Sensitivity analysis for principal ignorability violation in estimating complier and noncomplier average causal effects.

An important strategy for identifying principal causal effects (popular estimands in settings with noncompliance) is to invoke the principal ignorability (PI) assumption. As PI is untestable, it is important to gauge how sensitive effect estimates are to its violation. We focus on this task for the common one-sided noncompliance setting where there are two principal strata, compliers and noncompliers. Under PI, compliers and noncompliers share the same outcome-mean-given-covariates function under the control condition. For sensitivity analysis, we allow this function to differ between compliers and noncompliers in several ways, indexed by an odds ratio, a generalized odds ratio, a mean ratio, or a standardized mean difference sensitivity parameter. We tailor sensitivity analysis techniques (with any sensitivity parameter choice) to several types of PI-based main analysis methods, including outcome regression, influence function (IF) based and weighting methods. We discuss range selection for the sensitivity parameter. We illustrate the sensitivity analyses with several outcome types from the JOBS II study. This application estimates nuisance functions parametrically - for simplicity and accessibility. In addition, we establish rate conditions on nonparametric nuisance estimation for IF-based estimators to be asymptotically normal - with a view to inform nonparametric inference.

Finding influential subjects in a network using a causal framework.

Researchers across a wide array of disciplines are interested in finding the most influential subjects in a network. In a network setting, intervention effects and health outcomes can spill over from one node to another through network ties, and influential subjects are expected to have a greater impact than others. For this reason, network research in public health has attempted to maximize health and behavioral changes by intervening on a subset of influential subjects. Although influence is often defined only implicitly in most of the literature, the operative notion of influence is inherently causal in many cases: influential subjects are those we should intervene on to achieve the greatest overall effect across the entire network. In this work, we define a causal notion of influence using potential outcomes. We review existing influence measures, such as node centrality, that largely rely on the particular features of the network structure and/or on certain diffusion models that predict the pattern of information or diseases spreads through network ties. We provide simulation studies to demonstrate when popular centrality measures can agree with our causal measure of influence. As an illustrative example, we apply several popular centrality measures to the HIV risk network in the Transmission Reduction Intervention Project and demonstrate the assumptions under which each centrality can represent the causal influence of each participant in the study.

The Pregnancy, Arsenic, and Immune Response (PAIR) Study in rural northern Bangladesh.

BACKGROUND: Arsenic exposure and micronutrient deficiencies may alter immune reactivity to influenza vaccination in pregnant women, transplacental transfer of maternal antibodies to the foetus, and maternal and infant acute morbidity. OBJECTIVES: The Pregnancy, Arsenic, and Immune Response (PAIR) Study was designed to assess whether arsenic exposure and micronutrient deficiencies alter maternal and newborn immunity and acute morbidity following maternal seasonal influenza vaccination during pregnancy. POPULATION: The PAIR Study recruited pregnant women across a large rural study area in Gaibandha District, northern Bangladesh, 2018-2019. DESIGN: Prospective, longitudinal pregnancy and birth cohort. METHODS: We conducted home visits to enrol pregnant women in the late first or early second trimester (11-17 weeks of gestational age). Women received a quadrivalent seasonal inactivated influenza vaccine at enrolment. Follow-up included up to 13 visits between enrolment and 3 months postpartum. Arsenic was measured in drinking water and maternal urine. Micronutrient deficiencies were assessed using plasma biomarkers. Vaccine-specific antibody titres were measured in maternal and infant serum. Weekly telephone surveillance ascertained acute morbidity symptoms in women and infants. PRELIMINARY RESULTS: We enrolled 784 pregnant women between October 2018 and March 2019. Of 784 women who enrolled, 736 (93.9%) delivered live births and 551 (70.3%) completed follow-up visits to 3 months postpartum. Arsenic was detected (≥0.02 µg/L) in 99.7% of water specimens collected from participants at enrolment. The medians (interquartile ranges) of water and urinary arsenic at enrolment were 5.1 (0.5, 25.1) µg/L and 33.1 (19.6, 56.5) µg/L, respectively. Water and urinary arsenic were strongly correlated (Spearman's ⍴ = 0.72) among women with water arsenic ≥ median but weakly correlated (⍴ = 0.17) among women with water arsenic < median. CONCLUSIONS: The PAIR Study is well positioned to examine the effects of low-moderate arsenic exposure and micronutrient deficiencies on immune outcomes in women and infants. REGISTRATION: NCT03930017.

Long-Term Fine Particulate Matter Concentrations and Prevalence of Severe Acute Respiratory Syndrome Coronavirus 2: Differential Relationships by Socioeconomic Status Among Pregnant Individuals in New York City.

We aimed to determine whether long-term ambient concentrations of fine particulate matter (particulate matter with an aerodynamic diameter less than or equal to 2.5 µm (PM2.5)) were associated with increased risk of testing positive for coronavirus disease 2019 (COVID-19) among pregnant individuals who were universally screened at delivery and whether socioeconomic status (SES) modified this relationship. We used obstetrical data collected from New-York Presbyterian Hospital/Columbia University Irving Medical Center in New York, New York, between March and December 2020, including data on Medicaid use (a proxy for low SES) and COVID-19 test results. We linked estimated 2018-2019 PM2.5 concentrations (300-m resolution) with census-tract-level population density, household size, income, and mobility (as measured by mobile-device use) on the basis of residential address. Analyses included 3,318 individuals; 5% tested positive for COVID-19 at delivery, 8% tested positive during pregnancy, and 48% used Medicaid. Average long-term PM2.5 concentrations were 7.4 (standard deviation, 0.8) µg/m3. In adjusted multilevel logistic regression models, we saw no association between PM2.5 and ever testing positive for COVID-19; however, odds were elevated among those using Medicaid (per 1-µg/m3 increase, odds ratio = 1.6, 95% confidence interval: 1.0, 2.5). Further, while only 22% of those testing positive showed symptoms, 69% of symptomatic individuals used Medicaid. SES, including unmeasured occupational exposures or increased susceptibility to severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) due to concurrent social and environmental exposures, may explain the increased odds of testing positive for COVID-19 being confined to vulnerable pregnant individuals using Medicaid.

A Warning About Using Predicted Values From Regression Models for Epidemiologic Inquiry.

In many settings, researchers may not have direct access to data on 1 or more variables needed for an analysis and instead may use regression-based estimates of those variables. Using such estimates in place of original data, however, introduces complications and can result in uninterpretable analyses. In simulations and observational data, we illustrate the issues that arise when an average treatment effect is estimated from data where the outcome of interest is predicted from an auxiliary model. We show that bias in any direction can result, under both the null and alternative hypotheses.

High-dimensional multivariate mediation with application to neuroimaging data.

Mediation analysis is an important tool in the behavioral sciences for investigating the role of intermediate variables that lie in the path between a treatment and an outcome variable. The influence of the intermediate variable on the outcome is often explored using a linear structural equation model (LSEM), with model coefficients interpreted as possible effects. While there has been significant research on the topic, little work has been done when the intermediate variable (mediator) is a high-dimensional vector. In this work, we introduce a novel method for identifying potential mediators in this setting called the directions of mediation (DMs). DMs linearly combine potential mediators into a smaller number of orthogonal components, with components ranked based on the proportion of the LSEM likelihood each accounts for. This method is well suited for cases when many potential mediators are measured. Examples of high-dimensional potential mediators are brain images composed of hundreds of thousands of voxels, genetic variation measured at millions of single nucleotide polymorphisms (SNPs), or vectors of thousands of variables in large-scale epidemiological studies. We demonstrate the method using a functional magnetic resonance imaging study of thermal pain where we are interested in determining which brain locations mediate the relationship between the application of a thermal stimulus and self-reported pain.

Analysis of covariance in randomized trials: More precision and valid confidence intervals, without model assumptions.

"Covariate adjustment" in the randomized trial context refers to an estimator of the average treatment effect that adjusts for chance imbalances between study arms in baseline variables (called "covariates"). The baseline variables could include, for example, age, sex, disease severity, and biomarkers. According to two surveys of clinical trial reports, there is confusion about the statistical properties of covariate adjustment. We focus on the analysis of covariance (ANCOVA) estimator, which involves fitting a linear model for the outcome given the treatment arm and baseline variables, and trials that use simple randomization with equal probability of assignment to treatment and control. We prove the following new (to the best of our knowledge) robustness property of ANCOVA to arbitrary model misspecification: Not only is the ANCOVA point estimate consistent (as proved by Yang and Tsiatis, 2001) but so is its standard error. This implies that confidence intervals and hypothesis tests conducted as if the linear model were correct are still asymptotically valid even when the linear model is arbitrarily misspecified, for example, when the baseline variables are nonlinearly related to the outcome or there is treatment effect heterogeneity. We also give a simple, robust formula for the variance reduction (equivalently, sample size reduction) from using ANCOVA. By reanalyzing completed randomized trials for mild cognitive impairment, schizophrenia, and depression, we demonstrate how ANCOVA can achieve variance reductions of 4 to 32%.

Retirements of Coal and Oil Power Plants in California: Association With Reduced Preterm Birth Among Populations Nearby.

Coal and oil power plant retirements reduce air pollution nearby, but few studies have leveraged these natural experiments for public health research. We used California Department of Public Health birth records and US Energy Information Administration data from 2001-2011 to evaluate the relationship between the retirements of 8 coal and oil power plants and nearby preterm (gestational age of <37 weeks) birth. We conducted a difference-in-differences analysis using adjusted linear mixed models that included 57,005 births-6.3% of which were preterm-to compare the probability of preterm birth before and after power plant retirement among mothers residing within 0-5 km and 5-10 km of the 8 power plants. We found that power plant retirements were associated with a decrease in the proportion of preterm birth within 5 km (-0.019, 95% CI: -0.031, -0.008) and 5-10 km (-0.015, 95% CI: -0.024, -0.007), controlling for secular trends with mothers living 10-20 km away. For the 0-5-km area, this corresponds to a reduction in preterm birth from 7.0% to 5.1%. Subgroup analyses indicated a potentially larger association among non-Hispanic black and Asian mothers than among non-Hispanic white and Hispanic mothers and no differences in educational attainment. Future coal and oil power plant retirements may reduce preterm birth among nearby populations.

Increase in fertility following coal and oil power plant retirements in California.

BACKGROUND: Few studies have explored the relationship between air pollution and fertility. We used a natural experiment in California when coal and oil power plants retired to estimate associations with nearby fertility rates. METHODS: We used a difference-in-differences negative binomial model on the incident rate ratio scale to analyze the change in annual fertility rates among California mothers living within 0-5 km and 5-10 km of 8 retired power plants between 2001 and 2011. The difference-in-differences method isolates the portion of the pre- versus post-retirement contrast in the 0-5 km and 5-10 km bins, respectively, that is due to retirement rather than secular trends. We controlled for secular trends with mothers living 10-20 km away. Adjusted models included fixed effects for power plant, proportion Hispanic, Black, high school educated, and aged > 30 years mothers, and neighborhood poverty and educational attainment. RESULTS: Analyses included 58,909 live births. In adjusted models, we estimated that after power plant retirement annual fertility rates per 1000 women aged 15-44 years increased by 8 births within 5 km and 2 births within 5-10 km of power plants, corresponding to incident rate ratios of 1.2 (95% CI: 1.1-1.4) and 1.1 (95% CI: 1.0-1.2), respectively. We implemented a negative exposure control by randomly selecting power plants that did not retire and repeating our analysis with those locations using the retirement dates from original 8 power plants. There was no association, suggesting that statewide temporal trends may not account for results. CONCLUSIONS: Fertility rates among nearby populations appeared to increase after coal and oil power plant retirements. Our study design limited the possibility that our findings resulted from temporal trends or changes in population composition. These results require confirmation in other populations, given known methodological limitations of ecologic study designs.

Measuring personal beliefs and perceived norms about intimate partner violence: Population-based survey experiment in rural Uganda.

BACKGROUND: Demographic and Health Surveys (DHS) conducted throughout sub-Saharan Africa indicate there is widespread acceptance of intimate partner violence, contributing to an adverse health risk environment for women. While qualitative studies suggest important limitations in the accuracy of the DHS methods used to elicit attitudes toward intimate partner violence, to date there has been little experimental evidence from sub-Saharan Africa that can be brought to bear on this issue. METHODS AND FINDINGS: We embedded a randomized survey experiment in a population-based survey of 1,334 adult men and women living in Nyakabare Parish, Mbarara, Uganda. The primary outcomes were participants' personal beliefs about the acceptability of intimate partner violence and perceived norms about intimate partner violence in the community. To elicit participants' personal beliefs and perceived norms, we asked about the acceptability of intimate partner violence in five different vignettes. Study participants were randomly assigned to one of three survey instruments, each of which contained varying levels of detail about the extent to which the wife depicted in the vignette intentionally or unintentionally violated gendered standards of behavior. For the questions about personal beliefs, the mean (standard deviation) number of items where intimate partner violence was endorsed as acceptable was 1.26 (1.58) among participants assigned to the DHS-style survey variant (which contained little contextual detail about the wife's intentions), 2.74 (1.81) among participants assigned to the survey variant depicting the wife as intentionally violating gendered standards of behavior, and 0.77 (1.19) among participants assigned to the survey variant depicting the wife as unintentionally violating these standards. In a partial proportional odds regression model adjusting for sex and village of residence, with participants assigned to the DHS-style survey variant as the referent group, participants assigned the survey variant that depicted the wife as intentionally violating gendered standards of behavior were more likely to condone intimate partner violence in a greater number of vignettes (adjusted odds ratios [AORs] ranged from 3.87 to 5.74, with all p < 0.001), while participants assigned the survey variant that depicted the wife as unintentionally violating these standards were less likely to condone intimate partner violence (AORs ranged from 0.29 to 0.70, with p-values ranging from <0.001 to 0.07). The analysis of perceived norms displayed similar patterns, but the effects were slightly smaller in magnitude: participants assigned to the "intentional" survey variant were more likely to perceive intimate partner violence as normative (AORs ranged from 2.05 to 3.51, with all p < 0.001), while participants assigned to the "unintentional" survey variant were less likely to perceive intimate partner violence as normative (AORs ranged from 0.49 to 0.65, with p-values ranging from <0.001 to 0.14). The primary limitations of this study are that our assessments of personal beliefs and perceived norms could have been measured with error and that our findings may not generalize beyond rural Uganda. CONCLUSIONS: Contextual information about the circumstances under which women in hypothetical vignettes were perceived to violate gendered standards of behavior had a significant influence on the extent to which study participants endorsed the acceptability of intimate partner violence. Researchers aiming to assess personal beliefs or perceived norms about intimate partner violence should attempt to eliminate, as much as possible, ambiguities in vignettes and questions administered to study participants. TRIAL REGISTRATION: ClinicalTrials.gov NCT02202824.

Statistical Reasoning and Methods in Epidemiology to Promote Individualized Health: In Celebration of the 100th Anniversary of the Johns Hopkins Bloomberg School of Public Health.

Epidemiology is concerned with determining the distribution and causes of disease. Throughout its history, epidemiology has drawn upon statistical ideas and methods to achieve its aims. Because of the exponential growth in our capacity to measure and analyze data on the underlying processes that define each person's state of health, there is an emerging opportunity for population-based epidemiologic studies to influence health decisions made by individuals in ways that take into account the individuals' characteristics, circumstances, and preferences. We refer to this endeavor as "individualized health." The present article comprises 2 sections. In the first, we describe how graphical, longitudinal, and hierarchical models can inform the project of individualized health. We propose a simple graphical model for informing individual health decisions using population-based data. In the second, we review selected topics in causal inference that we believe to be particularly useful for individualized health. Epidemiology and biostatistics were 2 of the 4 founding departments in the world's first graduate school of public health at Johns Hopkins University, the centennial of which we honor. This survey of a small part of the literature is intended to demonstrate that the 2 fields remain just as inextricably linked today as they were 100 years ago.

Unconventional Natural Gas Development and Birth Outcomes in Pennsylvania, USA.

BACKGROUND: Unconventional natural gas development has expanded rapidly. In Pennsylvania, the number of producing wells increased from 0 in 2005 to 3,689 in 2013. Few publications have focused on unconventional natural gas development and birth outcomes. METHODS: We performed a retrospective cohort study using electronic health record data on 9,384 mothers linked to 10,946 neonates in the Geisinger Health System from January 2009 to January 2013. We estimated cumulative exposure to unconventional natural gas development activity with an inverse-distance squared model that incorporated distance to the mother's home; dates and durations of well pad development, drilling, and hydraulic fracturing; and production volume during the pregnancy. We used multilevel linear and logistic regression models to examine associations between activity index quartile and term birth weight, preterm birth, low 5-minute Apgar score and small size for gestational age birth, while controlling for potential confounding variables. RESULTS: In adjusted models, there was an association between unconventional natural gas development activity and preterm birth that increased across quartiles, with a fourth quartile odds ratio of 1.4 (95% confidence interval = 1.0, 1.9). There were no associations of activity with Apgar score, small for gestational age birth, or term birth weight (after adjustment for year). In a posthoc analysis, there was an association with physician-recorded high-risk pregnancy identified from the problem list (fourth vs. first quartile, 1.3 [95% confidence interval = 1.1, 1.7]). CONCLUSION: Prenatal residential exposure to unconventional natural gas development activity was associated with two pregnancy outcomes, adding to evidence that unconventional natural gas development may impact health.See Video Abstract at http://links.lww.com/EDE/B14.

Marital satisfaction and break-ups differ across on-line and off-line meeting venues.

Marital discord is costly to children, families, and communities. The advent of the Internet, social networking, and on-line dating has affected how people meet future spouses, but little is known about the prevalence or outcomes of these marriages or the demographics of those involved. We addressed these questions in a nationally representative sample of 19,131 respondents who married between 2005 and 2012. Results indicate that more than one-third of marriages in America now begin on-line. In addition, marriages that began on-line, when compared with those that began through traditional off-line venues, were slightly less likely to result in a marital break-up (separation or divorce) and were associated with slightly higher marital satisfaction among those respondents who remained married. Demographic differences were identified between respondents who met their spouse through on-line vs. traditional off-line venues, but the findings for marital break-up and marital satisfaction remained significant after statistically controlling for these differences. These data suggest that the Internet may be altering the dynamics and outcomes of marriage itself.

Demonstrating stratification in a European American population.

Population stratification occurs in case-control association studies when allele frequencies differ between cases and controls because of ancestry. Stratification may lead to false positive associations, although this issue remains controversial. Empirical studies have found little evidence of stratification in European-derived populations, but potentially significant levels of stratification could not be ruled out. We studied a European American panel discordant for height, a heritable trait that varies widely across Europe. Genotyping 178 SNPs and applying standard analytical methods yielded no evidence of stratification. But a SNP in the gene LCT that varies widely in frequency across Europe was strongly associated with height (P < 10(-6)). This apparent association was largely or completely due to stratification; rematching individuals on the basis of European ancestry greatly reduced the apparent association, and no association was observed in Polish or Scandinavian individuals. The failure of standard methods to detect this stratification indicates that new methods may be required.

Causal Inference for Social Network Data.

We describe semiparametric estimation and inference for causal effects using observational data from a single social network. Our asymptotic results are the first to allow for dependence of each observation on a growing number of other units as sample size increases. In addition, while previous methods have implicitly permitted only one of two possible sources of dependence among social network observations, we allow for both dependence due to transmission of information across network ties and for dependence due to latent similarities among nodes sharing ties. We propose new causal effects that are specifically of interest in social network settings, such as interventions on network ties and network structure. We use our methods to reanalyze an influential and controversial study that estimated causal peer effects of obesity using social network data from the Framingham Heart Study; after accounting for network structure we find no evidence for causal peer effects.

Causal mediation analysis: From simple to more robust strategies for estimation of marginal natural (in)direct effects.

This paper aims to provide practitioners of causal mediation analysis with a better understanding of estimation options. We take as inputs two familiar strategies (weighting and model-based prediction) and a simple way of combining them (weighted models), and show how a range of estimators can be generated, with different modeling requirements and robustness properties. The primary goal is to help build intuitive appreciation for robust estimation that is conducive to sound practice. We do this by visualizing the target estimand and the estimation strategies. A second goal is to provide a "menu" of estimators that practitioners can choose from for the estimation of marginal natural (in)direct effects. The estimators generated from this exercise include some that coincide or are similar to existing estimators and others that have not previously appeared in the literature. We note several different ways to estimate the weights for cross-world weighting based on three expressions of the weighting function, including one that is novel; and show how to check the resulting covariate and mediator balance. We use a random continuous weights bootstrap to obtain confidence intervals, and also derive general asymptotic variance formulas for the estimators. The estimators are illustrated using data from an adolescent alcohol use prevention study. R-code is provided.

Analytic results on the bias due to nondifferential misclassification of a binary mediator.

Consider a study in which the effect of a binary exposure on an outcome operates partly through a binary mediator but measurement of the mediator is nondifferentially misclassified. Suppose that an investigator wishes to estimate the direct and indirect effects of the exposure on the outcome. In this paper, the authors describe a mathematical correspondence between the empirical expressions for the natural direct effect and the effect of exposure among the unexposed standardized by a binary confounder. They then exploit this correspondence to prove that the direction of the bias due to nondifferential measurement error in estimating the natural direct and indirect effects is to overestimate the natural direct effect and underestimate the natural indirect effect.