Confidence Intervals for Maximin Effects in Inhomogeneous Large-Scale Data

One challenge of large-scale data analysis is that the assumption of an identical distribution for all samples is often not realistic. An optimal linear regression might, for example, be markedly different for distinct groups of the data. Maximin effects have been proposed as a computationally attractive way to estimate effects that are common across all data without fitting a mixture distribution explicitly. So far just point estimators of the common maximin effects have been proposed in Meinshausen and B\"uhlmann (2014). Here we propose asymptotically valid confidence regions for these effects

backShift: Learning causal cyclic graphs from unknown shift interventions

We propose a simple method to learn linear causal cyclic models in the presence of latent variables. The method relies on equilibrium data of the model recorded under a specific kind of interventions ("shift interventions"). The location and strength of these interventions do not have to be known and can be estimated from the data. Our method, called backShift, only uses second moments of the data and performs simple joint matrix diagonalization, applied to differences between covariance matrices. We give a sufficient and necessary condition for identifiability of the system, which is fulfilled almost surely under some quite general assumptions if and only if there are at least three distinct experimental settings, one of which can be pure observational data. We demonstrate the performance on some simulated data and applications in flow cytometry and financial time series. The code is made available as R-package backShift

THE EFFECTS OF CARDIAC SURGICAL PROCEDURES ON HEALTH – RELATED QUALITY OF LIFE, COGNITIVE PERFORMANCE, AND EMOTIONAL STATUS OUTCOMES: A PROSPECTIVE 6 – MONTH FOLLOW – UP STUDY

Introduction: The aim of this study was to assess the course of health – related quality of life, cognitive and emotional change during the six months after elective CABG, and to investigate how cognitive impairments, depression and posttraumatic stress symptoms were related to quality of life. Method: In a prospective study, we followed up for 6 months 138 of the original 147 patients who had undergone elective CABG surgery. Conclusion: Elective CABG is associated with significant improvements in HRQOL relative to the preoperative period, but impairments in HRQOL were found in a subgroup of post – CABG patients with evidence of PTSD, depression, or cognitive impairments at 6 – month follow – up

Distributionally robust and generalizable inference

We discuss recently developed methods that quantify the stability and generalizability of statistical findings under distributional changes. In many practical problems, the data is not drawn i.i.d. from the target population. For example, unobserved sampling bias, batch effects, or unknown associations might inflate the variance compared to i.i.d. sampling. For reliable statistical inference, it is thus necessary to account for these types of variation. We discuss and review two methods that allow quantifying distribution stability based on a single dataset. The first method computes the sensitivity of a parameter under worst-case distributional perturbations to understand which types of shift pose a threat to external validity. The second method treats distributional shifts as random which allows assessing average robustness (instead of worst-case). Based on a stability analysis of multiple estimators on a single dataset, it integrates both sampling and distributional uncertainty into a single confidence interval

One estimator, many estimands: fine-grained quantification of uncertainty using conditional inference

Statistical uncertainty has many components, such as measurement errors, temporal variation, or sampling. Not all of these sources are relevant when considering a specific application, since practitioners might view some attributes of observations as fixed. We study the statistical inference problem arising when data is drawn conditionally on some attributes. These attributes are assumed to be sampled from a super-population but viewed as fixed when conducting uncertainty quantification. The estimand is thus defined as the parameter of a conditional distribution. We propose methods to construct conditionally valid p-values and confidence intervals for these conditional estimands based on asymptotically linear estimators. In this setting, a given estimator is conditionally unbiased for potentially many conditional estimands, which can be seen as parameters of different populations. Testing different populations raises questions of multiple testing. We discuss simple procedures that control novel conditional error rates. In addition, we introduce a bias correction technique that enables transfer of estimators across conditional distributions arising from the same super-population. This can be used to infer parameters and estimators on future datasets based on some new data. The validity and applicability of the proposed methods are demonstrated on simulated and real-world data.Comment: 60 page