Causal Inference for time-to-event data

Truncation by death and the survival-incorporated median: What are we measuring? And why?
Judith J. Lok1, Qingyan Xiang2, Ronald J. Bosch3
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.

Multi-state modeling and causal censoring of treatment discontinuations in randomized clinical trials
Alexandra Nießl1, Jan Beyersmann1, Anja Loos2
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.


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

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 Carlson2
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.

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 Brenner5,6,7, Kayan Bozorgmehr8, Christian Stock9
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.