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While most methods for missing not at random (MNAR) data in regression models address MNAR outcomes assuming fully observed predictors, real-world observational health and longitudinal studies often violate this assumption. This paper compares several approaches for handling MNAR data in linear regression when missingness depends on both partially observed outcomes and predictors. Through extensive simulations, we evaluate complete-case analysis, multiple imputation assuming missing at random, maximum likelihood estimation via the Heckman selection model, uncertainty intervals, multiple imputation under the Heckman selection model, not-at-random fully conditional specification, imputation stacking, and random indicator imputation. None of the methods consistently produced unbiased estimates or nominal coverage across all scenarios. However, not-at-random fully conditional specification was straightforward to implement and yielded coverage close to the nominal level in most scenarios, provided that the sensitivity parameters were specified near their true values. Our results highlight the importance of sensitivity analyses exploring various full-data models and careful parameter specification when addressing MNAR in both outcomes and predictors. We illustrate such sensitivity analyses using Betula study data on the relationship between longitudinal memory change and grey matter volume in aging. The association remained significant across most considered MNAR scenarios, reinforcing existing evidence for this relationship.

This article contributes to the discussion on the relationship between the Neyman-Rubin and the graphical frameworks for causal inference. We present specific examples of data-generating mechanisms — such as those involving undirected or deterministic relationships and cycles — where analyses using a directed acyclic graph are challenging, but where the tools from the Neyman-Rubin causal framework are readily applicable. We also provide examples of data-generating mechanisms with M-bias, trapdoor variables, and complex front-door structures, where the covariate adjustment in the Neyman-Rubin approach provides biased estimators of causal effects, but the graphical approach helps analysts identify valid strategies for unbiased estimation. The examples offer insights into commonly used causal inference frameworks and aim to improve comprehension of the languages for causal reasoning among a broad audience. 

Artificial-intelligence systems are becoming ubiquitous in society, yet their predictions typically inherit biases with respect to protected attributes such as race, gender, or age. Classical fairness notions, most notably Statistical Parity (SP), demand that predictions be independent of the protected attributes, but are overly restrictive when these attributes influence mediating variables that are considered business necessities. Recent causal formulations relax SP by distinguishing allowed from not-allowed causal paths and by complementing SP with Predictive Parity (PP), requiring the predictor to replicate the legitimate influence of business necessities. Existing path-based definitions are mainly practical when applied to categorical attributes. This paper introduces a new framework for fairness in structural causal models that is tailored to continuous protected attributes. We formalize SP and PP through path-specific partial derivatives, establish conditions under which these criteria coincide with prior causal definitions, and characterize when a fair predictor, one that satisfies SP along not-allowed paths while achieving PP along allowed paths, exists. Building on this theory, we propose a fair tuning algorithm that either constructs such a predictor or, when not possible, allows for a trade-off between SP and PP. We present experiments on simulated and real data to evaluate our proposal, compare it with previously proposed methods, and show that it performs better when PP is considered.

Motivated by the Swedish Betula study, we consider the joint modeling of longitudinal memory assessments and the hazard of dementia. In the Betula data, the time-to-dementia onset or its absence is available for all participants, while some memory measurements are missing. In longitudinal studies of aging, one cannot rule out the possibility of dropout due to health issues resulting in missing not at random longitudinal measurements. We, therefore, propose a pattern-mixture sensitivity analysis for missing not-at-random data in the joint modeling framework. The sensitivity analysis is implemented via multiple imputation as follows: (i) multiply impute missing not at random longitudinal measurements under a set of plausible pattern-mixture imputation models that allow for acceleration of memory decline after dropout, (ii) fit the joint model to each imputed longitudinal memory and time-to-dementia dataset, and (iii) combine the results of step (ii). Our work illustrates that sensitivity analyses via multiple imputations are an accessible, pragmatic method to evaluate the consequences of missing not at-random data on inference and prediction. This flexible approach can accommodate a range of models for the longitudinal and event-time processes. In particular, the pattern-mixture modeling approach provides an accessible way to frame plausible missing not at random assumptions for different missing data patterns. Applying our approach to the Betula study shows that worse memory levels and steeper memory decline were associated with a higher risk of dementia for all considered scenarios.

Various methods have recently been proposed to estimate causal effects with confidence intervals that are uniformly valid over a set of data-generating processes when high-dimensional nuisance models are estimated by post-model-selection or machine learning estimators. These methods typically require that all the confounders are observed to ensure identification of the effects. We contribute by showing how valid semiparametric inference can be obtained in the presence of unobserved confounders and high-dimensional nuisance models. We propose uncertainty intervals that allow for unobserved confounding, and show that the resulting inference is valid when the amount of unobserved confounding is not arbitrarily large; the latter is formalized in terms of convergence rates. Simulation experiments illustrate the finite sample properties of the proposed intervals. Finally, a case study on the effect of smoking during pregnancy on birth weight is used to illustrate the use of the methods introduced to perform an informed sensitivity analysis to the presence of unobserved confounding.

Semiparametric inference on average causal effects from observational data is based on assumptions yielding identification of the effects. In practice, several distinct identifying assumptions may be plausible; an analyst has to make a delicate choice between these models. In this paper, we study three identifying assumptions based on the potential outcome framework:  the back-door assumption, which uses pre-treatment covariates, the front-door assumption, which uses mediators, and the two-door assumption using pre-treatment covariates and mediators simultaneously. We provide the efficient influence functions and the corresponding semiparametric efficiency bounds that hold under these assumptions, and their combinations. We demonstrate that neither of the identification models provides uniformly the most efficient estimation and give conditions under which some bounds are lower than others. We show when semiparametric estimating equation estimators based on influence functions  attain the bounds, and study the robustness of the estimators to misspecification of the nuisance models. The theory is complemented with simulation experiments on the finite sample behavior of the estimators. The results obtained are relevant for an analyst facing a choice between several plausible identifying assumptions and corresponding estimators. Our results show that this choice implies a trade-off between efficiency and robustness to misspecification of the nuisance models. 

Contemporary accounts of factors that may modify the risk for age-related neurocognitive disorders highlight education and its contribution to a cognitive reserve. By this view, individuals with higher educational attainment should show weaker associations between changes in brain and cognition than individuals with lower educational attainment. We tested this prediction in longitudinal data on hippocampus volume and episodic memory from 708 middle-aged and older individuals using local structural equation modeling. This technique does not require categorization of years of education and does not constrain the shape of relationships, thereby maximizing the chances of revealing an effect of education on the hippocampus-memory association. The results showed that the data were plausible under the assumption that there was no influence of education on the association between change in episodic memory and change in hippocampus volume. Restricting the sample to individuals with elevated genetic risk for dementia (APOE ε4 carriers) did not change these results. We conclude that the influence of education on changes in episodic memory and hippocampus volume is inconsistent with predictions by the cognitive reserve theory.

Concomitant exploration of structural, functional, and neurochemical brain mechanisms underlying age-related cognitive decline is crucial in promoting healthy aging. Here, we present the DopamiNe, Age, connectoMe, and Cognition (DyNAMiC) project, a multimodal, prospective 5-year longitudinal study spanning the adult human lifespan. DyNAMiC examines age-related changes in the brain’s structural and functional connectome in relation to changes in dopamine D1 receptor availability (D1DR), and their associations to cognitive decline. Critically, due to the complete lack of longitudinal D1DR data, the true trajectory of one of the most age-sensitive dopamine systems remains unknown. The first DyNAMiC wave included 180 healthy participants (20–80 years). Brain imaging included magnetic resonance imaging assessing brain structure (white matter, gray matter, iron), perfusion, and function (during rest and task), and positron emission tomography (PET) with the [¹¹C]SCH23390 radioligand. A subsample (n = 20, >65 years) was additionally scanned with [¹¹C]raclopride PET measuring D2DR. Age-related variation was evident for multiple modalities, such as D1DR; D2DR, and performance across the domains of episodic memory, working memory, and perceptual speed. Initial analyses demonstrated an inverted u-shaped association between D1DR and resting-state functional connectivity across cortical network nodes, such that regions with intermediate D1DR levels showed the highest levels of nodal strength. Evident within each age group, this is the first observation of such an association across the adult lifespan, suggesting that emergent functional architecture depends on underlying D1DR systems. Taken together, DyNAMiC is the largest D1DR study worldwide, and will enable a comprehensive examination of brain mechanisms underlying age-related cognitive decline.

Introduction: Adolescents have experienced decreased aerobic fitness levels and insufficient physical activity levels over the past decades. While both physical activity and aerobic fitness are related to physical and mental health, little is known concerning how they manifest in the brain during this stage of development, characterized by significant physical and psychosocial changes. The aim of the study is to examine the associations between both physical activity and aerobic fitness with brains’ functional connectivity.

Methods: Here, we examined how physical activity and aerobic fitness are associated with local and interhemispheric functional connectivity of the adolescent brain (n = 59), as measured with resting‐state functional magnetic resonance imaging. Physical activity was measured by hip‐worn accelerometers, and aerobic fitness by a maximal 20‐m shuttle run test.

Results: We found that higher levels of moderate‐to‐vigorous intensity physical activity, but not aerobic fitness, were linked to increased local functional connectivity as measured by regional homogeneity in 13–16‐year‐old participants. However, we did not find evidence for significant associations between adolescents’ physical activity or aerobic fitness and interhemispheric connectivity, as indicated by homotopic connectivity.

Conclusions: These results suggest that physical activity, but not aerobic fitness, is related to local functional connectivity in adolescents. Moreover, physical activity shows an association with a specific brain area involved in motor functions but did not display any widespread associations with other brain regions. These results can advance our understanding of the behavior–brain associations in adolescents.

Healthy aging is accompanied by progressive decline in cognitive performance and concomitant changes in brain structure and functional architecture. Age-accompanied alterations in brain function have been characterized on a network level as weaker functional connections within brain networks along with stronger interactions between networks. This phenomenon has been described as age-related differences in functional network segregation. It has been suggested that functional networks related to associative processes are particularly sensitive to age-related deterioration in segregation, possibly related to cognitive decline in aging. However, there have been only a few longitudinal studies with inconclusive results. Here, we used a large longitudinal sample of 284 participants between 25 to 80 years of age at baseline, with cognitive and neuroimaging data collected at up to three time points over a 10-year period. We investigated age-related changes in functional segregation among two large-scale systems comprising associative and sensorimotor-related resting-state networks. We found that functional segregation of associative systems declines in aging with exacerbated deterioration from the late fifties. Changes in associative segregation were positively associated with changes in global cognitive ability, suggesting that decreased segregation has negative consequences for domain-general cognitive functions. Age-related changes in system segregation were partly accounted for by changes in white matter integrity, but white matter integrity only weakly influenced the association between segregation and cognition. Together, these novel findings suggest a cascade where reduced white-matter integrity leads to less distinctive functional systems which in turn contributes to cognitive decline in aging.