New approaches in statistical modeling

Diese kumulative Dissertation befasst sich mit der statistischen Modellierung von räumlichen Netzwerkdaten, sowie von Daten zur Pandemie des SARS-CoV-2-Virus. Statistische Modellierung kann im übertragenden Sinne als ein großer "Werkzeugkasten'' verstanden werden, mit dem man Phänomene der realen Welt durch eine geeignete mathematische Formalisierung approximiert. Die in dieser Arbeit verwendeten Modelle beruhen in erster Linie auf Regression, wobei die Schwerpunkte auf der Glättung mit penalisierten Splines unter Einbeziehung von zufälligen Effekten liegen. Im Allgemeinen bestehen die Vorteile von Regressions- und statistischen Modellen darin, dass sie interpretierbare Modellergebnisse liefern und Vorhersagen über unbeobachtete Zustände erlauben. Gleichzeitig ist eine Beurteilung der zugrunde liegenden Unsicherheit der Schätzungen möglich. Diese drei Schlüsselaspekte des statistischen Modellierens spielen eine entscheidende Rolle in den fünf Beiträgen dieser kumulativen Dissertation. Die ersten drei Artikel befassen sich mit statistischen Modellen und ihrer Anwendung auf Daten, die auf Netzwerken beobachtet werden. Netzwerke sind Strukturen, die aus durch Kanten verbundene Knoten bestehen. Während Netzwerke in natürlicher Weise abstrakte Beziehungen wie soziale Netzwerke oder ein Netzwerk von Geschäftspartnern darstellen können, liegt der Schwerpunkt in dieser Arbeit auf Netzwerken mit einer räumlichen Interpretation. Im ersten Artikel wird ein neues Modell entwickelt, welches erlaubt, statistische Rückschlüsse auf unbeobachtete Fahrten in Bike-Sharing-Netzwerken zu ziehen. Dabei stellen die Fahrradstationen die Eckpunkte des Netzwerks dar, und die Wege zwischen den Fahrradstationen entsprechen den Kanten. Der darauf folgende Artikel behandelt räumliche Netzwerke und die Schätzung der Intensität von stochastischen Prozessen, deren Realisierungen in räumlichen Netzwerken beobachtet werden. Die Methodik erlaubt auch die Einbeziehung von Kovariablen bei der Schätzung der Intensität. Diese Art der Modellierung ist neu und mit den aktuellen, auf Kerndichteschätzung basierenden Methoden, nicht möglich. Um die Methode frei zugänglich zu machen, wurde ein \textbf{R}-Paket implementiert. Der letzte Beitrag im Bereich der Netzwerke befasst sich mit der Vorhersage der Belegung von Parkplätzen, die entlang eines Straßennetzes verteilt sind. In diesem Zusammenhang wird die Netzwerkstruktur genutzt, um räumliche Abhängigkeiten zu modellieren. Darüber hinaus basieren die Vorhersagen auf einem Semi-Markov-Modell, um die nicht-exponentielle Dauer der einzelnen Zustände zu berücksichtigen. Die Übergangsintensitäten werden mit Hilfe von Überlebenszeitmodellen geschätzt. Der zweite Teil dieser Dissertation befasst sich mit der Pandemie des SARS-CoV-2-Virus, das die Krankheit COVID-19 verursacht. Das deutsche Robert-Koch-Institut (RKI) stellt täglich Daten zu COVID-19-Infektionen und Todesfällen im Zusammenhang mit COVID-19 zur Verfügung, mit zusätzlichen Angaben zu Region, Geschlecht und Alter der Infizierten. Aus verschiedenen Gründen geben die Rohdaten keinen ausreichenden Aufschluss über den Schweregrad der Pandemie, weswegen statistische Modelle auf die Daten angewandt werden. Ein Beitrag befasst sich mit der Vorhersage tödlicher Infektionen auf regionaler Ebene unter Berücksichtigung der lokalen Bevölkerungsstruktur. Damit ist das Modell in der Lage, auch eine regionalspezifische Beurteilung der Schwere der Pandemie vorzunehmen. In einem zweiten Beitrag werden die tödlich endenden Infektionen mit der Anzahl der registrierten Infektionen zueinander in Beziehung gesetzt, um die Veränderung der Fallentdeckungsrate im Laufe der Zeit zu quantifizieren. Darüber hinaus ermöglicht die Methode, den Verlauf der tatsächlichen Zahl der Infektionen zu schätzen, während die gemeldeten Infektionszahlen durch verschiedene Teststrategien beeinflusst sind.This cumulative dissertation is concerned with statistical modeling of data observed on geometric networks and data related to the pandemic of the SARS-CoV-2 virus. Statistical modeling in its broadest sense encompasses a large "toolbox'' to approximate real-world phenomena in a mathematically formalized manner. Models used in this work are primarily regression-based, with an emphasis on penalized spline smoothing and the inclusion of random effects to control for latent heterogeneities. In general, the benefits of regression and statistical models include creating interpretable model results and making predictions about unobserved states while adequately communicating the underlying uncertainty. These three key aspects of statistical modeling play a crucial role in the five contributions of this cumulative dissertation. The first three articles cover statistical models and their application to data observed on networks, i.e. structures consisting of vertices connected by a set of edges. While networks serve as a natural device to represent abstract relationships such as social networks or a network of commercial partners, the focus here is on spatial networks. The first article develops a new model to draw statistical inference about unobserved trips in bike-sharing networks. Here, bike stations represent the network's vertices, and the paths between the bike stations correspond to the edges. The consecutive article treats spatial networks, focusing on estimating stochastic processes' intensity functions with realizations observed on spatial networks. The methodology also allows fitting the intensity with covariates, which is novel and not feasible with the current state-of-the-art methods based on kernel smoothing. To make the methodology freely available, an \textbf{R} package has been implemented. The last contribution in the field of networks covers the prediction of on-street parking occupancy, where parking lots are distributed along a street network. In this context, the network structure is utilized to model spatial dependencies. Moreover, predictions are based on a semi-Markov model to account for non-exponential duration times in each state and the transition intensities are estimated employing time to event models. The second part of this dissertation deals with the pandemic of the SARS-CoV-2 virus, which causes the disease COVID-19. The German Robert Koch Institute (RKI) daily provides data concerning COVID-19 infections and deaths related to COVID-19 with information on the infected's region, gender, and age. For several reasons, the raw data do not indicate the seriousness of the pandemic sufficiently well, which is why statistical models are used to get a clearer picture of the pandemic. One contribution is concerned with nowcasting fatal infections on a regional level while accounting for the local population structure. Thus, the model is capable of evaluating the region-specific seriousness of the pandemic. A second paper relates infections ending fatally to registered infections aiming at quantifying the change of the case detection ratio over time. Furthermore, the method allows assessing the relative course of the actual number of infections while testing strategies influence the reported numbers

Regional now- and forecasting for data reported with delay: toward surveillance of COVID-19 infections

Governments around the world continue to act to contain and mitigate the spread of COVID-19. The rapidly evolving situation compels officials and executives to continuously adapt policies and social distancing measures depending on the current state of the spread of the disease. In this context, it is crucial for policymakers to have a firm grasp on what the current state of the pandemic is, and to envision how the number of infections is going to evolve over the next days. However, as in many other situations involving compulsory registration of sensitive data, cases are reported with delay to a central register, with this delay deferring an up-to-date view of the state of things. We provide a stable tool for monitoring current infection levels as well as predicting infection numbers in the immediate future at the regional level. We accomplish this through nowcasting of cases that have not yet been reported as well as through predictions of future infections. We apply our model to German data, for which our focus lies in predicting and explain infectious behavior by district. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s10182-021-00433-5

Nowcasting fatal COVID-19 infections on a regional level in Germany

We analyse the temporal and regional structure in mortality rates related to COVID‐19 infections, making use of the openly available data on registered cases in Germany published by the Robert Koch Institute on a daily basis. Estimates for the number of present‐day infections that will, at a later date, prove to be fatal are derived through a nowcasting model, which relates the day of death of each deceased patient to the corresponding day of registration of the infection. Our district‐level modelling approach for fatal infections disentangles spatial variation into a global pattern for Germany, district‐specific long‐term effects and short‐term dynamics, while also taking the age and gender structure of the regional population into account. This enables to highlight areas with unexpectedly high disease activity. The analysis of death counts contributes to a better understanding of the spread of the disease while being, to some extent, less dependent on testing strategy and capacity in comparison to infection counts. The proposed approach and the presented results thus provide reliable insight into the state and the dynamics of the pandemic during the early phases of the infection wave in spring 2020 in Germany, when little was known about the disease and limited data were available

A statistical model for the dynamics of COVID-19 infections and their case detection ratio in 2020

The case detection ratio of coronavirus disease 2019 (COVID-19) infections varies over time due to changing testing capacities, different testing strategies, and the evolving underlying number of infections itself. This note shows a way of quantifying these dynamics by jointly modeling the reported number of detected COVID-19 infections with nonfatal and fatal outcomes. The proposed methodology also allows to explore the temporal development of the actual number of infections, both detected and undetected, thereby shedding light on the infection dynamics. We exemplify our approach by analyzing German data from 2020, making only use of data available since the beginning of the pandemic. Our modeling approach can be used to quantify the effect of different testing strategies, visualize the dynamics in the case detection ratio over time, and obtain information about the underlying true infection numbers, thus enabling us to get a clearer picture of the course of the COVID-19 pandemic in~2020

Effect of general anaesthesia on functional outcome in patients with anterior circulation ischaemic stroke having endovascular thrombectomy versus standard care: a meta-analysis of individual patient data

Background: General anaesthesia (GA) during endovascular thrombectomy has been associated with worse patient outcomes in observational studies compared with patients treated without GA. We assessed functional outcome in ischaemic stroke patients with large vessel anterior circulation occlusion undergoing endovascular thrombectomy under GA, versus thrombectomy not under GA (with or without sedation) versus standard care (ie, no thrombectomy), stratified by the use of GA versus standard care. Methods: For this meta-analysis, patient-level data were pooled from all patients included in randomised trials in PuMed published between Jan 1, 2010, and May 31, 2017, that compared endovascular thrombectomy predominantly done with stent retrievers with standard care in anterior circulation ischaemic stroke patients (HERMES Collaboration). The primary outcome was functional outcome assessed by ordinal analysis of the modified Rankin scale (mRS) at 90 days in the GA and non-GA subgroups of patients treated with endovascular therapy versus those patients treated with standard care, adjusted for baseline prognostic variables. To account for between-trial variance we used mixed-effects modelling with a random effect for trials incorporated in all models. Bias was assessed using the Cochrane method. The meta-analysis was prospectively designed, but not registered. Findings: Seven trials were identified by our search; of 1764 patients included in these trials, 871 were allocated to endovascular thrombectomy and 893 were assigned standard care. After exclusion of 74 patients (72 did not undergo the procedure and two had missing data on anaesthetic strategy), 236 (30%) of 797 patients who had endovascular procedures were treated under GA. At baseline, patients receiving GA were younger and had a shorter delay between stroke onset and randomisation but they had similar pre-treatment clinical severity compared with patients who did not have GA. Endovascular thrombectomy improved functional outcome at 3 months both in patients who had GA (adjusted common odds ratio (cOR) 1·52, 95% CI 1·09–2·11, p=0·014) and in those who did not have GA (adjusted cOR 2·33, 95% CI 1·75–3·10, p<0·0001) versus standard care. However, outcomes were significantly better for patients who did not receive GA versus those who received GA (covariate-adjusted cOR 1·53, 95% CI 1·14–2·04, p=0·0044). The risk of bias and variability between studies was assessed to be low. Interpretation: Worse outcomes after endovascular thrombectomy were associated with GA, after adjustment for baseline prognostic variables. These data support avoidance of GA whenever possible. The procedure did, however, remain effective versus standard care in patients treated under GA, indicating that treatment should not be withheld in those who require anaesthesia for medical reasons