Reproducibility of Neuroretinal Rim Measurements Obtained from High-Density Spectral Domain Optical Coherence Tomography Volume Scans.

Purpose: To compare the reproducibility of two-dimensional (2D) peripapillary retinal nerve fiber layer (RNFL) thickness and three-dimensional (3D) neuroretinal rim measurements using spectral domain optical coherence tomography (SDOCT) in normal and glaucoma subjects. Methods: One eye per subject for 27 normal and 40 glaucoma subjects underwent repeat SDOCT RNFL thickness scans and optic nerve volume scans on the same day. From the volume scan, custom software calculated five neuroretinal rim parameters: 3D minimum distance band (MDB) thickness, 3D MDB area, 3D rim volume, 2D rim area, and 2D rim thickness. Within-subject variance (Sw), coefficient of variation (CV), and intraclass correlation coefficient (ICC) were analyzed. Results: MDB thickness and RNFL thickness have similar reproducibility among normal and glaucoma subjects (eg, global MDB thickness CVs of 2.4% and 3.6%, and global RNFL thickness CVs of 1.3% and 2.2%; P > 0.05 for both comparisons). Reproducibility of MDB thickness was lower in glaucoma patients for the superior and inferior quadrants compared to normal subjects (CVs of 9.6% versus 3.4% and 6.9% versus 2.7%; P < 0.05, respectively). There were no statistically significant differences between both groups for RNFL thickness in the four quadrants. For both patient groups and for all regions, MDB thickness had the lowest CVs among all five neuroretinal rim parameters (eg, global MDB thickness CVs of 2.4% and 3.6% versus 3.0% and 18.9% for the other four neuroretinal rim parameters). Conclusion: Global MDB and global RNFL thickness are similarly reproducible among normal and glaucoma subjects, though MDB thickness for the superior and inferior quadrants is less reproducible among glaucoma subjects.

Discussion on "Spatial+: a novel approach to spatial confounding" by Emiko Dupont, Simon N. Wood, and Nicole H. Augustin.

I congratulate Dupont, Wood, and Augustin (DWA hereon) for providing an easy-to-implement method for estimation in the presence of spatial confounding, and for addressing some of the complicated aspects on the topic. I discuss conceptual and operational issues that are fundamental to inference in spatial settings: (i) the target quantity and its interpretability, (ii) the nonspatial aspect of covariates and their relative spatial scales, and (iii) the impact of spatial smoothing. While DWA provide some insights on these issues, I believe that the audience might benefit from a deeper discussion.

Causal inference in high dimensions: A marriage between Bayesian modeling and good frequentist properties.

We introduce a framework for estimating causal effects of binary and continuous treatments in high dimensions. We show how posterior distributions of treatment and outcome models can be used together with doubly robust estimators. We propose an approach to uncertainty quantification for the doubly robust estimator, which utilizes posterior distributions of model parameters and (1) results in good frequentist properties in small samples, (2) is based on a single run of a Markov chain Monte Carlo (MCMC) algorithm, and (3) improves over frequentist measures of uncertainty which rely on asymptotic properties. We consider a flexible framework for modeling the treatment and outcome processes within the Bayesian paradigm that reduces model dependence, accommodates nonlinearity, and achieves dimension reduction of the covariate space. We illustrate the ability of the proposed approach to flexibly estimate causal effects in high dimensions and appropriately quantify uncertainty. We show that our proposed variance estimation strategy is consistent when both models are correctly specified, and we see empirically that it performs well in finite samples and under model misspecification. Finally, we estimate the effect of continuous environmental exposures on cholesterol and triglyceride levels.

Clarifying selection bias in cluster randomized trials.

BACKGROUND: In cluster randomized trials, patients are typically recruited after clusters are randomized, and the recruiters and patients may not be blinded to the assignment. This often leads to differential recruitment and consequently systematic differences in baseline characteristics of the recruited patients between intervention and control arms, inducing post-randomization selection bias. We aim to rigorously define causal estimands in the presence of selection bias. We elucidate the conditions under which standard covariate adjustment methods can validly estimate these estimands. We further discuss the additional data and assumptions necessary for estimating causal effects when such conditions are not met. METHODS: Adopting the principal stratification framework in causal inference, we clarify there are two average treatment effect (ATE) estimands in cluster randomized trials: one for the overall population and one for the recruited population. We derive analytical formula of the two estimands in terms of principal-stratum-specific causal effects. Furthermore, using simulation studies, we assess the empirical performance of the multivariable regression adjustment method under different data generating processes leading to selection bias. RESULTS: When treatment effects are heterogeneous across principal strata, the average treatment effect on the overall population generally differs from the average treatment effect on the recruited population. A naïve intention-to-treat analysis of the recruited sample leads to biased estimates of both average treatment effects. In the presence of post-randomization selection and without additional data on the non-recruited subjects, the average treatment effect on the recruited population is estimable only when the treatment effects are homogeneous between principal strata, and the average treatment effect on the overall population is generally not estimable. The extent to which covariate adjustment can remove selection bias depends on the degree of effect heterogeneity across principal strata. CONCLUSION: There is a need and opportunity to improve the analysis of cluster randomized trials that are subject to post-randomization selection bias. For studies prone to selection bias, it is important to explicitly specify the target population that the causal estimands are defined on and adopt design and estimation strategies accordingly. To draw valid inferences about treatment effects, investigators should (1) assess the possibility of heterogeneous treatment effects, and (2) consider collecting data on covariates that are predictive of the recruitment process, and on the non-recruited population from external sources such as electronic health records.

Propensity score weighting for causal subgroup analysis.

A common goal in comparative effectiveness research is to estimate treatment effects on prespecified subpopulations of patients. Though widely used in medical research, causal inference methods for such subgroup analysis (SGA) remain underdeveloped, particularly in observational studies. In this article, we develop a suite of analytical methods and visualization tools for causal SGA. First, we introduce the estimand of subgroup weighted average treatment effect and provide the corresponding propensity score weighting estimator. We show that balancing covariates within a subgroup bounds the bias of the estimator of subgroup causal effects. Second, we propose to use the overlap weighting (OW) method to achieve exact balance within subgroups. We further propose a method that combines OW and LASSO, to balance the bias-variance tradeoff in SGA. Finally, we design a new diagnostic graph-the Connect-S plot-for visualizing the subgroup covariate balance. Extensive simulation studies are presented to compare the proposed method with several existing methods. We apply the proposed methods to the patient-centered results for uterine fibroids (COMPARE-UF) registry data to evaluate alternative management options for uterine fibroids for relief of symptoms and quality of life.

Bipartite Causal Inference with Interference.

Statistical methods to evaluate the effectiveness of interventions are increasingly challenged by the inherent interconnectedness of units. Specifically, a recent flurry of methods research has addressed the problem of interference between observations, which arises when one observational unit's outcome depends not only on its treatment but also the treatment assigned to other units. We introduce the setting of bipartite causal inference with interference, which arises when 1) treatments are defined on observational units that are distinct from those at which outcomes are measured and 2) there is interference between units in the sense that outcomes for some units depend on the treatments assigned to many other units. The focus of this work is to formulate definitions and several possible causal estimands for this setting, highlighting similarities and differences with more commonly considered settings of causal inference with interference. Towards an empirical illustration, an inverse probability of treatment weighted estimator is adapted from existing literature to estimate a subset of simplified, but interesting, estimands. The estimators are deployed to evaluate how interventions to reduce air pollution from 473 power plants in the U.S. causally affect cardiovascular hospitalization among Medicare beneficiaries residing at 18,807 zip code locations.

Soft Tensor Regression.

Statistical methods relating tensor predictors to scalar outcomes in a regression model generally vectorize the tensor predictor and estimate the coefficients of its entries employing some form of regularization, use summaries of the tensor covariate, or use a low dimensional approximation of the coefficient tensor. However, low rank approximations of the coefficient tensor can suffer if the true rank is not small. We propose a tensor regression framework which assumes a soft version of the parallel factors (PARAFAC) approximation. In contrast to classic PARAFAC where each entry of the coefficient tensor is the sum of products of row-specific contributions across the tensor modes, the soft tensor regression (Softer) framework allows the row-specific contributions to vary around an overall mean. We follow a Bayesian approach to inference, and show that softening the PARAFAC increases model flexibility, leads to improved estimation of coefficient tensors, more accurate identification of important predictor entries, and more precise predictions, even for a low approximation rank. From a theoretical perspective, we show that employing Softer leads to a weakly consistent posterior distribution of the coefficient tensor, irrespective of the true or approximation tensor rank, a result that is not true when employing the classic PARAFAC for tensor regression. In the context of our motivating application, we adapt Softer to symmetric and semi-symmetric tensor predictors and analyze the relationship between brain network characteristics and human traits.

A causal exposure response function with local adjustment for confounding: Estimating health effects of exposure to low levels of ambient fine particulate matter.

In the last two decades, ambient levels of air pollution have declined substantially. At the same time, the Clean Air Act mandates that the National Ambient Air Quality Standards (NAAQS) must be routinely assessed to protect populations based on the latest science. Therefore, researchers should continue to address the following question: is exposure to levels of air pollution below the NAAQS harmful to human health? Furthermore, the contentious nature surrounding environmental regulations urges us to cast this question within a causal inference framework. Several parametric and semi-parametric regression approaches have been used to estimate the exposure-response (ER) curve between long-term exposure to ambient air pollution concentrations and health outcomes. However, most of the existing approaches are not formulated within a formal framework for causal inference, adjust for the same set of potential confounders across all levels of exposure, and do not account for model uncertainty regarding covariate selection and the shape of the ER. In this paper, we introduce a Bayesian framework for the estimation of a causal ER curve called LERCA (Local Exposure Response Confounding Adjustment), which a) allows for different confounders and different strength of confounding at the different exposure levels; and b) propagates model uncertainty regarding confounders' selection and the shape of the ER. Importantly, LERCA provides a principled way of assessing the observed covariates' confounding importance at different exposure levels, providing researchers with important information regarding the set of variables to measure and adjust for in regression models. Using simulation studies, we show that state of the art approaches perform poorly in estimating the ER curve in the presence of local confounding. LERCA is used to evaluate the relationship between long-term exposure to ambient PM2.5, a key regulated pollutant, and cardiovascular hospitalizations for 5,362 zip codes in the continental U.S. and located near a pollution monitoring site, while adjusting for a potentially varying set of confounders across the exposure range. Our data set includes rich health, weather, demographic, and pollution information for the years of 2011-2013. The estimated exposure-response curve is increasing indicating that higher ambient concentrations lead to higher cardiovascular hospitalization rates, and ambient PM2.5 was estimated to lead to an increase in cardiovascular hospitalization rates when focusing at the low exposure range. Our results indicate that there is no threshold for the effect of PM2.5 on cardiovascular hospitalizations.

Analysis of Neuroretinal Rim by Age, Race, and Sex Using High-Density 3-Dimensional Spectral-Domain Optical Coherence Tomography.

PRéCIS:: Neuroretinal rim minimum distance band (MDB) thickness is significantly lower in older subjects and African Americans compared with whites. It is similar in both sexes. PURPOSE: To evaluate the relationship between age, race, and sex with the neuroretinal rim using high-density spectral-domain optical coherence tomography optic nerve volume scans of normal eyes. METHODS: A total of 256 normal subjects underwent Spectralis spectral-domain optical coherence tomography optic nerve head volume scans. One eye was randomly selected and analyzed for each subject. Using custom-designed software, the neuroretinal rim MDB thickness was calculated from volume scans, and global and quadrant neuroretinal rim thickness values were determined. The MDB is a 3-dimensional neuroretinal rim band comprised of the shortest distance between the internal limiting membrane and the termination of the retinal pigment epithelium/Bruch's membrane complex. Multiple linear regression analysis was performed to determine the associations of age, race, and sex with neuroretinal rim MDB measurements. RESULTS: The population was 57% female and 69% white with a mean age of 58.4±15.3 years. The mean MDB thickness in the normal population was 278.4±47.5 µm. For this normal population, MDB thickness decreased by 0.84 µm annually (P<0.001). African Americans had thinner MDBs compared with whites (P=0.003). Males and females had similar MDB thickness values (P=0.349). CONCLUSION: Neuroretinal rim MDB thickness measurements decreased significantly with age. African Americans had thinner MDB neuroretinal rims than whites.

Diagnostic Capability of 3D Peripapillary Retinal Volume for Glaucoma Using Optical Coherence Tomography Customized Software.

PRéCIS:: The diagnostic capability of peripapillary retinal volume is similar to peripapillary retinal nerve fiber layer thickness for diagnosing glaucoma, but with fewer artifacts. PURPOSE: To compare the diagnostic capability of 3-dimensional peripapillary retinal volume (RV) versus 2-dimensional peripapillary retinal nerve fiber layer (RNFL) thickness for open-angle glaucoma. PATIENTS AND METHODS: A retrospective cross-sectional analysis was conducted. A total of 180 subjects (113 open-angle glaucoma, 67 normal participants) had spectral domain optical coherence tomography volume scans and RNFL thickness measurements. Peripapillary RV values were calculated using a custom-designed program with 4 circumpapillary annuli (CA): CA1 had circle diameters of 2.5 and 3.5 mm; CA2, 3 and 4 mm; CA3, 3.5 and 4.5 mm; and CA4, 4 and 5 mm. Area under the receiver operating characteristic curves were calculated for global, quadrant, and octant regions for RV (CA1 to CA4) and RNFL thickness. Pair-wise comparisons were conducted. Artifacts rates were determined. RESULTS: Mean age was 62.7±15.4 years, and 47.8% (86/180) were male. Among RV measurements, best diagnostic performances were for the smallest 2 annuli for inferior RV (CA1: 0.964, CA2: 0.955). Of the 4 annuli, CA1 had the highest diagnostic performance. Of specific regions, the inferior RV quadrant had the highest performance across CA1 to CA4. Peripapillary RV had similar diagnostic capability compared with RNFL thickness (P>0.05). The artifact rate per B-scan for RV was 6.0%, which was significantly lower compared with 2-dimensional RNFL thickness in the same patient population (32.2%, P<0.0001). CONCLUSIONS: The diagnostic capability of RV is similar to RNFL thickness for perimetric open-angle glaucoma, but RV had fewer artifacts compared with RNFL thickness.

Low Levels of Air Pollution and Health: Effect Estimates, Methodological Challenges, and Future Directions.

PURPOSE OF REVIEW: Fine particle (PM2.5) levels have been decreasing in the USA over the past decades. Our goal was to assess the current literature to characterize the association between PM2.5 and adverse health at low exposure levels. RECENT FINDINGS: We reviewed 26 papers that examined the association between short- and long-term exposure to PM2.5 and cardio-respiratory morbidity and mortality. There is evidence suggesting that these associations are stronger at lower levels. However, there are certain methodological and interpretational limitations specific to studies of low PM2.5 levels, and further methodological development is warranted. There is strong agreement across studies that air pollution effects on adverse health are still observable at low concentrations, even well below current US standards. These findings suggest that US standards need to be reevaluated, given that further improving air quality has the potential of benefiting public health.

Causal inference with interfering units for cluster and population level treatment allocation programs.

Interference arises when an individual's potential outcome depends on the individual treatment level, but also on the treatment level of others. A common assumption in the causal inference literature in the presence of interference is partial interference, implying that the population can be partitioned in clusters of individuals whose potential outcomes only depend on the treatment of units within the same cluster. Previous literature has defined average potential outcomes under counterfactual scenarios where treatments are randomly allocated to units within a cluster. However, within clusters there may be units that are more or less likely to receive treatment based on covariates or neighbors' treatment. We define new estimands that describe average potential outcomes for realistic counterfactual treatment allocation programs, extending existing estimands to take into consideration the units' covariates and dependence between units' treatment assignment. We further propose entirely new estimands for population-level interventions over the collection of clusters, which correspond in the motivating setting to regulations at the federal (vs. cluster or regional) level. We discuss these estimands, propose unbiased estimators and derive asymptotic results as the number of clusters grows. For a small number of observed clusters, a bootstrap approach for confidence intervals is proposed. Finally, we estimate effects in a comparative effectiveness study of power plant emission reduction technologies on ambient ozone pollution.

Adjusting for unmeasured spatial confounding with distance adjusted propensity score matching.

Propensity score matching is a common tool for adjusting for observed confounding in observational studies, but is known to have limitations in the presence of unmeasured confounding. In many settings, researchers are confronted with spatially-indexed data where the relative locations of the observational units may serve as a useful proxy for unmeasured confounding that varies according to a spatial pattern. We develop a new method, termed distance adjusted propensity score matching (DAPSm) that incorporates information on units' spatial proximity into a propensity score matching procedure. We show that DAPSm can adjust for both observed and some forms of unobserved confounding and evaluate its performance relative to several other reasonable alternatives for incorporating spatial information into propensity score adjustment. The method is motivated by and applied to a comparative effectiveness investigation of power plant emission reduction technologies designed to reduce population exposure to ambient ozone pollution. Ultimately, DAPSm provides a framework for augmenting a "standard" propensity score analysis with information on spatial proximity and provides a transparent and principled way to assess the relative trade-offs of prioritizing observed confounding adjustment versus spatial proximity adjustment.

Effects of Age, Race, and Ethnicity on the Optic Nerve and Peripapillary Region Using Spectral-Domain OCT 3D Volume Scans.

PURPOSE: To evaluate the effects of age, race, and ethnicity on the optic nerve and peripapillary retina using spectral-domain optical coherence tomography (SD-OCT) three-dimensional (3D) volume scans in normal subjects. METHODS: This is a cross-sectional study performed at a single institution in Boston. All patients received retinal nerve fiber layer (RNFL) scans and an optic nerve 3D volume scan. The SD-OCT software calculated peripapillary RNFL thickness, retinal thickness (RT), and retinal volume (RV). Custom-designed software calculated neuroretinal rim minimum distance band (MDB) thickness and area. RESULTS: There were 272 normal subjects, including 175 whites, 40 blacks, 40 Asians, and 17 Hispanics. Rates of age-related decline were 2.3%, 2.0%, 1.7%, 3.3%, and 4.3% per decade for RNFL, RT, RV, MDB neuroretinal rim thickness, and MDB area, respectively. The RNFL was most affected by racial and ethnic variations, with Asians having thicker global, superior, and inferior RNFL, Hispanics having thicker inferior RNFL, and blacks having thinner temporal RNFL, compared to whites. For MDB thickness and area, Asians had smaller nasal values and blacks had smaller temporal values. Peripapillary RT and RV parameters were not influenced by race and ethnicity. CONCLUSIONS: All of the parameters exhibited age-related declines. RNFL, MDB thickness, and MDB area demonstrated racial and ethnic variations, while peripapillary RT and RV did not. TRANSLATIONAL RELEVANCE: This study demonstrates that both normal aging and ethnicity affect several novel 3D OCT parameters used to diagnose and monitor glaucoma (i.e., RT, RV, and MDB), and this should be factored in when making clinical decisions based on these parameters.

Diagnostic Capability of Three-Dimensional Macular Parameters for Glaucoma Using Optical Coherence Tomography Volume Scans.

Purpose: To compare the diagnostic capability of three-dimensional (3D) macular parameters against traditional two-dimensional (2D) retinal nerve fiber layer (RNFL) thickness using spectral domain optical coherence tomography. To determine if manual correction and interpolation of B-scans improve the ability of 3D macular parameters to diagnose glaucoma. Methods: A total of 101 open angle glaucoma patients (29 with early glaucoma) and 57 healthy subjects had peripapillary 2D RNFL thickness and 3D macular volume scans. Four parameters were calculated for six different-sized annuli: total macular thickness (M-thickness), total macular volume (M-volume), ganglion cell complex (GCC) thickness, and GCC volume of the innermost 3 macular layers (retinal nerve fiber layer + ganglion cell layer + inner plexiform layer). All macular parameters were calculated with and without correction and interpolation of frames with artifacts. The areas under the receiver operating characteristic curves (AUROC) were calculated for all the parameters. Results: The 3D macular parameter with the best diagnostic performance was GCC-volume-34, with an inner diameter of 3 mm and an outer of 4 mm. The AUROC for RNFL thickness and GCC-volume-34 were statistically similar for all regions (global: RNFL thickness 0.956, GCC-volume-34 0.939, P value = 0.3827), except for the temporal GCC-volume-34, which was significantly better than temporal RNFL thickness (P value = 0.0067). Correction of artifacts did not significantly change the AUROC of macular parameters (P values between 0.8452 and 1.0000). Conclusions: The diagnostic performance of best macular parameters (GCC-volume-34 and GCC-thickness-34) were similar to or better than 2D RNFL thickness. Manual correction of artifacts with data interpolation is unnecessary in the clinical setting.

Diagnostic Capability of Peripapillary Three-dimensional Retinal Nerve Fiber Layer Volume for Glaucoma Using Optical Coherence Tomography Volume Scans.

PURPOSE: To determine the diagnostic capability of peripapillary 3-dimensional (3D) retinal nerve fiber layer (RNFL) volume measurements from spectral-domain optical coherence tomography (OCT) volume scans for open-angle glaucoma (OAG). DESIGN: Assessment of diagnostic accuracy. METHODS: Setting: Academic clinical setting. STUDY POPULATION: Total of 180 patients (113 OAG and 67 normal subjects). OBSERVATION PROCEDURES: One eye per subject was included. Peripapillary 3D RNFL volumes were calculated for global, quadrant, and sector regions, using 4 different-size annuli. Peripapillary 2D RNFL thickness circle scans were also obtained. MAIN OUTCOME MEASURES: Area under the receiver operating characteristic curve (AUROC) values, sensitivity, specificity, positive and negative predictive values, positive and negative likelihood ratios. RESULTS: Among all 2D and 3D RNFL parameters, best diagnostic capability was associated with inferior quadrant 3D RNFL volume of the smallest annulus (AUROC value 0.977). Otherwise, global 3D RNFL volume AUROC values were comparable to global 2D RNFL thickness AUROC values for all 4 annulus sizes (P values: .0593 to .6866). When comparing the 4 annulus sizes for global RNFL volume, the smallest annulus had the best AUROC values (P values: .0317 to .0380). The smallest-size annulus may have the best diagnostic potential, partly owing to having no areas excluded for being larger than the 6 × 6 mm2 scanned region. CONCLUSION: Peripapillary 3D RNFL volume showed excellent diagnostic performance for detecting glaucoma. Peripapillary 3D RNFL volume parameters have the same or better diagnostic capability compared to peripapillary 2D RNFL thickness measurements, although differences were not statistically significant.