Coherent modeling of longitudinal causal effects on binary outcomes.

Analyses of biomedical studies often necessitate modeling longitudinal causal effects. The current focus on personalized medicine and effect heterogeneity makes this task even more challenging. Toward this end, structural nested mean models (SNMMs) are fundamental tools for studying heterogeneous treatment effects in longitudinal studies. However, when outcomes are binary, current methods for estimating multiplicative and additive SNMM parameters suffer from variation dependence between the causal parameters and the noncausal nuisance parameters. This leads to a series of difficulties in interpretation, estimation, and computation. These difficulties have hindered the uptake of SNMMs in biomedical practice, where binary outcomes are very common. We solve the variation dependence problem for the binary multiplicative SNMM via a reparameterization of the noncausal nuisance parameters. Our novel nuisance parameters are variation independent of the causal parameters, and hence allow for coherent modeling of heterogeneous effects from longitudinal studies with binary outcomes. Our parameterization also provides a key building block for flexible doubly robust estimation of the causal parameters. Along the way, we prove that an additive SNMM with binary outcomes does not admit a variation independent parameterization, thereby justifying the restriction to multiplicative SNMMs.

Atmospheric Sampling on Ascension Island Using Multirotor UAVs.

As part of an NERC-funded project investigating the southern methane anomaly, a team drawn from the Universities of Bristol, Birmingham and Royal Holloway flew small unmanned multirotors from Ascension Island for the purposes of atmospheric sampling. The objective of these flights was to collect air samples from below, within and above a persistent atmospheric feature, the Trade Wind Inversion, in order to characterise methane concentrations and their isotopic composition. These parameters allow the methane in the different air masses to be tied to different source locations, which can be further analysed using back trajectory atmospheric computer modelling. This paper describes the campaigns as a whole including the design of the bespoke eight rotor aircraft and the operational requirements that were needed in order to collect targeted multiple air samples up to 2.5 km above the ground level in under 20 min of flight time. Key features of the system described include real-time feedback of temperature and humidity, as well as system health data. This enabled detailed targeting of the air sampling design to be realised and planned during the flight mission on the downward leg, a capability that is invaluable in the presence of uncertainty in the pre-flight meteorological data. Environmental considerations are also outlined together with the flight plans that were created in order to rapidly fly vertical transects of the atmosphere whilst encountering changing wind conditions. Two sampling campaigns were carried out in September 2014 and July 2015 with over one hundred high altitude sampling missions. Lessons learned are given throughout, including those associated with operating in the testing environment encountered on Ascension Island.

Accounting for Life-Course Exposures in Epigenetic Biomarker Association Studies: Early Life Socioeconomic Position, Candidate Gene DNA Methylation, and Adult Cardiometabolic Risk.

Recent studies suggest that epigenetic programming may mediate the relationship between early life environment, including parental socioeconomic position, and adult cardiometabolic health. However, interpreting associations between early environment and adult DNA methylation may be difficult because of time-dependent confounding by life-course exposures. Among 613 adult women (mean age = 32 years) of the Jerusalem Perinatal Study Family Follow-up (2007-2009), we investigated associations between early life socioeconomic position (paternal occupation and parental education) and mean adult DNA methylation at 5 frequently studied cardiometabolic and stress-response genes (ABCA1, INS-IGF2, LEP, HSD11B2, and NR3C1). We used multivariable linear regression and marginal structural models to estimate associations under 2 causal structures for life-course exposures and timing of methylation measurement. We also examined whether methylation was associated with adult cardiometabolic phenotype. Higher maternal education was consistently associated with higher HSD11B2 methylation (e.g., 0.5%-point higher in 9-12 years vs. ≤8 years, 95% confidence interval: 0.1, 0.8). Higher HSD11B2 methylation was also associated with lower adult weight and total and low-density lipoprotein cholesterol. We found that associations with early life socioeconomic position measures were insensitive to different causal assumption; however, exploratory analysis did not find evidence for a mediating role of methylation in socioeconomic position-cardiometabolic risk associations.

Are Early-Life Socioeconomic Conditions Directly Related to Birth Outcomes? Grandmaternal Education, Grandchild Birth Weight, and Associated Bias Analyses.

Grandmaternal education may be related to grandchild birth weight (GBW) through maternal early-life development; however, conventional regression models may be endogenously confounded. Alternative models employing explicit structural assumptions may provide incrementally clearer evidence. We used data from the US National Longitudinal Study of Adolescent to Adult Health (1995-2009; 1,681 mother-child pairs) to estimate "direct effects" of grandmaternal educational level (less than high school, high school diploma or equivalent, or college degree) at the time of the mother's birth on GBW, adjusted for maternal life-course factors: maltreatment as a child, education and income as an adult, prepregnancy overweight, and prenatal smoking. Using conventional and marginal structural model (MSM) approaches, we estimated 54-g (95% confidence interval: -14.0, 122.1) and 87-g (95% confidence interval: 10.9, 162.5) higher GBWs per increase in educational level, respectively. The MSM allowed simultaneous mediation by and adjustment for prepregnancy overweight. Estimates were insensitive to alternate structural assumptions and mediator parameterizations. Bias analysis suggested that a single unmeasured confounder would have to have a strong influence on GBW (approximately 150 g) or be greatly imbalanced across exposure groups (approximately 25%) to completely explain the findings. Coupling an MSM with sensitivity analyses provides some evidence that maternal early-life socioeconomic environment is directly associated with offspring birth weight.

GENERAL THEORY FOR INTERACTIONS IN SUFFICIENT CAUSE MODELS WITH DICHOTOMOUS EXPOSURES.

The sufficient-component cause framework assumes the existence of sets of sufficient causes that bring about an event. For a binary outcome and an arbitrary number of binary causes any set of potential outcomes can be replicated by positing a set of sufficient causes; typically this representation is not unique. A sufficient cause interaction is said to be present if within all representations there exists a sufficient cause in which two or more particular causes are all present. A singular interaction is said to be present if for some subset of individuals there is a unique minimal sufficient cause. Empirical and counterfactual conditions are given for sufficient cause interactions and singular interactions between an arbitrary number of causes. Conditions are given for cases in which none, some or all of a given set of causes affect the outcome monotonically. The relations between these results, interactions in linear statistical models and Pearl's probability of causation are discussed.

Rescuing loading induced bone formation at senescence.

The increasing incidence of osteoporosis worldwide requires anabolic treatments that are safe, effective, and, critically, inexpensive given the prevailing overburdened health care systems. While vigorous skeletal loading is anabolic and holds promise, deficits in mechanotransduction accrued with age markedly diminish the efficacy of readily complied, exercise-based strategies to combat osteoporosis in the elderly. Our approach to explore and counteract these age-related deficits was guided by cellular signaling patterns across hierarchical scales and by the insight that cell responses initiated during transient, rare events hold potential to exert high-fidelity control over temporally and spatially distant tissue adaptation. Here, we present an agent-based model of real-time Ca(2+)/NFAT signaling amongst bone cells that fully described periosteal bone formation induced by a wide variety of loading stimuli in young and aged animals. The model predicted age-related pathway alterations underlying the diminished bone formation at senescence, and hence identified critical deficits that were promising targets for therapy. Based upon model predictions, we implemented an in vivo intervention and show for the first time that supplementing mechanical stimuli with low-dose Cyclosporin A can completely rescue loading induced bone formation in the senescent skeleton. These pre-clinical data provide the rationale to consider this approved pharmaceutical alongside mild physical exercise as an inexpensive, yet potent therapy to augment bone mass in the elderly. Our analyses suggested that real-time cellular signaling strongly influences downstream bone adaptation to mechanical stimuli, and quantification of these otherwise inaccessible, transient events in silico yielded a novel intervention with clinical potential.

Acyclic Linear SEMs Obey the Nested Markov Property.

The conditional independence structure induced on the observed marginal distribution by a hidden variable directed acyclic graph (DAG) may be represented by a graphical model represented by mixed graphs called maximal ancestral graphs (MAGs). This model has a number of desirable properties, in particular the set of Gaussian distributions can be parameterized by viewing the graph as a path diagram. Models represented by MAGs have been used for causal discovery [22], and identification theory for causal effects [28]. In addition to ordinary conditional independence constraints, hidden variable DAGs also induce generalized independence constraints. These constraints form the nested Markov property [20]. We first show that acyclic linear SEMs obey this property. Further we show that a natural parameterization for all Gaussian distributions obeying the nested Markov property arises from a generalization of maximal ancestral graphs that we call maximal arid graphs (MArG). We show that every nested Markov model can be associated with a MArG; viewed as a path diagram this MArG parametrizes the Gaussian nested Markov model. This leads directly to methods for ML fitting and computing BIC scores for Gaussian nested models.

Partial Identification of the Average Treatment Effect Using Instrumental Variables: Review of Methods for Binary Instruments, Treatments, and Outcomes.

Several methods have been proposed for partially or point identifying the average treatment effect (ATE) using instrumental variable (IV) type assumptions. The descriptions of these methods are widespread across the statistical, economic, epidemiologic, and computer science literature, and the connections between the methods have not been readily apparent. In the setting of a binary instrument, treatment, and outcome, we review proposed methods for partial and point identification of the ATE under IV assumptions, express the identification results in a common notation and terminology, and propose a taxonomy that is based on sets of identifying assumptions. We further demonstrate and provide software for the application of these methods to estimate bounds. Supplementary materials for this article are available online.

Rest-inserted loading rapidly amplifies the response of bone to small increases in strain and load cycles.

We hypothesized that a 10-s rest interval (at zero load) inserted between each load cycle would increase the osteogenic effects of mechanical loading near previously identified thresholds for strain magnitude and cycle numbers. We tested our hypothesis by subjecting the right tibiae of female C57BL/6J mice (16 wk, n = 70) to exogenous mechanical loading within a peri-threshold physiological range of strain magnitudes and load cycle numbers using a noninvasive murine tibia loading device. Bone responses to mechanical loading were determined via dynamic histomorphometry. More specifically, we contrasted bone formation induced by cyclic vs. rest-inserted loading (10-s rest at zero load inserted between each load cycle) by first varying peak strains (1,000, 1,250, or 1,600 micro epsilon) at fixed cycle numbers (50 cycles/day, 3 days/wk for 3 wk) and then varying cycle numbers (10, 50, or 250 cycles/day) at a fixed strain magnitude (1,250 micro epsilon). Within the range of strain magnitudes tested, the slope of periosteal bone formation rate (p.BFR/BS) with increasing strain magnitudes was significantly increased by rest-inserted compared with cyclical loading. Within the range of load cycles tested, the slope of p.BFR/BS with increasing load cycles of rest-inserted loading was also significantly increased by rest-inserted compared with cyclical loading. In sum, the data of this study indicate that inserting a 10-s rest interval between each load cycle amplifies bone's response to mechanical loading, even within a peri-threshold range of strain magnitudes and cycle numbers.

Causal analysis of ordinal treatments and binary outcomes under truncation by death.

It is common that in multi-arm randomized trials, the outcome of interest is "truncated by death," meaning that it is only observed or well-defined conditioning on an intermediate outcome. In this case, in addition to pairwise contrasts, the joint inference for all treatment arms is also of interest. Under a monotonicity assumption we present methods for both pairwise and joint causal analyses of ordinal treatments and binary outcomes in presence of truncation by death. We illustrate via examples the appropriateness of our assumptions in different scientific contexts.

On falsification of the binary instrumental variable model.

Instrumental variables are widely used for estimating causal effects in the presence of unmeasured confounding. The discrete instrumental variable model has testable implications for the law of the observed data. However, current assessments of instrumental validity are typically based solely on subject-matter arguments rather than these testable implications, partly due to a lack of formal statistical tests with known properties. In this paper, we develop simple procedures for testing the binary instrumental variable model. Our methods are based on existing techniques for comparing two treatments, such as the [Formula: see text]-test and the Gail-Simon test. We illustrate the importance of testing the instrumental variable model by evaluating the exogeneity of college proximity using the National Longitudinal Survey of Young Men.

Identification and estimation of causal effects with outcomes truncated by death.

It is common in medical studies that the outcome of interest is truncated by death, meaning that a subject has died before the outcome could be measured. In this case, restricted analysis among survivors may be subject to selection bias. Hence, it is of interest to estimate the survivor average causal effect, defined as the average causal effect among the subgroup consisting of subjects who would survive under either exposure. In this paper, we consider the identification and estimation problems of the survivor average causal effect. We propose to use a substitution variable in place of the latent membership in the always-survivor group. The identification conditions required for a substitution variable are conceptually similar to conditions for a conditional instrumental variable, and may apply to both randomized and observational studies. We show that the survivor average causal effect is identifiable with use of such a substitution variable, and propose novel model parameterizations for estimation of the survivor average causal effect under our identification assumptions. Our approaches are illustrated via simulation studies and a data analysis.

Marginal log-linear parameters for graphical Markov models.

Marginal log-linear (MLL) models provide a flexible approach to multivariate discrete data. MLL parametrizations under linear constraints induce a wide variety of models, including models defined by conditional independences. We introduce a subclass of MLL models which correspond to Acyclic Directed Mixed Graphs (ADMGs) under the usual global Markov property. We characterize for precisely which graphs the resulting parametrization is variation independent. The MLL approach provides the first description of ADMG models in terms of a minimal list of constraints. The parametrization is also easily adapted to sparse modelling techniques, which we illustrate using several examples of real data.

Resolving Contested Elections: The Limited Power of Post-Vote Vote-Choice Data.

In close elections, the losing side has an incentive to obtain evidence that the election result is incorrect. Sometimes this evidence comes in the form of court testimony from a sample of invalid voters, and this testimony is used to adjust vote totals (Borders v King County, 2005; Belcher v Mayor of Ann Arbor, 1978). However, while courts may be reluctant to make explicit findings about out-of-sample data (e.g. invalid voters that do not testify), when samples are used to adjust vote totals, the court is implicitly making findings about this out-of-sample data. In this paper, we show that the practice of adjusting vote totals on the basis of potentially unrepresentative samples can lead to incorrectly voided election results. More generally, we show that given the difficulties of sampling and non-response in this context, even when frame error is minimal and if voter testimony is accurate, such testimony has limited power to detect incorrect election results without precinct level polarization or the acceptance of large Type I error rates. Therefore in U.S. election disputes, even high quality post-vote vote-choice data will often not be sufficient to resolve contested elections without modeling assumptions (whether or not these assumptions are acknowledged).

Estimating Optimal Dynamic Regimes: Correcting Bias under the Null: [Optimal dynamic regimes: bias correction].

A dynamic regime provides a sequence of treatments that are tailored to patient-specific characteristics and outcomes. In 2004 James Robins proposed g-estimation using structural nested mean models for making inference about the optimal dynamic regime in a multi-interval trial. The method provides clear advantages over traditional parametric approaches. Robins' g-estimation method always yields consistent estimators, but these can be asymptotically biased under a given structural nested mean model for certain longitudinal distributions of the treatments and covariates, termed exceptional laws. In fact, under the null hypothesis of no treatment effect, every distribution constitutes an exceptional law under structural nested mean models which allow for interaction of current treatment with past treatments or covariates. This paper provides an explanation of exceptional laws and describes a new approach to g-estimation which we call Zeroing Instead of Plugging In (ZIPI). ZIPI provides nearly identical estimators to recursive g-estimators at non-exceptional laws while providing substantial reduction in the bias at an exceptional law when decision rule parameters are not shared across intervals.

Alleviating Linear Ecological Bias and Optimal Design with Sub-sample Data.

In this paper, we illustrate that combining ecological data with subsample data in situations in which a linear model is appropriate provides three main benefits. First, by including the individual level subsample data, the biases associated with linear ecological inference can be eliminated. Second, by supplementing the subsample data with ecological data, the information about parameters will be increased. Third, we can use readily available ecological data to design optimal subsampling schemes, so as to further increase the information about parameters. We present an application of this methodology to the classic problem of estimating the effect of a college degree on wages. We show that combining ecological data with subsample data provides precise estimates of this value, and that optimal subsampling schemes (conditional on the ecological data) can provide good precision with only a fraction of the observations.

Demystifying optimal dynamic treatment regimes.

A dynamic regime is a function that takes treatment and covariate history and baseline covariates as inputs and returns a decision to be made. Murphy (2003, Journal of the Royal Statistical Society, Series B 65, 331-366) and Robins (2004, Proceedings of the Second Seattle Symposium on Biostatistics, 189-326) have proposed models and developed semiparametric methods for making inference about the optimal regime in a multi-interval trial that provide clear advantages over traditional parametric approaches. We show that Murphy's model is a special case of Robins's and that the methods are closely related but not equivalent. Interesting features of the methods are highlighted using the Multicenter AIDS Cohort Study and through simulation.