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Missing data are ubiquitous in public health research. When estimating causal effects, there are well-established methods to address bias to due missing outcomes. Commonly, causal estimands are defined under hypothetical interventions to…
The multilevel model (MLM) is the popular approach to describe dependences of hierarchically clustered observations. A main feature is the capability to estimate (cluster-specific) random effect parameters, while their distribution…
Anomaly detection (AD) is a fundamental research problem in machine learning and computer vision, with practical applications in industrial inspection, video surveillance, and medical diagnosis. In medical imaging, AD is especially vital…
Consider a finite sample from an unknown distribution over a countable alphabet. Unobserved events are alphabet symbols which do not appear in the sample. Estimating the probabilities of unobserved events is a basic problem in statistics…
Familiar statistical tests and estimates are obtained by the direct observation of cases of interest: a clinical trial of a new drug, for instance, will compare the drug's effects on a relevant set of patients and controls. Sometimes,…
Biomarker measurements can be relatively easy and quick to obtain and they are useful to investigate whether a compound works as intended on a mechanistic, pharmacological level. In some situations, it is realistic to assume that patients,…
Time series anomaly detection (TSAD) is an evolving area of research motivated by its critical applications, such as detecting seismic activity, sensor failures in industrial plants, predicting crashes in the stock market, and so on. Across…
The interpretation of randomised clinical trial results is often complicated by intercurrent events. For instance, rescue medication is sometimes given to patients in response to worsening of their disease, either in addition to the…
We propose an original and general NOn-SEgmental (NOSE) approach for the detection of multiple change-points. NOSE identifies change-points by the non-negligibility of posterior estimates of the jump heights. Alternatively, under the…
Model-assisted designs have garnered significant attention in recent years due to their high accuracy in identifying the maximum tolerated dose (MTD) and their operational simplicity. To identify the MTD, they employ estimated dose limiting…
Two-sample summary-data Mendelian randomization (MR) has become a popular research design to estimate the causal effect of risk exposures. With the sample size of GWAS continuing to increase, it is now possible to utilize genetic…
Phase I dose escalation trials in oncology generally aim to find the maximum tolerated dose (MTD). However, with the advent of molecular targeted therapies and antibody drug conjugates, dose limiting toxicities are less frequently observed,…
When assessing the causal effect of a binary exposure using observational data, confounder imbalance across exposure arms must be addressed. Matching methods, including propensity score-based matching, can be used to deconfound the causal…
Our approach to Mendelian Randomization (MR) analysis is designed to increase reproducibility of causal effect "discoveries" by: (i) using a Bayesian approach to inference; (ii) replacing the point null hypothesis with a region of practical…
By means of the techniques of Boolean valued analysis, we provide a transfer principle between duality theory of classical convex risk measures and duality theory of conditional risk measures. Namely, a conditional risk measure can be…
Personalized optimal decision making, finding the optimal decision rule (ODR) based on individual characteristics, has attracted increasing attention recently in many fields, such as education, economics, and medicine. Current ODR methods…
The Regression Discontinuity (RD) design is a quasi-experimental design which emulates a randomised study by exploiting situations where treatment is assigned according to a continuous variable as is common in many drug treatment…
How should we evaluate the effect of a policy on the likelihood of an undesirable event, such as conflict? The significance test has three limitations. First, relying on statistical significance misses the fact that uncertainty is a…
Comparing counterfactual distributions can provide more nuanced and valuable measures for causal effects, going beyond typical summary statistics such as averages. In this work, we consider characterizing causal effects via distributional…
This Element offers a practical guide to estimating conditional marginal effects-how treatment effects vary with a moderating variable-using modern statistical methods. Commonly used approaches, such as linear interaction models, often…