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Recent research in causal inference has made important progress in addressing challenges to the external validity of trial findings. Such methods weight trial participant data to more closely resemble the distribution of effect-modifying covariates in a well-defined target population. In the presence of participant non-adherence to study medication, these methods effectively transport an intention-to-treat effect that averages over heterogeneous compliance behaviors. In this paper, we develop a principal stratification framework to identify causal effects conditioning on both compliance behavior and membership in the target population. We also develop non-parametric efficiency theory for and construct efficient estimators of such "transported" principal causal effects and characterize their finite-sample performance in simulation experiments. While this work focuses on treatment non-adherence, the framework is applicable to a broad class of estimands that target effects in clinically-relevant, possibly latent subsets of a target population.

Meta-analysis is commonly used to combine results from multiple clinical trials, but traditional meta-analysis methods do not refer explicitly to a population of individuals to whom the results apply and it is not clear how to use their results to assess a treatment's effect for a population of interest. We describe recently-introduced causally-interpretable meta-analysis methods and apply their treatment effect estimators to two individual-participant data sets. These estimators transport estimated treatment effects from studies in the meta-analysis to a specified target population using individuals' potentially effect-modifying covariates. We consider different regression and weighting methods within this approach and compare the results to traditional aggregated-data meta-analysis methods. In our applications, certain versions of the causally-interpretable methods performed somewhat better than the traditional methods, but the latter generally did well. The causally-interpretable methods offer the most promise when covariates modify treatment effects and our results suggest that traditional methods work well when there is little effect heterogeneity. The causally-interpretable approach gives meta-analysis an appealing theoretical framework by relating an estimator directly to a specific population and lays a solid foundation for future developments., Comment: 31 pages, 2 figures Submitted to Research Synthesis Methods

Recent work has made important contributions in the development of causally-interpretable meta-analysis. These methods transport treatment effects estimated in a collection of randomized trials to a target population of interest. Ideally, estimates targeted toward a specific population are more interpretable and relevant to policy-makers and clinicians. However, between-study heterogeneity not arising from differences in the distribution of treatment effect modifiers can raise difficulties in synthesizing estimates across trials. The existence of such heterogeneity, including variations in treatment modality, also complicates the interpretation of transported estimates as a generic effect in the target population. We propose a conceptual framework and estimation procedures that attempt to account for such heterogeneity, and develop inferential techniques that aim to capture the accompanying excess variability in causal estimates. This framework also seeks to clarify the kind of treatment effects that are amenable to the techniques of generalizability and transportability.

A primary purpose of charter schooling is to provide education options and alternatives for families that are neither satisfied with nor well served by their current schooling options. For that reason, many of today's charter schools are focused on improving educational opportunities for low-income and minority students. Their families seek high-quality school options, yet many lack the means to move out of neighborhoods with unsatisfactory schools or to transport their children to attend schools that are better, but farther from home. School choice policies seek to address this problem in several ways, such as by creating public charter schools. Yet such schools are not evenly distributed across the communities that would benefit from them. For a host of reasons, it's difficult--or impossible--to establish charter schools in many places. There are political, legal, and fiscal obstacles, such as low per-pupil funding for charter students, no access to (or financial help with) suitable facilities, and laws or regulations that confine charters to certain communities or neighborhoods. Yet for a school to serve the children who need and would welcome it--particularly children from poor families--that school must be close to home. This is particularly true of elementary schools, as parents are understandably hesitant to send young children long distances to attend school. This report examines patterns of charter school locations, seeking to answer one fundamental question: "What high-need areas lack charter schools?" The authors analyze the distribution of chartered elementary schools across the country to provide educators and policymakers with information about which needy communities have no ready access to charter schools. [Foreword by Michael J. Petrilli and Amber M. Northern.]

Social scientists have frequently sought to understand the distinct effects of age, period, and cohort, but disaggregation of the three dimensions is difficult because cohort = period - age. We argue that this technical difficulty reflects a disconnection between how cohort effect is conceptualized and how it is modeled in the traditional age-period-cohort framework. We propose a new method, called the age-period-cohort-interaction (APC-I) model, that is qualitatively different from previous methods in that it represents Ryder's (1965) theoretical account about the conditions under which cohort differentiation may arise. This APC-I model does not require problematic statistical assumptions and the interpretation is straightforward. It quantifies inter-cohort deviations from the age and period main effects and also permits hypothesis testing about intra-cohort life-course dynamics. We demonstrate how this new model can be used to examine age, period, and cohort patterns in women's labor force participation.

This paper is about how we study statistical methods. As an example, it uses the random regressions model, in which the intercept and slope of cluster-specific regression lines are modeled as a bivariate random effect. Maximizing this model's restricted likelihood often gives a boundary value for the random effect correlation or variances. We argue that this is a problem; that it is a problem because our discipline has little understanding of how contemporary models and methods map data to inferential summaries; that we lack such understanding, even for models as simple as this, because of a near-exclusive reliance on mathematics as a means of understanding; and that math alone is no longer sufficient. We then argue that as a discipline, we can and should break open our black-box methods by mimicking the five steps that molecular biologists commonly use to break open Nature's black boxes: design a simple model system, formulate hypotheses using that system, test them in experiments on that system, iterate as needed to reformulate and test hypotheses, and finally test the results in an "in vivo" system. We demonstrate this by identifying conditions under which the random-regressions restricted likelihood is likely to be maximized at a boundary value. Resistance to this approach seems to arise from a view that it lacks the certainty or intellectual heft of mathematics, perhaps because simulation experiments in our literature rarely do more than measure a new method's operating characteristics in a small range of situations. We argue that such work can make useful contributions including, as in molecular biology, the findings themselves and sometimes the designs used in the five steps; that these contributions have as much practical value as mathematical results; and that therefore they merit publication as much as the mathematical results our discipline esteems so highly.

Random effects (RE) models have been widely used to study the contextual effects of structures such as neighborhood or school. The RE approach has recently been applied to age-period-cohort (APC) models that are unidentified because the predictors are exactly linearly dependent. However, it has not been fully understood how the RE specification identifies these otherwise unidentified APC models. We address this challenge by first making explicit that RE-APC models have greater -- not less -- rank deficiency than the traditional fixed-effects model, followed by two empirical examples. We then provide intuition and a mathematical proof to explain that for APC models with one RE, treating one effect as an RE is equivalent to constraining the estimates of that effect's linear component and the random intercept to be zero. For APC models with two RE's, the effective constraints implied by the model depend on the true (i.e., in the data-generating mechanism) non-linear components of the effects that are modeled as RE's, so that the estimated linear components of the RE's are determined by the true non-linear components of those effects. In conclusion, RE-APC models impose arbitrary though highly obscure constraints and thus do not differ qualitatively from other constrained APC estimators., Comment: Submitted to "Sociological Methodology"

Gaussian processes (GPs) are widely used as distributions of random effects in linear mixed models, which are fit using the restricted likelihood or the closely-related Bayesian analysis. This article addresses two problems. First, we propose tools for understanding how data determine estimates in these models, using a spectral basis approximation to the GP under which the restricted likelihood is formally identical to the likelihood for a gamma-errors GLM with identity link. Second, to examine the data's support for a covariate and to understand how adding that covariate moves variation in the outcome y out of the GP and error parts of the fit, we apply a linear-model diagnostic, the added variable plot (AVP), both to the original observations and to projections of the data onto the spectral basis functions. The spectral- and observation-domain AVPs estimate the same coefficient for a covariate but emphasize low- and high-frequency data features respectively and thus highlight the covariate's effect on the GP and error parts of the fit respectively. The spectral approximation applies to data observed on a regular grid; for data observed at irregular locations, we propose smoothing the data to a grid before applying our methods. The methods are illustrated using the forest-biomass data of Finley et al.~(2008).

PbTe, one of the most promising thermoelectric materials, has recently demonstrated thermoelectric figure of merit ($ZT$) of above 2.0 when alloyed with group II elements. The improvements are due mainly to significant reduction of lattice thermal conductivity ($\kappa_{l}$), which was in turn attributed to nanoparticle precipitates. However, a fundamental understanding of various phonon scattering mechanisms within the bulk alloy is still lacking. In this work, we apply the newly-developed density-functional-theory (DFT)-based compressive sensing lattice dynamics (CSLD) approach to model lattice heat transport in PbTe, MTe, and Pb$_{0.94}$M$_{0.06}$Te (M=Mg, Ca, Sr and Ba), compare our results with experimental measurements, with focus on strain effect and mass disorder scattering. We find that (1) CaTe, SrTe and BaTe in the rock-salt structure exhibit much higher $\kappa_{l}$ than PbTe, while MgTe in the same structure shows anomalously low $\kappa_{l}$; (2) lattice heat transport of PbTe is extremely sensitive to static strain induced by alloying atoms in solid solution form; (3) mass disorder scattering plays a major role in reducing $\kappa_{l}$ for Mg/Ca/Sr-alloyed PbTe through strongly suppressing the lifetimes of intermediate- and high-frequency phonons, while for Ba-alloyed PbTe, precipitated nanoparticles are also important.

Hierarchical models for regionally aggregated disease incidence data commonly involve region specific latent random effects that are modeled jointly as having a multivariate Gaussian distribution. The covariance or precision matrix incorporates the spatial dependence between the regions. Common choices for the precision matrix include the widely used ICAR model, which is singular, and its nonsingular extension which lacks interpretability. We propose a new parametric model for the precision matrix based on a directed acyclic graph (DAG) representation of the spatial dependence. Our model guarantees positive definiteness and, hence, in addition to being a valid prior for regional spatially correlated random effects, can also directly model the outcome from dependent data like images and networks. Theoretical results establish a link between the parameters in our model and the variance and covariances of the random effects. Substantive simulation studies demonstrate that the improved interpretability of our model reaps benefits in terms of accurately recovering the latent spatial random effects as well as for inference on the spatial covariance parameters. Under modest spatial correlation, our model far outperforms the CAR models, while the performances are similar when the spatial correlation is strong. We also assess sensitivity to the choice of the ordering in the DAG construction using theoretical and empirical results which testify to the robustness of our model. We also present a large-scale public health application demonstrating the competitive performance of the model.