEs) achieve this by a non-linear mapping of data into a low-dimensional latent space. Motivated by an application to psychological resilience in the Mainz Resilience Project (MARP), which features intermittent longitudinal measurements of stressors and mental health, we propose an approach for individualized, dynamic modeling in this latent space. Specifically, we utilize ordinary differential equations (ODEs) and develop a novel technique for obtaining person-specific ODE parameters even in settings with a rather small number of individuals and observations, incomplete data, and a differing number of observations per individual. This technique allows us to subsequently investigate individual reactions to stimuli, such as the mental health impact of stressors. A potentially large number of baseline characteristics can then be linked to this individual response by regularized regression, e.g., for identifying resilience factors. Thus, our new method provides a way of connecting different kinds of complex longitudinal and baseline measures via individualized, dynamic models. The promising results obtained in the exemplary resilience application indicate that our proposal for dynamic deep learning might also be more generally useful for other application domains.

Chairs: Fabian Scheipl and Gernot Wassmer

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A Web-Application to determine statistical optimal designs for dose-response trials, especially with interactions.
Tim Holland-Letz, Annette Kopp-Schneider
German Cancer Research Center DKFZ, Germany

Statistical optimal design theory is well developed, but almost never used in practical applications in fields such as toxicology. For the area of dose response trials we therefore present an R-shiny based web application which calculates D-optimal designs for the most commonly fitted dose response functions, namely the log-logistic and the Weibull function. In this context, the application also generates a graphical representation of the design space (a “design heatmap”). Furthermore, the application allows checking the efficiencies of user specified designs. In addition, uncertainty in regard to the assumptions about the true parameters can be included in the form of average optimal designs. Thus, the user can find a design which is a compromise between rigid optimality and more practical designs which also incorporate specific preferences and technical requirements.

Finally, the app can also be used to compute designs for substance interaction trials between two substances combined in a ray design setup, including an a-priori estimate for the parameters of the combination to be expected under the (Loewe-) additivity assumption.

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Distributed Computation of the AUROC-GLM Confidence Intervals Using DataSHIELD
Daniel Schalk¹, Stefan Buchka², Ulrich Mansmann², Verena Hoffmann^2
1Department of Statistics, LMU Munich; ²The Institute for Medical Information Processing, Biometry, and Epidemiology, LMU Munich

Distributed calculation protects data privacy without ruling out complex statistical analyses. Individual data stays in local databases invisible to the analyst who only receives aggregated results. A distributed algorithm that calculates a ROC curve, its AUC estimate with confidence interval is presented to evaluate a therapeutic decision rule. It will be embedded in the DataSHIELD framework [1].

Starting point is the ROC-GLM approach by Pepe et al. [2]. The additivity of the Fisher information matrix, of the score vector, and of the CI proposed by DeLong [3] to aggregate intermediate results allows to design a distributed algorithm to calculate estimates of the ROC-GLM, its AUC, and CI.

We simulate scores and labels (responses) to create AUC values within the range of [0.5, 1]. The size of individual studies is uniformly distributed on [100, 2500] while the percentage of treatment-response covers [0.2,0.8]. Per scenario, 10000 studies are produced. Per study, the AUC is calculated within a non-distributed empiric as well as a distributed setting. The difference in AUC between both approaches is independent of the number of distributed components and is within the range of [-0.019, 0.013]. The boundaries of bootstrapped CIs in the non-distributed empirical setting are close to those in the distributed approach with the CI of DeLong: Range of differences in the lower boundary [-0.015, 0.03]; range of the upper boundary deviations [-0.012, 0.026].

The distributed algorithm allows anonymous multicentric validation of the discrimination of a classification rules. A specific application is the audit use case within the MII consortium DIFUTURE (difuture.de). The multicentric prospective ProVAL-MS study (DRKS: 00014034) on patients with newly diagnosed relapsing-remitting multiple sclerosis provides the data for a privacy-protected validation of a treatment decision score (also developed by DIFUTURE) regarding discrimination between good and insufficient treatment response. The simulation results demonstrate that our algorithm is suitable for the planned validation. The algorithm is implemented in R to be used within DataSHIELD. It will be made publicly available.

[1] Amadou Gaye et al (2014). DataSHIELD: taking the analysis to the data, not the data to the analysis. International Journal of Epidemiology

[2] Pepe, M. S. (2003). The statistical evaluation of medical tests for classification and prediction. Medicine.

[3] DeLong, E. R., DeLong, D. M., and Clarke-Pearson, D. L. (1988). Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach.Biometrics, pages 837–845.

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Interactive review of safety data during a data monitoring committee using R-Shiny
Tobias Mütze¹, Bo Wang², Douglas Robinson^2
1Statistical Methodology, Novartis Pharma AG, Switzerland; ²Scientific Computing and Consulting, Novartis Pharma AG, Switzerland

In clinical trials it is common that the safety of patients is monitored by a data monitoring committee (DMC) that operates independently of the clinical trial teams. After each review of the accumulating trial data, it is within the DMC’s responsibility to decide on whether to continue or stop the trial. The data are generally presented to DMCs in a static report through tables, listing, and sometimes figures. In this presentation, we share our experiences with supplementing the safety data review with an interactive R-Shiny app. We will first present the layout and content of the app. Then, we outline the advantages of reviewing (safety) data by means of an interactive app compared to the standard review of a DMC report, namely, extensive use of graphical illustrations in addition to tables, ability to quickly change the level of detail, and to switch between study-level data and subject-level data. We argue that this leads to a robust collaborative discussion and a more complete understanding of the data. Finally, we discuss the qualification process itself of an R Shiny app and outline how the learnings may be applied to enhance standard DMC reports

References

[1] Wang, W., Revis, R., Nilsson, M. and Crowe, B., 2020. Clinical Trial Drug Safety Assessment with Interactive Visual Analytics. Statistics in Biopharmaceutical Research, pp.1-12.

[2] Fleming, T.R., Ellenberg, S.S. and DeMets, D.L., 2018. Data monitoring committees: current issues. Clinical Trials, 15(4), pp.321-328.

[3] Mütze, T. and Friede, T., 2020. Data monitoring committees for clinical trials evaluating treatments of COVID-19. Contemporary Clinical Trials, 98, 106154.

[4] Buhr, K.A., Downs, M., Rhorer, J., Bechhofer, R. and Wittes, J., 2018. Reports to independent data monitoring committees: an appeal for clarity, completeness, and comprehensibility. Therapeutic innovation & regulatory science, 52(4), pp.459-468.

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An R package for an integrated evaluation of statistical approaches to cancer incidence projection
Maximilian Knoll^1,2,3,4, Jennifer Furkel^1,2,3,4, Jürgen Debus^1,3,4, Amir Abdollahi^1,3,4, André Karch⁵, Christian Stock^6,7
1Department of Radiation Oncology, Heidelberg University Hospital, Heidelberg, Germany; ²Faculty of Biosciences, Heidelberg University, Heidelberg, Germany; ³Clinical Cooperation Unit Radiation Oncology, German Cancer Research Center (DKFZ), Heidelberg, Germany; ⁴German Cancer Consortium (DKTK) Core Center Heidelberg, Heidelberg, Germany; ⁵Institute of Epidemiology and Social Medicine, University of Muenster, Muenster, Germany.; ⁶Institute of Medical Biometry and Informatics (IMBI), University of Heidelberg, Heidelberg, Germany; ⁷Division of Clinical Epidemiology and Aging Research, German Cancer Research Center (DKFZ), Heidelberg, Germany

Background: Projection of future cancer incidence is an important task in cancer epidemiology. The results are of interest also for biomedical research and public health policy. Age-Period-Cohort (APC) models, usually based on long-term cancer registry data (>20yrs), are established for such projections. In many countries (including Germany), however, nationwide long-term data are not yet available. It is unclear which statistical approach should be recommended for projections using rather short-term data.

Methods: To enable a comparative analysis of the performance of statistical approaches to cancer incidence projection, we developed an R package (incAnalysis), supporting in particular Bayesian models fitted by Integrated Nested Laplace Approximations (INLA). Its use is demonstrated by an extensive empirical evaluation of operating characteristics (bias, coverage and precision) of potentially applicable models differing by complexity. Observed long-term data from three cancer registries (SEER-9, NORDCAN, Saarland) was used for benchmarking.

Results: Overall, coverage was high (mostly >90%) for Bayesian APC models (BAPC), whereas less complex models showed differences in coverage dependent on projection-period. Intercept-only models yielded values below 20% for coverage. Bias increased and precision decreased for longer projection periods (>15 years) for all except intercept-only models. Precision was lowest for complex models such as BAPC models, generalized additive models with multivariate smoothers and generalized linear models with age x period interaction effects.

Conclusion: The incAnalysis R package allows a straightforward comparison of cancer incidence rate projection approaches. Further detailed and targeted investigations into model performance in addition to the presented empirical results are recommended to derive guidance on appropriate statistical projection methods in a given setting.

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Using Differentiable Programming for Flexible Statistical Modeling
Maren Hackenberg¹, Marlon Grodd¹, Clemens Kreutz¹, Martina Fischer², Janina Esins², Linus Grabenhenrich², Christian Karagiannidis³, Harald Binder^1
1Institute of Medical Biometry and Statistics, Faculty of Medicine and Medical Center, University of Freiburg, Germany; ²Robert Koch Institute, Berlin, Germany; ³Department of Pneumology and Critical Care Medicine, Cologne-Merheim Hospital, ARDS and ECMO Center, Kliniken der Stadt Köln, Witten/Herdecke University Hospital, Cologne, Germany

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.