Biometrisches Kolloquium 2021

Dynamic weighted ordinary least squares (dWOLS) was proposed as a simple analytic tool for estimating optimal adaptive treatment strategies. The approach aimed to combine the double robustness of G-estimation with the ease of implementation of Q-learning, however early methodology was limited to only the continuous outcome/binary treatment setting. In this talk, I will introduce generalized dWOLS, an extension that allowed for continuous-valued treatments to estimate optimal dosing strategies, and demonstrate the approach in estimating an optimal Warfarin dosing rule.

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Efficient, doubly robust estimation of the effect of dose switching for switchers in a randomised clinical trial
Kelly Van Lancker¹, An Vandebosch², Stijn Vansteelandt^1,3
1Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Ghent, Belgium; ²Janssen R&D, a division of Janssen Pharmaceutica NV, Beerse, Belgium; ³Department of Medical Statistics, London School of Hygiene and Tropical Medicine, London, United Kingdom

The interpretation of intention-to-treat analyses of randomised clinical trials is often hindered as a result of noncompliance and treatment switching. This has recently given rise to a vigorous research activity on the identification and estimation of so-called estimands.

Motivated by an ongoing clinical trial conducted by Janssen Pharmaceutica in which a flexible dosing regimen is compared to placebo, we evaluate how switchers in the treatment arm (i.e., patients who were switched to the higher dose) would have fared had they been kept on the low dose in order to understand whether flexible dosing is potentially beneficial for them. Comparing these patients’ responses with those of patients who stayed on the low dose does not likely entail a satisfactory evaluation because the latter patients are usually in a better health condition and the available information is too limited to enable a reliable adjustment. In view of this, we will transport data from a fixed dosing trial that has been conducted concurrently on the same target, albeit not in an identical patient population.

In particular, we will propose a doubly robust estimator, which relies on an outcome model and a propensity score model for the association between study and patient characteristics. The proposed estimator is easy to evaluate, asymptotically unbiased if either model is correctly specified and efficient (under the restricted semi-parametric model where the randomisation probabilities are known and independent of baseline covariates) when both models are correctly specified. Theoretical properties are also evaluated through Monte Carlo simulations and the method will be illustrated based on the motivating example.

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New causal criteria for decisions making under fairness constraints
Mats Stensrud
Ecole Polytechnique Fédérale de Lausanne, Switzerland

To justify that a decision is fair, causal reasoning is important: we usually evaluate how the decision was made (the causes of the decision) and what would happen if a different was made (the effects of the decision).

Several causal (counterfactual) definitions of fairness have recently been suggested, but these definitions suffer from any of the following caveats: they rely on ill-defined interventions, require identification conditions that are unreasonably strong, can be gamed by decision makers with malicious intentions, or fail to capture arguably reasonable notions of discrimination.

Motivated by the shortcomings of the existing definitions of fairness, we introduce two new causal criteria to prevent discrimination in practice. These criteria can be applied to settings with non-binary and time-varying decisions. We suggest strategies to evaluate whether these criteria hold in observed data and give conditions that allow identification of counterfactual outcomes under new, non-discriminatory decision rules. The interpretation of our criteria is discussed in several examples.

Chairs: Sarah Friedrich and Jan Feifel

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Truncation by death and the survival-incorporated median: What are we measuring? And why?
Judith J. Lok¹, Qingyan Xiang², Ronald J. Bosch^3
1Department of Mathematics and Statistics, Boston University, United States of America; ²Department of Biostatistics, Boston University, United States of America; ³Center for Biostatistics in AIDS Research, Harvard University, United States of America

One could argue that if a person dies, their subsequent health outcomes are missing. On the other hand, one could argue that if a person dies, their health outcomes are completely obvious. This talk considers the second point of view, and advocates to not always see death as a mechanism through which health outcomes are missing, but rather as part of the outcome measure. This is especially useful when some people’s lives may be saved by a treatment we wish to study. We will show that both the median health score in those alive and the median health score in the always-survivors can lead one to believe that there is a trade-off between survival and good health scores, even in cases where in clinical practice both the probability of survival and the probability of a good health score are better for one treatment arm. To overcome this issue, we propose the survival-incorporated median as an alternative summary measure of health outcomes in the presence of death. It is the outcome value such that 50% of the population is alive with an outcome above that value. The survival-incorporated median can be interpreted as what happens to the “average” person. The survival-incorporated median is particularly relevant in settings with non-negligible mortality. We will illustrate our approach by estimating the effect of statins on neurocognitive function.

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Multi-state modeling and causal censoring of treatment discontinuations in randomized clinical trials
Alexandra Nießl¹, Jan Beyersmann¹, Anja Loos^2
1University of Ulm, Germany; ²Global Biostatistics, Merck KGaA, Darmstadt, Germany

The current COVID-19 pandemic and subsequent restrictions have various consequences on planned and ongoing clinical trials. Its effects on the conduct of a clinical trial create several challenges in analyzing and interpreting study data. In particular, a substantial amount of COVID-19-related treatment interruptions will affect the ability of the study to show the primary objective of the trial.

Recently, we investigated the impact of treatment discontinuations due to a clinical hold on the treatment effect of a clinical trial. A clinical hold order by the Food and Drug Administration (FDA) to the sponsor of a clinical trial is a measure to delay a proposed or to suspend an ongoing clinical investigation. The phase III clinical trial START with primary endpoint overall survival served as the motivating data example to explore implications and potential statistical approaches for a trial continuing after a clinical hold is lifted. We proposed a multistate model incorporating the clinical hold as well as disease progression as intermediate events to investigate the impact of the clinical hold on the treatment effect. The multistate modeling approach offers several advantages: Firstly, it naturally models the dependence between PFS and OS. Secondly, it could easily be extended to additionally account for time-dependent exposures. Thirdly, it provides the framework for a simple causal analysis of treatment effects using censoring. Here, we censor patients at the beginning of the clinical hold. Using a realistic simulation study informed by the START data, we showed that our censoring approach is flexible and it provides reasonable estimates of the treatment effect, which would be observed if no clinical hold has occurred. We pointed out that the censoring approach coincides with the causal g-computation formula and has a causal interpretation regarding the intention of the initial treatment.

Within the talk, we will present our multistate model approach and show our results with a focus on the censoring approach and the link to causal inference. Furthermore, we also propose a causal filtering approach. We will discuss the assumptions that have to be fulfilled for the ‘causal’ censoring or filtering to address treatment interruptions in general settings with an external time-dependent covariate inducing a time-varying treatment and, particularly, in the context of COVID-19.

References

Nießl, Alexandra, Jan Beyersmann, and Anja Loos. „Multistate modeling of clinical hold in randomized clinical trials.“ Pharmaceutical Statistics 19.3 (2020): 262-275

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Examining the causal mediating role of brain pathology on the relationship between subclinical cardiovascular disease and cognitive impairment: The Cardiovascular Health Study
Ryan M Andrews¹, Vanessa Didelez¹, Ilya Shpitser², Michelle C Carlson^2
1Leibniz Institute for Prevention Research and Epidemiology – BIPS, Germany; ²Johns Hopkins University

Accumulating evidence suggests that there is a link between subclinical cardiovascular disease and the onset of cognitive impairment in later life. Less is known about possible causal mechanisms underlying this relationship; however, a leading hypothesis is that brain biomarkers play an intermediary role. In this study, we aimed to estimate the proportion of the total effect of subclinical cardiovascular disease on incident cognitive impairment that is mediated through two brain biomarkers–brain hypoperfusion and white matter disease. To do this, we used data from the Cardiovascular Health Study, a large longitudinal cohort study of older adults across the United States. Because brain hypoperfusion and white matter disease may themselves be causally linked with an uncertain temporal ordering, we could not use most multiple mediator methods because we did not believe their assumptions would be met (i.e., that we had independent and causally ordered mediators). We overcame this challenge by applying an innovative causal mediation method—inverse odds ratio weighting—that can accommodate multiple mediators regardless of their temporal ordering or possible effects on each other.

We found that after imposing inclusion and exclusion criteria, approximately 20% of the effect of subclinical cardiovascular disease on incident cognitive impairment was jointly mediated by brain hypoperfusion and white matter disease. We also found that the mediated proportion varied by the type of cognitive impairment, with 21% of the effect being mediated among those with Mild Cognitive Impairment and 12% being mediated among those with dementia.

Interpreting our results as causal effects relies on the plausibility of many assumptions and must be done carefully. Based on subject matter knowledge and the results of several sensitivity analyses, we conclude that most (if not all) assumptions are indeed plausible; consequently, we believe our findings support the idea that brain hypoperfusion and white matter disease are on the causal pathway between subclinical cardiovascular disease and cognitive impairment, particularly Mild Cognitive Impairment. To our knowledge, our study is the first epidemiological study to support the existence of this etiological mechanism. We encourage future studies to extend and to replicate these results.

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Statistical Methods for Spatial Cluster Detection in Rare Diseases: A Simulation Study of Childhood Cancer Incidence
Michael Schündeln¹, Toni Lange², Maximilian Knoll³, Claudia Spix⁴, Hermann Brenner^5,6,7, Kayan Bozorgmehr⁸, Christian Stock^9
1Pediatric Hematology and Oncology, Department of Pediatrics III, University Hospital Essen and the University of Duisburg-Essen, Essen, Germany.; ²Center for Evidence-based Healthcare, University Hospital and Faculty of Medicine Carl Gustav Carus, TU Dresden, Germany.; ³Clinical Cooperation Unit Radiation Oncology, German Cancer Research Center (DKFZ), Heidelberg, Germany.; ⁴German Childhood Cancer Registry, Institute for Medical Biostatistics, Epidemiology and Informatics (IMBEI), University Medical Centre of the Johannes Gutenberg University Mainz, Mainz, Germany.; ⁵Division of Clinical Epidemiology and Aging Research, German Cancer Research Center (DKFZ), Heidelberg, Germany; ⁶Division of Preventive Oncology, German Cancer Research Center (DKFZ) and National Center for Tumor Diseases (NCT), Heidelberg, Germany; ⁷German Cancer Consortium (DKTK), German Cancer Research Center (DKFZ), Heidelberg, Germany; ⁸Department of Population Medicine and Health Services Research, School of Public Health, Bielefeld University, Bielefeld, Germany; ⁹Institute of Medical Biometry and Informatics (IMBI), University of Heidelberg, Heidelberg, Germany

Background and objective: The potential existence of spatial clusters in childhood cancer incidence is a debated topic. Identification of such clusters may help to better understand etiology and develop preventive strategies. We evaluated widely used statistical approaches of cluster detection in this context.

Simulation Study: We simulated the incidence of newly diagnosed childhood cancer (140/1,000,000 children under 15 years) and nephroblastoma (7/1,000,000). Clusters of defined size (1 to 50) and relative risk (1 to 100) were randomly assembled on the district level in Germany. For each combination of size and RR 2000 iterations were performed. We then applied three local clustering tests to the simulated data. The Besag-Newell method, the spatial scan statistic and the Bayesian Besag-York-Mollié with Integrated Nested Laplace Approximation approach. We then described the operating characteristics of the tests systematically (such as sensitivity, specificity, predictive values, power etc.).

Results: Depending on the simulated setting, the performance of the tests varied considerably within and between methods. In all methods, the sensitivity was positively associated with increasing size, incidence and RR of the high-risk area. In low RR scenarios, the BYM method showed the highest specificity. In the nephroblastoma scenario compared with the scenario including all cancer cases the performance of all methods was lower.

Conclusion: Reliable inferences on the existence of spatial clusters based on single statistical approaches in childhood cancer remains a challenge. The application of multiple methods, ideally with known operating characteristics, and a critical discussion of the joint evidence is required when aiming to identify high-risk clusters.

Chairs: Anke Huels and Jörg Rahnenführer

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Epidemiologische Modelle in der Öffentlichkeit – mit Statistik durch die Pandemie
Lars Koppers
Science Media Center Germany; Department für Wissenschaftskommunikation, Karlsruher Institut für Technologie, Germany

Die Corona-Pandemie hat gezeigt, wie wichtig mathematisches und statistisches Grundwissen auch im Alltag ist. Seit Anfang 2020 werden auch in der Öffentlichkeit statistische Maßzahlen und Modelle diskutiert. Die Bandbreite reicht dabei von einfachen Meldezahlen über Mittelwerte bis zu SIR-Modellen und Simulationen von aktiven Teilchen. Aber welche Modelle und Maßzahlen helfen in welchen Situationen? Welche Schlüsse können aus einer Simulation gezogen werden und welche nicht? Und wie können komplexe Zusammenhänge so vermittelt werden, dass diese auch in der Öffentlichkeit ankommen?

Das gemeinnützige Science Media Center Germany (SMC) wurde 2015 als Intermediär zwischen Wissenschaft und Wissenschaftsjournalismus gegründet. Es stellt dazu zeitnah Einschätzungen und Zitate zu tagesaktuellen Geschehnissen aus der Wissenschaft zur Verfügung und bieten zu unübersichtlichen oder vielschichtigen Themen Expertise und Hintergrundwissen. Das SMC Lab entwickelt als Datenlabor des SMC Software und Services für die eigene Redaktion und für die journalistische Community.

Im Zuge der Corona-Pandemie wuchs der Bedarf an statistischer Expertise im Jounalismus exponentiell. Maßzahlen wie die Verdopplungszeit, der Reproduktionsfaktor R oder die Eigenschaften eines exponentiellen Wachstums müssen so erklärt werden, dass Journalist*innen dazu befähigt werden kompetent über die Pandemie zu berichten. Ein wichtiger Schwerpunkt dabei sind auch die Limitationen eines jeden Modells, schließlich mag ein exponentielles Wachstum für einen kurzen Zeitraum eine treffende Beschreibung einer Zeitreihe sein, in einer endlichen Population kommt dieses Modell aber schnell an seine Grenzen.

Mit zuerst täglichen, inzwischen wöchentlichen Corona-Reports hilft das SMC die aktuelle Datenlage, wie zum Beispiel die Meldezahlen des Robert Koch-Instituts (RKI) und des DIVI-Intensivregisters einzuordnen und zu erklären. Insbesondere die Meldedaten des RKI erzeugen dabei einen hohen Erklärungsbedarf, da Meldeverzug und die Tatsache, dass es sich hier nicht um eine Zufallsstichprobe handelt, dazu verleiten, falsche Schlüsse zu ziehen.

Im Bereich der epidemiologischen Modelle wurden im vergangenen Jahr von vielen Gruppen Preprints und Paper veröffentlicht, oft begleitet von online zugänglichen Dashboards und der Pressemitteilung der zugehörigen Einrichtung. Nicht jedes neue Modell trägt allerdings zum Erkenntnisstand bei, zuweilen fehlt es an fachlicher Expertise in der Modellierung einer Pandemie, die Validierung von Prognosen ist oft unzureichend. Eine Auseinandersetzung mit der Öffentlichkeitswirkung der publizierten Arbeit ist hier notwendig, erst recht wenn dies außerhalb der üblichen Peer Review Verfahren geschieht.

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Correcting for bias due to misclassification in dietary patterns using 24 hour dietary recall data
Timm Intemann¹, Iris Pigeot^1,2
1Leibniz Institute for Prevention Research and Epidemiology – BIPS, Germany; ²Institute of Statistics, Faculty of Mathematics and Computer Science, University of Bremen, Germany

The development of statistical methods for nutritional epidemiology is a challenge, as nutritional data are usually multidimensional and error-prone. Analysing dietary data requires an appropriate method taking into account both multidimensionality and measurement error, but measurement error is often ignored when such data is analysed (1). For example, associations between dietary patterns and health outcomes are commonly investigated by first applying cluster analysis algorithms to derive dietary patterns and then fitting a regression model to estimate the associations. In such a naïve approach, errors in the underlying continuous dietary variables lead to misclassified dietary patterns and to biased effect estimates. To reduce this bias, we developed three correction algorithms for data assessed with a 24 hour dietary recall (24HDR), which has become the preferred dietary assessment tool in large epidemiological studies.

The newly developed correction algorithms combine the measurement error correction methods regression calibration (RC), simulation extrapolation (SIMEX) and multiple imputation (MI) with the cluster methods k-means cluster algorithm and the Gaussian mixture model. These new algorithms are based on univariate correction methods for Box-Cox transformed data (2) and consider the measurement error structure of 24HDR data. They consist mainly of the following three stages: (i) estimation of usual intakes, (ii) deriving patterns based on usual intakes and (iii) estimation of the association between these patterns and an outcome.

We apply the correction algorithms to real data from the IDEFICS/I.Family cohort to estimate the association between meal timing patterns and a marker for the long-term blood sugar level (HbA1c) in European children. Furthermore, we use the fitted parameters from this analysis to mimic the real cohort data in a simulation study. In this simulation study, we consider continuous and binary outcomes in different scenarios and compare the performance of the proposed correction algorithms and the naïve approach with respect to absolute, maximum and relative bias.

Simulation results show that the correction algorithms based on RC and MI perform better than the naïve and the SIMEX-based algorithms. Furthermore, the MI-based approach, which can use outcome information in the error model, is superior to the RC-based approach in most scenarios.

References

1. Shaw, P. et al. (2018). Epidemiologic analyses with error-prone exposures: Review of current practice and recommendations. Ann Epidemiol 28, 821-828.

2. Intemann, T. et al. (2019). SIMEX for correction of dietary exposure effects with Box-Cox transformed data. Biom J 62, 221-237

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Statistical analysis of Covid-19 data in Rhineland-Palatinate
Markus Schepers¹, Konstantin Strauch¹, Klaus Jahn³, Philipp Zanger², Emilio Gianicolo^1
1IMBEI Unimedizin Mainz, Germany; ²Institut für Hygiene und Infektionsschutz Abteilung Humanmedizin, Landesuntersuchungsamt; ³Gesundheitsministerium (MSAGD)

In this ongoing project we study the infection dynamics and settings of Covid-19 in Rhineland-Palatinate: what are the most common infection pathways? How does the virus typically spread?

Our analysis is based on data of all reported cases (positively tested individuals) in Rhineland-Palatinate during a specific time period, including at least 17 August – 10 November 2020. Around 20% of the reported cases have been traced to an infection cluster. This leads to a second data set of infection clusters, whose observation variables include size of the infection cluster and infection setting (such as `private household‘ or `restaurant‘). In line with previous studies, we found that the majority of infection clusters occurs in `private households‘ (including gatherings where multiple households are involved). Therefore, we are collecting additional information for a stratified sample of infection clusters with infection setting `private household‘. Here, the stratification is according to counties (Landkreise) with separate public health departments (Gesundheitsämter) and size of the infection cluster. We developed a questionnaire whose responses will provide the additional information. The questionnaire contains questions on contact persons, specific occasions and activities promoting the spread of the virus. We calculate descriptive statistics such as mean, median, standard deviation, min and max of the quantities of interest.

Results and observations so far include: Cities have a higher prevalence of Covid-19 cases than the countryside. Most of the infection clusters are local rather than over-regional. We also observe a phenomenon often called over-dispersion or super-spreading, meaning that a relatively small number of individuals and clusters is responsible for the majority of all infection transmissions.

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Simultanes regionales Monitorieren von SARS-CoV-2 Infektionen und COVID-19 Sterblichkeit in Bayern durch die standardisierte Infektionsmortalitätsrate (sIFR)
Kirsi Manz, Ulrich Mansmann
Ludwig-Maximilians-Universität München, Deutschland

Hintergrund

Regionale Karten erlauben einen schnellen Überblick über die räumliche Verteilung des SARS-CoV-2 Infektionsgeschehens und erlauben regionale Unterschiede zu identifizieren. Zur Vermeidung falsch-positiver Signale werden Gesundheitskarten geglättet. Dies macht eine sachgerechte Interpretation der geographischen Informationen möglich.

Ziel des Beitrags

Wir stellen die standardisierte Infektionsmortalitätsrate (sIFR) als Maßzahl vor, mit der sich simultan das Divergieren von standardisierten COVID-19 spezifischen Infektions- und Sterberaten regional monitorieren lässt. Regionale Abweichungen beider Prozesse von einem globalen Standard erlauben eine Priorisierung regionaler Maßnahmen zwischen Infektionsschutz und Patientenversorgung.

Materialien und Methoden

Die regionale sIFR ist der Quotient zwischen standardisierter Mortalitäts- und Infektionsrate. Sie beschreibt um wieviel mehr die regionale Abweichung im Sterbeprozess sich von der regionalen Abweichung im Infektionsprozess unterscheidet. Die sIFR-Werte werden mittels eines bayesianischen Konvolutionsmodells geschätzt und in Karten dargestellt. Unsere Analysen verwenden die Meldedaten zum SARS-CoV-2 Geschehen in Bayern im Jahr 2020 und betrachten 4 Zeitperioden zu je drei Monaten.

Ergebnisse und Diskussion

Die empirische Infektionssterblichkeit in Bayern zeigt einen abfallenden Trend über die Zeitperioden. Regionen mit höheren Abweichungen im Sterben vom bayerischen Standard verglichen zum Infektionsgeschehen (sIFR > 2) sind in den ersten drei Monaten nur in der Oberpfalz zu beobachten. Im Sommer befinden sie sich im gesamten Osten, im Spätsommer/Herbst dann im Norden Bayerns. Wir zeigen regionale Veränderungen der sIFR-Werte für Bayerns Regionen über die Zeit. Damit werden Regionen identifiziert, die zusätzlich zum Management der Infektionsausbreitung Maßnahmen zur Kontrolle der Sterblichkeit benötigen.