Prediction sets adaptive to unknown covariate shift

Predicting sets of outcomes-instead of unique outcomes-is a promising solution to uncertainty quantification in statistical learning. Despite a rich literature on constructing prediction sets with statistical guarantees, adapting to unknown covariate shift-a prevalent issue in practice-poses a serious unsolved challenge. In this article, we show that prediction sets with finite-sample coverage guarantee are uninformative and propose a novel flexible distribution-free method, PredSet-1Step, to efficiently construct prediction sets with an asymptotic coverage guarantee under unknown covariate shift. We formally show that our method is asymptotically probably approximately correct, having well-calibrated coverage error with high confidence for large samples. We illustrate that it achieves nominal coverage in a number of experiments and a data set concerning HIV risk prediction in a South African cohort study. Our theory hinges on a new bound for the convergence rate of the coverage of Wald confidence intervals based on general asymptotically linear estimators.

Mendelian randomization mixed-scale treatment effect robust identification and estimation for causal inference

Standard Mendelian randomization (MR) analysis can produce biased results if the genetic variant defining an instrumental variable (IV) is confounded and/or has a horizontal pleiotropic effect on the outcome of interest not mediated by the treatment variable. We provide novel identification conditions for the causal effect of a treatment in the presence of unmeasured confounding by leveraging a possibly invalid IV for which both the IV independence and exclusion restriction assumptions may be violated. The proposed Mendelian randomization mixed-scale treatment effect robust identification (MR MiSTERI) approach relies on (i) an assumption that the treatment effect does not vary with the possibly invalid IV on the additive scale; (ii) that the confounding bias does not vary with the possibly invalid IV on the odds ratio scale; and (iii) that the residual variance for the outcome is heteroskedastic with respect to the possibly invalid IV. Although assumptions (i) and (ii) have, respectively, appeared in the IV literature, assumption (iii) has not; we formally establish that their conjunction can identify a causal effect even with an invalid IV. MR MiSTERI is shown to be particularly advantageous in the presence of pervasive heterogeneity of pleiotropic effects on the additive scale. We propose a simple and consistent three-stage estimator that can be used as a preliminary estimator to a carefully constructed efficient one-step-update estimator. In order to incorporate multiple, possibly correlated, and weak invalid IVs, a common challenge in MR studies, we develop a MAny Weak Invalid Instruments (MR MaWII MiSTERI) approach for strengthened identification and improved estimation accuracy. Both simulation studies and UK Biobank data analysis results demonstrate the robustness of the proposed methods.

Impact of family networks on uptake of health interventions: evidence from a community-randomized control trial aimed at increasing HIV testing in South Africa

INTRODUCTION

While it is widely acknowledged that family relationships can influence health outcomes, their impact on the uptake of individual health interventions is unclear. In this study, we quantified how the efficacy of a randomized health intervention is shaped by its pattern of distribution in the family network.

METHODS

The "Home-Based Intervention to Test and Start" (HITS) was a 2×2 factorial community-randomized controlled trial in Umkhanyakude, KwaZulu-Natal, South Africa, embedded in the Africa Health Research Institute's population-based demographic and HIV surveillance platform (ClinicalTrials.gov # NCT03757104). The study investigated the impact of two interventions: a financial micro-incentive and a male-targeted HIV-specific decision support programme. The surveillance area was divided into 45 community clusters. Individuals aged ≥15 years in 16 randomly selected communities were offered a micro-incentive (R50 [$3] food voucher) for rapid HIV testing (intervention arm). Those living in the remaining 29 communities were offered testing only (control arm). Study data were collected between February and November 2018. Using routinely collected data on parents, conjugal partners, and co-residents, a socio-centric family network was constructed among HITS-eligible individuals. Nodes in this network represent individuals and ties represent family relationships. We estimated the effect of offering the incentive to people with and without family members who also received the offer on the uptake of HIV testing. We fitted a linear probability model with robust standard errors, accounting for clustering at the community level.

RESULTS

Overall, 15,675 people participated in the HITS trial. Among those with no family members who received the offer, the incentive's efficacy was a 6.5 percentage point increase (95% CI: 5.3-7.7). The efficacy was higher among those with at least one family member who received the offer (21.1 percentage point increase (95% CI: 19.9-22.3). The difference in efficacy was statistically significant (21.1-6.5 = 14.6%; 95% CI: 9.3-19.9).

CONCLUSIONS

Micro-incentives appear to have synergistic effects when distributed within family networks. These effects support family network-based approaches for the design of health interventions.

Non-parametric inference about mean functionals of non-ignorable non-response data without identifying the joint distribution

We consider identification and inference about mean functionals of observed covariates and an outcome variable subject to non-ignorable missingness. By leveraging a shadow variable, we establish a necessary and sufficient condition for identification of the mean functional even if the full data distribution is not identified. We further characterize a necessary condition for n -estimability of the mean functional. This condition naturally strengthens the identifying condition, and it requires the existence of a function as a solution to a representer equation that connects the shadow variable to the mean functional. Solutions to the representer equation may not be unique, which presents substantial challenges for non-parametric estimation, and standard theories for non-parametric sieve estimators are not applicable here. We construct a consistent estimator of the solution set and then adapt the theory of extremum estimators to find from the estimated set a consistent estimator of an appropriately chosen solution. The estimator is asymptotically normal, locally efficient and attains the semi-parametric efficiency bound under certain regularity conditions. We illustrate the proposed approach via simulations and a real data application on home pricing.

Proximal Causal Inference without Uniqueness Assumptions

We consider identification and inference about a counterfactual outcome mean when there is unmeasured confounding using tools from proximal causal inference. Proximal causal inference requires existence of solutions to at least one of two integral equations. We motivate the existence of solutions to the integral equations from proximal causal inference by demonstrating that, assuming the existence of a solution to one of the integral equations, n -estimability of a mean functional of that solution requires the existence of a solution to the other integral equation. Solutions to the integral equations may not be unique, which complicates estimation and inference. We construct a consistent estimator for the solution set for one of the integral equations and then adapt the theory of extremum estimators to find from the estimated set a consistent estimator for a uniquely defined solution. A debiased estimator is shown to be root-n consistent, regular, and semiparametrically locally efficient under additional regularity conditions.

Double Negative Control Inference in Test-Negative Design Studies of Vaccine Effectiveness

The test-negative design (TND) has become a standard approach to evaluate vaccine effectiveness against the risk of acquiring infectious diseases in real-world settings, such as Influenza, Rotavirus, Dengue fever, and more recently COVID-19. In a TND study, individuals who experience symptoms and seek care are recruited and tested for the infectious disease which defines cases and controls. Despite TND's potential to reduce unobserved differences in healthcare seeking behavior (HSB) between vaccinated and unvaccinated subjects, it remains subject to various potential biases. First, residual confounding bias may remain due to unobserved HSB, occupation as healthcare worker, or previous infection history. Second, because selection into the TND sample is a common consequence of infection and HSB, collider stratification bias may exist when conditioning the analysis on testing, which further induces confounding by latent HSB. In this paper, we present a novel approach to identify and estimate vaccine effectiveness in the target population by carefully leveraging a pair of negative control exposure and outcome variables to account for potential hidden bias in TND studies. We illustrate our proposed method with extensive simulation and an application to study COVID-19 vaccine effectiveness using data from the University of Michigan Health System.

On the double-robustness and semiparametric efficiency of matching-adjusted indirect comparisons

Matching-adjusted indirect comparison (MAIC) enables indirect comparisons of interventions across separate studies when individual patient-level data (IPD) are available for only one study. Due to its similarity with propensity score weighting, it has been speculated that MAIC can be combined with outcome regression models in the spirit of augmented inverse probability weighting estimators to improve robustness and efficiency. We show that MAIC enjoys intrinsic double-robustness and semiparametric efficiency properties for estimating the average treatment effect on the treated in the limited IPD setting without explicit augmentation. A connection between MAIC and the method of simulated treatment comparisons is highlighted. These results clarify conditions under which MAIC is consistent and efficient, informing appropriate application and interpretation of MAIC analyses.

Regression-based negative control of homophily in dyadic peer effect analysis

A prominent threat to causal inference about peer effects in social science studies is the presence of homophily bias , that is, social influence between friends and families is entangled with common characteristics or underlying similarities that form close connections. Analysis of social study data has suggested that certain health conditions such as obesity and psychological states including happiness and loneliness can spread between friends and relatives. However, such analyses of peer effects or contagion effects have come under criticism because homophily bias may compromise the causal statement. We develop a regression-based approach which leverages a negative control exposure for identification and estimation of contagion effects on additive or multiplicative scales, in the presence of homophily bias. We apply our methods to evaluate the peer effect of obesity in Framingham Offspring Study.

Deep-sequence phylogenetics to quantify patterns of HIV transmission in the context of a universal testing and treatment trial - BCPP/ Ya Tsie trial

Background: Mathematical models predict that community-wide access to HIV testing-and-treatment can rapidly and substantially reduce new HIV infections. Yet several large universal test-and-treat HIV prevention trials in high-prevalence epidemics demonstrated variable reduction in population-level incidence.

Methods: To elucidate patterns of HIV spread in universal test-and-treat trials we quantified the contribution of geographic-location, gender, age and randomized-HIV-intervention to HIV transmissions in the 30-community Ya Tsie trial in Botswana. We sequenced HIV viral whole genomes from 5,114 trial participants among the 30 trial communities.

Results: Deep-sequence phylogenetic analysis revealed that most inferred HIV transmissions within the trial occurred within the same or between neighboring communities, and between similarly-aged partners. Transmissions into intervention communities from control communities were more common than the reverse post-baseline (30% [12.2 - 56.7] versus 3% [0.1 - 27.3]) than at baseline (7% [1.5 - 25.3] versus 5% [0.9 - 22.9]) compatible with a benefit from treatment-as-prevention.

Conclusion: Our findings suggest that population mobility patterns are fundamental to HIV transmission dynamics and to the impact of HIV control strategies.

Funding: This study was supported by the National Institute of General Medical Sciences (U54GM088558); the Fogarty International Center (FIC) of the U.S. National Institutes of Health (D43 TW009610); and the President's Emergency Plan for AIDS Relief through the Centers for Disease Control and Prevention (CDC) (Cooperative agreements U01 GH000447 and U2G GH001911).

Machine intelligence for individualized decision making under a counterfactual world: A rejoinder

This JASA rejoinder concerns the problem of individualized decision making under point, sign, and partial identification. The paper unifies various classical decision making strategies through a lower bound perspective proposed in Cui and Tchetgen Tchetgen (2020b) in the context of optimal treatment regimes under uncertainty due to unmeasured confounding. Building on this unified framework, the paper also provides a novel minimax solution (i.e., a rule that minimizes the maximum regret for so-called opportunists) for individualized decision making/policy assignment.

A Selective Review of Negative Control Methods in Epidemiology

PURPOSE OF REVIEW

Negative controls are a powerful tool to detect and adjust for bias in epidemiological research. This paper introduces negative controls to a broader audience and provides guidance on principled design and causal analysis based on a formal negative control framework.

RECENT FINDINGS

We review and summarize causal and statistical assumptions, practical strategies, and validation criteria that can be combined with subject-matter knowledge to perform negative control analyses. We also review existing statistical methodologies for the detection, reduction, and correction of confounding bias, and briefly discuss recent advances towards nonparametric identification of causal effects in a double-negative control design.

SUMMARY

There is great potential for valid and accurate causal inference leveraging contemporary healthcare data in which negative controls are routinely available. Design and analysis of observational data leveraging negative controls is an area of growing interest in health and social sciences. Despite these developments, further effort is needed to disseminate these novel methods to ensure they are adopted by practicing epidemiologists.

Efficient estimation of human immunodeficiency virus incidence rate using a pooled cross-sectional cohort study design

Development of methods to accurately estimate human immunodeficiency virus (HIV) incidence rate remains a challenge. Ideally, one would follow a random sample of HIV-negative individuals under a longitudinal study design and identify incident cases as they arise. Such designs can be prohibitively resource intensive and therefore alternative designs may be preferable. We propose such a simple, less resource-intensive study design and develop a weighted log likelihood approach which simultaneously accounts for selection bias and outcome misclassification error. The design is based on a cross-sectional survey which queries individuals' time since last HIV-negative test, validates their test results with formal documentation whenever possible, and tests all persons who do not have documentation of being HIV-positive. To gain efficiency, we update the weighted log likelihood function with potentially misclassified self-reports from individuals who could not produce documentation of a prior HIV-negative test and investigate large sample properties of validated sub-sample only versus pooled sample estimators through extensive Monte Carlo simulations. We illustrate our method by estimating incidence rate for individuals who tested HIV-negative within 1.5 and 5 years prior to Botswana Combination Prevention Project enrolment. This article establishes that accurate estimates of HIV incidence rate can be obtained from individuals' history of testing in a cross-sectional cohort study design by appropriately accounting for selection bias and misclassification error. Moreover, this approach is notably less resource-intensive compared to longitudinal and laboratory-based methods.

A semiparametric instrumental variable approach to optimal treatment regimes under endogeneity

There is a fast-growing literature on estimating optimal treatment regimes based on randomized trials or observational studies under a key identifying condition of no unmeasured confounding. Because confounding by unmeasured factors cannot generally be ruled out with certainty in observational studies or randomized trials subject to noncompliance, we propose a general instrumental variable approach to learning optimal treatment regimes under endogeneity. Specifically, we establish identification of both value function E [ Y D ( L ) ] for a given regime D and optimal regimes arg max D E [ Y D ( L ) ] with the aid of a binary instrumental variable, when no unmeasured confounding fails to hold. We also construct novel multiply robust classification-based estimators. Furthermore, we propose to identify and estimate optimal treatment regimes among those who would comply to the assigned treatment under a monotonicity assumption. In this latter case, we establish the somewhat surprising result that complier optimal regimes can be consistently estimated without directly collecting compliance information and therefore without the complier average treatment effect itself being identified. Our approach is illustrated via extensive simulation studies and a data application on the effect of child rearing on labor participation.

IDENTIFICATION AND INFERENCE FOR MARGINAL AVERAGE TREATMENT EFFECT ON THE TREATED WITH AN INSTRUMENTAL VARIABLE

In observational studies, treatments are typically not randomized and therefore estimated treatment effects may be subject to confounding bias. The instrumental variable (IV) design plays the role of a quasi-experimental handle since the IV is associated with the treatment and only affects the outcome through the treatment. In this paper, we present a novel framework for identification and inference using an IV for the marginal average treatment effect amongst the treated (ETT) in the presence of unmeasured confounding. For inference, we propose three different semiparametric approaches: (i) inverse probability weighting (IPW), (ii) outcome regression (OR), and (iii) doubly robust (DR) estimation, which is consistent if either (i) or (ii) is consistent, but not necessarily both. A closed-form locally semiparametric efficient estimator is obtained in the simple case of binary IV and outcome and the efficiency bound is derived for the more general case.

A causal proportional hazards estimator under homogeneous or heterogeneous selection in an IV setting

In this paper we present a framework to do estimation in a structural Cox model when there may be unobserved confounding. The model is phrased in terms of a selection bias function and a baseline model that describes how covariates affect the survival time in a scenario without exposure. In this way model congeniality is ensured. The method uses an instrumental variable. Interestingly, the formulated model turns out to have similarities to the so-called Cox-Aalen survival model for the observed data. We exploit this to enhance estimation of the unknown parameters. This also allows us to derive large sample properties of the proposed estimator.

Universal Testing, Expanded Treatment, and Incidence of HIV Infection in Botswana

BACKGROUND

The feasibility of reducing the population-level incidence of human immunodeficiency virus (HIV) infection by increasing community coverage of antiretroviral therapy (ART) and male circumcision is unknown.

METHODS

We conducted a pair-matched, community-randomized trial in 30 rural or periurban communities in Botswana from 2013 to 2018. Participants in 15 villages in the intervention group received HIV testing and counseling, linkage to care, ART (started at a higher CD4 count than in standard care), and increased access to male circumcision services. The standard-care group also consisted of 15 villages. Universal ART became available in both groups in mid-2016. We enrolled a random sample of participants from approximately 20% of households in each community and measured the incidence of HIV infection through testing performed approximately once per year. The prespecified primary analysis was a permutation test of HIV incidence ratios. Pair-stratified Cox models were used to calculate 95% confidence intervals.

RESULTS

Of 12,610 enrollees (81% of eligible household members), 29% were HIV-positive. Of the 8974 HIV-negative persons (4487 per group), 95% were retested for HIV infection over a median of 29 months. A total of 57 participants in the intervention group and 90 participants in the standard-care group acquired HIV infection (annualized HIV incidence, 0.59% and 0.92%, respectively). The unadjusted HIV incidence ratio in the intervention group as compared with the standard-care group was 0.69 (P = 0.09) by permutation test (95% confidence interval [CI], 0.46 to 0.90 by pair-stratified Cox model). An end-of-trial survey in six communities (three per group) showed a significantly greater increase in the percentage of HIV-positive participants with an HIV-1 RNA level of 400 copies per milliliter or less in the intervention group (18 percentage points, from 70% to 88%) than in the standard-care group (8 percentage points, from 75% to 83%) (relative risk, 1.12; 95% CI, 1.09 to 1.16). The percentage of men who underwent circumcision increased by 10 percentage points in the intervention group and 2 percentage points in the standard-care group (relative risk, 1.26; 95% CI, 1.17 to 1.35).

CONCLUSIONS

Expanded HIV testing, linkage to care, and ART coverage were associated with increased population viral suppression. (Funded by the President's Emergency Plan for AIDS Relief and others; Ya Tsie ClinicalTrials.gov number, NCT01965470.).

Genetic effects on the commensal microbiota in inflammatory bowel disease patients

Several bacteria in the gut microbiota have been shown to be associated with inflammatory bowel disease (IBD), and dozens of IBD genetic variants have been identified in genome-wide association studies. However, the role of the microbiota in the etiology of IBD in terms of host genetic susceptibility remains unclear. Here, we studied the association between four major genetic variants associated with an increased risk of IBD and bacterial taxa in up to 633 IBD cases. We performed systematic screening for associations, identifying and replicating associations between NOD2 variants and two taxa: the Roseburia genus and the Faecalibacterium prausnitzii species. By exploring the overall association patterns between genes and bacteria, we found that IBD risk alleles were significantly enriched for associations concordant with bacteria-IBD associations. To understand the significance of this pattern in terms of the study design and known effects from the literature, we used counterfactual principles to assess the fitness of a few parsimonious gene-bacteria-IBD causal models. Our analyses showed evidence that the disease risk of these genetic variants were likely to be partially mediated by the microbiome. We confirmed these results in extensive simulation studies and sensitivity analyses using the association between NOD2 and F. prausnitzii as a case study.

Cross-sectional estimates revealed high HIV incidence in Botswana rural communities in the era of successful ART scale-up in 2013-2015

BACKGROUND

Botswana is close to reaching the UNAIDS "90-90-90" HIV testing, antiretroviral treatment (ART), and viral suppression goals. We sought to determine HIV incidence in this setting with both high HIV prevalence and high ART coverage.

METHODS

We used a cross-sectional approach to assessing HIV incidence. A random, population-based sample of adults age 16-64 years was enrolled in 30 rural and peri-urban communities as part of the Botswana Combination Prevention Project (BCPP), from October 2013 -November 2015. Data and samples from the baseline household survey were used to estimate cross-sectional HIV incidence, following an algorithm that combined Limiting-Antigen Avidity Assay (LAg-Avidity EIA), ART status (documented or by testing ARV drugs in plasma) and HIV-1 RNA load. The LAg-Avidity EIA cut-off normalized optical density (ODn) was set at 1.5. The HIV-1 RNA cut-off was set at 400 copies/mL. For estimation purposes, the Mean Duration of Recent Infection was 130 days and the False Recent Rate (FRR) was evaluated at values of either 0 or 0.39%.

RESULTS

Among 12,610 individuals participating in the baseline household survey, HIV status was available for 12,570 participants and 3,596 of them were HIV positive. LAg-Avidity EIA data was generated for 3,581 (99.6%) of HIV-positive participants. Of 326 participants with ODn ≤1.5, 278 individuals were receiving ART verified through documentation and were considered to represent longstanding HIV infections. Among the remaining 48 participants who reported no use of ART, 14 had an HIV-1 RNA load ≤400 copies/mL (including 3 participants with ARVs in plasma) and were excluded, as potential elite/viremic controllers or undisclosed ART. Thus, 34 LAg-Avidity-EIA-recent, ARV-naïve individuals with detectable HIV-1 RNA (>400 copies/mL) were classified as individuals with recent HIV infections. The annualized HIV incidence among 16-64 year old adults was estimated at 1.06% (95% CI 0.68-1.45%) with zero FRR, and at 0.64% (95% CI 0.24-1.04%) using a previously defined FRR of 0.39%. Within a subset of younger individuals 16-49 years old, the annualized HIV incidence was estimated at 1.29% (95% CI 0.82-1.77%) with zero FRR, and at 0.90% (95% CI 0.42-1.38%) with FRR set to 0.39%.

CONCLUSIONS

Using a cross-sectional estimate of HIV incidence from 2013-2015, we found that at the time of near achievement of the UNAIDS 90-90-90 targets, ~1% of adults (age 16-64 years) in Botswana's rural and peri-urban communities became HIV infected annually.

Identification and inference with nonignorable missing covariate data

We study identification of parametric and semiparametric models with missing covariate data. When covariate data are missing not at random, identification is not guaranteed even under fairly restrictive parametric assumptions, a fact that is illustrated with several examples. We propose a general approach to establish identification of parametric and semiparametric models when a covariate is missing not at random. Without auxiliary information about the missingness process, identification of parametric models is strongly dependent on model specification. However, in the presence of a fully observed shadow variable, which is correlated with the missing covariate but otherwise independent of its missingness, identification is more broadly achievable, including in fairly large semiparametric models. With a shadow variable, special consideration is given to the generalized linear models with the missingness process unrestricted. Under such a setting, the outcome model is identified for familiar generalized linear models, and we provide counterexamples when identification fails. For estimation, we describe an inverse probability weighted estimator that incorporates the shadow variable to estimate the missingness process, and we evaluate its performance via simulations.

Lack of Virological Suppression Among Young HIV-Positive Adults in Botswana

BACKGROUND

HIV-1 RNA load is the best biological predictor of HIV transmission and treatment response. The rate of virologic suppression among key subpopulations can guide HIV prevention programs.

METHODS

The Botswana Combination Prevention Project performed a population-based household survey among adults in 30 communities in Botswana. Data collected included knowledge of HIV-positive status, antiretroviral therapy (ART) coverage, and virologic suppression (HIV-1 RNA ≤400 copies per milliliter). Individuals aged 16-29 years were considered young adults.

RESULTS

Among 552 young people living with HIV enrolled with RNA load data and ART status available, 51% (n = 279) had undetectable HIV-1 RNA, including 54% of young women and 32% of young men [sex prevalence ratio (PR): 0.53; 95% confidence interval (CI): 0.43 to 0.80; P < 0.001]. Compared with older adults (30-64 years old), young HIV-infected adults were significantly less likely to have undetectable HIV-1 RNA (PR: 0.65; 95% CI: 0.59 to 0.70; P < 0.0001), including both men (PR: 0.43; 95% CI: 0.34 to 0.56; P < 0.0001) and women (PR: 0.67; 95% CI: 0.62 to 0.74; P < 0.0001). Among a subset of people living with HIV receiving ART, young adults also were less likely to have undetectable HIV-1 RNA load than older adults (PR: 0.93; 95% CI: 0.90 to 0.95; P = <0.0001). Analysis of the care continuum revealed that inferior HIV diagnosis and suboptimal linkage to care are the primary reasons for low virologic suppression among young adults.

CONCLUSIONS

Young adults in Botswana are significantly less likely to have undetectable HIV-1 RNA load compared with older adults. In the era of broad scale-up of ART, interventions able to diagnose young adults living with HIV and link them to effective therapy are urgently needed.

Identifying Causal Effects With Proxy Variables of an Unmeasured Confounder

We consider a causal effect that is confounded by an unobserved variable, but with observed proxy variables of the confounder. We show that, with at least two independent proxy variables satisfying a certain rank condition, the causal effect is nonparametrically identified, even if the measurement error mechanism, i.e., the conditional distribution of the proxies given the confounder, may not be identified. Our result generalizes the identification strategy of Kuroki & Pearl (2014) that rests on identification of the measurement error mechanism. When only one proxy for the confounder is available, or the required rank condition is not met, we develop a strategy to test the null hypothesis of no causal effect.

Bounded, efficient and multiply robust estimation of average treatment effects using instrumental variables

Instrumental variables (IVs) are widely used for estimating causal effects in the presence of unmeasured confounding. Under the standard IV model, however, the average treatment effect (ATE) is only partially identifiable. To address this, we propose novel assumptions that allow for identification of the ATE. Our identification assumptions are clearly separated from model assumptions needed for estimation, so that researchers are not required to commit to a specific observed data model in establishing identification. We then construct multiple estimators that are consistent under three different observed data models, and multiply robust estimators that are consistent in the union of these observed data models. We pay special attention to the case of binary outcomes, for which we obtain bounded estimators of the ATE that are guaranteed to lie between -1 and 1. Our approaches are illustrated with simulations and a data analysis evaluating the causal effect of education on earnings.

HIGHER ORDER ESTIMATING EQUATIONS FOR HIGH-DIMENSIONAL MODELS

We introduce a new method of estimation of parameters in semi-parametric and nonparametric models. The method is based on estimating equations that are U-statistics in the observations. The U-statistics are based on higher order influence functions that extend ordinary linear influence functions of the parameter of interest, and represent higher derivatives of this parameter. For parameters for which the representation cannot be perfect the method leads to a bias-variance trade-off, and results in estimators that converge at a slower than n -rate . In a number of examples the resulting rate can be shown to be optimal. We are particularly interested in estimating parameters in models with a nuisance parameter of high dimension or low regularity, where the parameter of interest cannot be estimated at n -rate , but we also consider efficient n -estimation using novel nonlinear estimators. The general approach is applied in detail to the example of estimating a mean response when the response is not always observed.

Social Integration and Reduced Risk of Coronary Heart Disease in Women: The Role of Lifestyle Behaviors

RATIONALE

Higher social integration is associated with lower cardiovascular mortality; however, whether it is associated with incident coronary heart disease (CHD), especially in women, and whether associations differ by case fatality are unclear.

OBJECTIVES

This study sought to examine the associations between social integration and risk of incident CHD in a large female prospective cohort.

METHODS AND RESULTS

Seventy-six thousand three hundred and sixty-two women in the Nurses' Health Study, free of CHD and stroke at baseline (1992), were followed until 2014. Social integration was assessed by a simplified Berkman-Syme Social Network Index every 4 years. End points included nonfatal myocardial infarction and fatal CHD. Two thousand three hundred and seventy-two incident CHD events occurred throughout follow-up. Adjusting for demographic, health/medical risk factors, and depressive symptoms, being socially integrated was significantly associated with lower CHD risk, particularly fatal CHD. The most socially integrated women had a hazard ratio of 0.55 (95% confidence interval, 0.41-0.73) of developing fatal CHD compared with those least socially integrated (P for trend <0.0001). When additionally adjusting for lifestyle behaviors, findings for fatal CHD were maintained but attenuated (P for trend =0.02), whereas the significant associations no longer remained for nonfatal myocardial infarction. The inverse associations between social integration and nonfatal myocardial infarction risk were largely explained by health-promoting behaviors, particularly through differences in cigarette smoking; however, the association with fatal CHD risk remained after accounting for these behaviors and, thus, may involve more direct biological mechanisms.

CONCLUSIONS

Social integration is inversely associated with CHD incidence in women, but is largely explained by lifestyle/behavioral pathways.

Invited Commentary: Bias Attenuation and Identification of Causal Effects With Multiple Negative Controls

In this commentary, we describe several extensions to the interesting and important negative control exposure approach for partial confounding adjustment in time-series analysis proposed by Flanders et al. (Am J Epidemiol. 2017;185(10):941-949). Specifically, by leveraging the availability of exposure time series, we show that under certain additional fairly reasonable assumptions, one can incorporate both past and future exposures as multiple negative control exposures to further attenuate confounding bias. We further describe 2 specific settings in which multiple controls can be used to fully account for confounding bias; the first assumes a forward-in-time version of the familiar autoregressive model for the exposure time series, while the second combines a negative control exposure with a negative control outcome for joint indirect adjustment of confounding. We briefly illustrate how one might apply our proposed framework in time-series studies. Both the original method of Flanders et al. and our proposed extensions are particularly well-suited for time-series data such as the air pollution study considered in their paper, and as such should be considered in routine environmental health studies.

Accounting for interactions and complex inter-subject dependency in estimating treatment effect in cluster-randomized trials with missing outcomes

Semi-parametric methods are often used for the estimation of intervention effects on correlated outcomes in cluster-randomized trials (CRTs). When outcomes are missing at random (MAR), Inverse Probability Weighted (IPW) methods incorporating baseline covariates can be used to deal with informative missingness. Also, augmented generalized estimating equations (AUG) correct for imbalance in baseline covariates but need to be extended for MAR outcomes. However, in the presence of interactions between treatment and baseline covariates, neither method alone produces consistent estimates for the marginal treatment effect if the model for interaction is not correctly specified. We propose an AUG-IPW estimator that weights by the inverse of the probability of being a complete case and allows different outcome models in each intervention arm. This estimator is doubly robust (DR); it gives correct estimates whether the missing data process or the outcome model is correctly specified. We consider the problem of covariate interference which arises when the outcome of an individual may depend on covariates of other individuals. When interfering covariates are not modeled, the DR property prevents bias as long as covariate interference is not present simultaneously for the outcome and the missingness. An R package is developed implementing the proposed method. An extensive simulation study and an application to a CRT of HIV risk reduction-intervention in South Africa illustrate the method.

CAUSAL INFERENCE WITH A GRAPHICAL HIERARCHY OF INTERVENTIONS

Identifying causal parameters from observational data is fraught with subtleties due to the issues of selection bias and confounding. In addition, more complex questions of interest, such as effects of treatment on the treated and mediated effects may not always be identified even in data where treatment assignment is known and under investigator control, or may be identified under one causal model but not another. Increasingly complex effects of interest, coupled with a diversity of causal models in use resulted in a fragmented view of identification. This fragmentation makes it unnecessarily difficult to determine if a given parameter is identified (and in what model), and what assumptions must hold for this to be the case. This, in turn, complicates the development of estimation theory and sensitivity analysis procedures. In this paper, we give a unifying view of a large class of causal effects of interest, including novel effects not previously considered, in terms of a hierarchy of interventions, and show that identification theory for this large class reduces to an identification theory of random variables under interventions from this hierarchy. Moreover, we show that one type of intervention in the hierarchy is naturally associated with queries identified under the Finest Fully Randomized Causally Interpretable Structure Tree Graph (FFRCISTG) model of Robins (via the extended g-formula), and another is naturally associated with queries identified under the Non-Parametric Structural Equation Model with Independent Errors (NPSEM-IE) of Pearl, via a more general functional we call the edge g-formula. Our results motivate the study of estimation theory for the edge g-formula, since we show it arises both in mediation analysis, and in settings where treatment assignment has unobserved causes, such as models associated with Pearl's front-door criterion.

Limitations of empirical calibration of p-values using observational data

Controversy over non-reproducible published research reporting a statistically significant result has produced substantial discussion in the literature. p-value calibration is a recently proposed procedure for adjusting p-values to account for both random and systematic errors that address one aspect of this problem. The method's validity rests on the key assumption that bias in an effect estimate is drawn from a normal distribution whose mean and variance can be correctly estimated. We investigated the method's control of type I and type II error rates using simulated and real-world data. Under mild violations of underlying assumptions, control of the type I error rate can be conservative, while under more extreme departures, it can be anti-conservative. The extent to which the assumption is violated in real-world data analyses is unknown. Barriers to testing the plausibility of the assumption using historical data are discussed. Our studies of the type II error rate using simulated and real-world electronic health care data demonstrated that calibrating p-values can substantially increase the type II error rate. The use of calibrated p-values may reduce the number of false-positive results, but there will be a commensurate drop in the ability to detect a true safety or efficacy signal. While p-value calibration can sometimes offer advantages in controlling the type I error rate, its adoption for routine use in studies of real-world health care datasets is premature. Separate characterizations of random and systematic errors provide a richer context for evaluating uncertainty surrounding effect estimates. Copyright © 2016 John Wiley & Sons, Ltd.

Tuberculosis Incidence and Risk Factors Among Human Immunodeficiency Virus (HIV)-Infected Adults Receiving Antiretroviral Therapy in a Large HIV Program in Nigeria

Background. Despite the benefits of antiretroviral therapy (ART), tuberculosis (TB) is the leading cause of mortality among human immunodeficiency virus (HIV)-infected persons in Africa. Nigeria bears the highest TB burden in Africa and second highest HIV burden globally. This long-term multicenter study aimed to determine the incidence rate and predictors of TB in adults in the Harvard/AIDS Prevention Initiative in Nigeria (APIN) and President's Emergency Plan for AIDS Relief (PEPFAR) Nigeria ART program.

Methods. This retrospective evaluation used data collected from 2004 to 2012 through the Harvard/APIN PEPFAR program. Risk factors for incident TB were determined using multivariate Cox proportional hazards regression with time-dependent covariates.

Results. Of 50 320 adults enrolled from 2005 to 2010, 11 092 (22%) had laboratory-confirmed active TB disease at ART initiation, and 2021 (4%) developed active TB after commencing ART. During 78 228 total person-years (PY) of follow-up, the TB incidence rate was 25.8 cases per 1000 PY (95% confidence interval [CI], 24.7–27.0) overall, and it decreased significantly both with duration on ART and calendar year. Risk factors at ART initiation for incident TB included the following: earlier ART enrollment year, tenofovir-containing initial ART regimen, and World Health Organization clinical stage above 1. Time-updated risk factors included the following: low body mass index, low CD4⁺ cell count, unsuppressed viral load, anemia, and ART adherence below 80%.

Conclusions. The rate of incident TB decreased with longer duration on ART and over the program years. The strongest TB risk factors were time-updated clinical markers, reinforcing the importance of consistent clinical and laboratory monitoring of ART patients in prompt diagnosis and treatment of TB and other coinfections.

Assessment and indirect adjustment for confounding by smoking in cohort studies using relative hazards models

Workers' smoking histories are not measured in many occupational cohort studies. Here we discuss the use of negative control outcomes to detect and adjust for confounding in analyses that lack information on smoking. We clarify the assumptions necessary to detect confounding by smoking and the additional assumptions necessary to indirectly adjust for such bias. We illustrate these methods using data from 2 studies of radiation and lung cancer: the Colorado Plateau cohort study (1950-2005) of underground uranium miners (in which smoking was measured) and a French cohort study (1950-2004) of nuclear industry workers (in which smoking was unmeasured). A cause-specific relative hazards model is proposed for estimation of indirectly adjusted associations. Among the miners, the proposed method suggests no confounding by smoking of the association between radon and lung cancer--a conclusion supported by adjustment for measured smoking. Among the nuclear workers, the proposed method suggests substantial confounding by smoking of the association between radiation and lung cancer. Indirect adjustment for confounding by smoking resulted in an 18% decrease in the adjusted estimated hazard ratio, yet this cannot be verified because smoking was unmeasured. Assumptions underlying this method are described, and a cause-specific proportional hazards model that allows easy implementation using standard software is presented.

The control outcome calibration approach for causal inference with unobserved confounding

Unobserved confounding can seldom be ruled out with certainty in nonexperimental studies. Negative controls are sometimes used in epidemiologic practice to detect the presence of unobserved confounding. An outcome is said to be a valid negative control variable to the extent that it is influenced by unobserved confounders of the exposure effects on the outcome in view, although not directly influenced by the exposure. Thus, a negative control outcome found to be empirically associated with the exposure after adjustment for observed confounders indicates that unobserved confounding may be present. In this paper, we go beyond the use of control outcomes to detect possible unobserved confounding and propose to use control outcomes in a simple but formal counterfactual-based approach to correct causal effect estimates for bias due to unobserved confounding. The proposed control outcome calibration approach is developed in the context of a continuous or binary outcome, and the control outcome and the exposure can be discrete or continuous. A sensitivity analysis technique is also developed, which can be used to assess the degree to which a violation of the main identifying assumption of the control outcome calibration approach might impact inference about the effect of the exposure on the outcome in view.

Are genetic variations in OXTR, AVPR1A, and CD38 genes important to social integration? Results from two large U.S. cohorts

Some evidence suggests that genetic polymorphisms in oxytocin pathway genes influence various social behaviors, but findings thus far have been mixed. Many studies have been based in small samples and there is possibility of publication bias. Using data from 2 large U.S. prospective cohorts with over 11,000 individuals, we investigated 88 SNPs in OXTR, AVPR1A, and CD38, in relation to social integration (measured as social connectedness in both binary and continuous forms and being continuously married). After correction for multiple testing only one SNP in CD38 (rs12644506) was significantly associated with social integration and that SNP predicted when using a dichotomized indicator of social connectedness (adjusted p=0.02), but not a continuous measure of social connectedness or the continuously married outcome. A significant gender-heterogeneous effect was identified in one OXTR SNP on dichotomized social connectedness; specifically, rs4686302 T allele was nominally associated with social connectedness in men, whereas the association direction was opposite in women (adjusted gender heterogeneity p=0.02). Furthermore, the rs53576 A allele was significantly associated with social connectedness only in women, and the effect magnitude was stronger in a dominant genetic model (adjusted p=0.003). In summary, our findings suggested that common genetic variants of OXTR, CD38, and AVPR1A are not associated with social integration as measured in this study using the simplified Berkman-Syme Social Network Index, but these findings and other work hint that effects may be modified by gender or other social experiences. Further work considering genetic pathways in relation to social integration may be more fruitful if these additional factors can be more comprehensively evaluated.

The effect of HIV-related immunosuppression on the risk of tuberculosis transmission to household contacts

BACKGROUND

Coinfection with human immunodeficiency virus (HIV) may modify the risk of transmitting tuberculosis. Some previous investigations suggest that patients coinfected with HIV and tuberculosis are less likely to transmit infection, whereas others do not support this conclusion. Here, we estimated the relative risk of tuberculosis transmission from coinfected patients compared to HIV-negative patients with tuberculosis.

METHODS

Between September 2009 and August 2012, we identified and enrolled 4841 household contacts of 1608 patients with drug-sensitive tuberculosis in Lima, Peru. We assessed the HIV status and CD4 counts of index patients, as well as other risk factors for infection specific to the index patient, the household, and the exposed individuals. Contacts underwent tuberculin skin testing to determine tuberculosis infection status.

RESULTS

After adjusting for covariates, we found that household contacts of HIV-infected tuberculosis patients with a CD4 count ≤250 cells/µL were less likely to be infected with tuberculosis (risk ratio = 0.49 [95% confidence interval, .24-.96]) than the contacts of HIV-negative tuberculosis patients. No children younger than 15 years who were exposed to HIV-positive patients with a CD4 count ≤250 cells/µL were infected with tuberculosis, compared to 22% of those exposed to non-HIV-infected patients. There was no significant difference in the risk of infection between contacts of HIV-infected index patients with CD4 counts >250 cells/µL and contacts of index patients who were not HIV-infected.

CONCLUSIONS

We found a reduced risk of tuberculosis infection among the household contacts of patients with active tuberculosis who had advanced HIV-related immunosuppression, suggesting reduced transmission from these index patients.

Estimation of risk ratios in cohort studies with a common outcome: a simple and efficient two-stage approach

The risk ratio effect measure is often the main parameter of interest in epidemiologic studies with a binary outcome. In this paper, the author presents a simple and efficient two-stage approach to estimate the risk ratios directly, which does not directly rely on consistency for an estimate of the baseline risk. This latter property is a key advantage of the approach over existing methods, because, unlike these other methods, the proposed approach obviates the need to restrict the predicted risk probabilities to fall below one, in order to recover efficient inferences about risk ratios. An additional appeal of the approach is that it is easy to implement. Finally, when the primary interest is in the effect of a specific binary exposure, a simple doubly robust closed-form estimator is derived, for the multiplicative effect of the exposure. Specifically, we show how one can adjust for confounding by incorporating a working regression model for the propensity score so that the correct inferences about the multiplicative effect of the exposure are recovered if either this model is correct or a working model for the association between confounders and outcome risk is correct, but both do not necessarily hold.

Differential mental health effects of neighborhood relocation among youth in vulnerable families: results from a randomized trial

CONTEXT Extensive observational evidence indicates that youth in high-poverty neighborhoods exhibit poor mental health, although not all children may be affected similarly. OBJECTIVE To use experimental evidence to assess whether gender and family health problems modify the mental health effects of moving from high- to low-poverty neighborhoods. DESIGN Randomized controlled trial. SETTING Volunteer low-income families in public housing in 5 US cities between 1994-1997. PARTICIPANTS We analyze 4- to 7-year outcomes in youth aged 12 to 19 years (n = 2829, 89% effective response rate) in the Moving to Opportunity Study. INTERVENTION Families were randomized to remain in public housing (control group) or to receive government-funded rental subsidies to move into private apartments (experimental group). Intention-to-treat analyses included intervention interactions by gender and health vulnerability (defined as prerandomization health/developmental limitations or disabilities in family members). MAIN OUTCOME MEASURES Past-year psychological distress (Kessler 6 scale [K6]) and the Behavioral Problems Index (BPI). Supplemental analyses used past-year major depressive disorder (MDD). RESULTS Male gender (P = .02) and family health vulnerability (P = .002) significantly adversely modified the intervention effect on K6 scores; male gender (P = .01), but not health vulnerability (P = .17), significantly adversely modified the intervention effect on the BPI. Girls without baseline health vulnerabilities were the only subgroup to benefit on any outcome (K6: β = -0.21; 95% CI, -0.34 to -0.07; P = .003; MDD: odds ratio = 0.42; 95% CI, 0.20 to 0.85; P = .02). For boys with health vulnerabilities, intervention was associated with worse K6 (β = 0.26; 95% CI, 0.09 to 0.44; P = .003) and BPI (β = 0.24; 95% CI, 0.09 to 0.40; P = .002) values. Neither girls with health vulnerability nor boys without health vulnerability experienced intervention benefits. Adherence-adjusted instrumental variable analysis found intervention effects twice as large. Patterns were similar for MDD, but estimates were imprecise owing to low prevalence. CONCLUSIONS Although some girls benefited, boys and adolescents from families with baseline health problems did not experience mental health benefits from housing mobility policies and may need additional program supports.

Searching for sharp drops in the incidence of pandemic A/H1N1 influenza by single year of age

Background

During the 2009 H1N1 pandemic (pH1N1), morbidity and mortality sparing was observed among the elderly population; it was hypothesized that this age group benefited from immunity to pH1N1 due to cross-reactive antibodies generated from prior infection with antigenically similar influenza viruses. Evidence from serologic studies and genetic similarities between pH1N1 and historical influenza viruses suggest that the incidence of pH1N1 cases should drop markedly in age cohorts born prior to the disappearance of H1N1 in 1957, namely those at least 52–53 years old in 2009, but the precise range of ages affected has not been delineated.

Methods and Findings

To test for any age-associated discontinuities in pH1N1 incidence, we aggregated laboratory-confirmed pH1N1 case data from 8 jurisdictions in 7 countries, stratified by single year of age, sex (when available), and hospitalization status. Using single year of age population denominators, we generated smoothed curves of the weighted risk ratio of pH1N1 incidence, and looked for sharp drops at varying age bandwidths, defined as a significantly negative second derivative. Analyses stratified by hospitalization status and sex were used to test alternative explanations for observed discontinuities. We found that the risk of laboratory-confirmed infection with pH1N1 declines with age, but that there was a statistically significant leveling off or increase in risk from about 45 to 50 years of age, after which a sharp drop in risk occurs until the late fifties. This trend was more pronounced in hospitalized cases and in women and was independent of the choice in smoothing parameters. The age range at which the decline in risk accelerates corresponds to the cohort born between 1951–1959 (hospitalized) and 1953–1960 (not hospitalized).

Conclusions

The reduced incidence of pH1N1 disease in older individuals shows a detailed age-specific pattern consistent with protection conferred by exposure to influenza A/H1N1 viruses circulating before 1957.

Estimating rates of carriage acquisition and clearance and competitive ability for pneumococcal serotypes in Kenya with a Markov transition model

BACKGROUND

There are more than 90 serotypes of Streptococcus pneumoniae, with varying biologic and epidemiologic properties. Animal studies suggest that carriage induces an acquired immune response that reduces duration of colonization in a nonserotype-specific fashion.

METHODS

We studied pneumococcal nasopharyngeal carriage longitudinally in Kenyan children 3-59 months of age, following up positive swabs at days 2, 4, 8, 16, and 32 and then monthly thereafter until 2 swabs were negative for the original serotype. As previously reported, 1868/2840 (66%) of children swabbed at baseline were positive. We estimated acquisition, clearance, and competition parameters for 27 serotypes using a Markov transition model.

RESULTS

Point estimates of type-specific acquisition rates ranged from 0.00025/d (type 1) to 0.0031/d (type 19F). Point estimates of time to clearance (inverse of type-specific immune clearance rate) ranged from 28 days (type 20) to 124 days (type 6A). For the serotype most resistant to competition (type 19F), acquisition of other serotypes was 52% less likely (95% confidence interval = 37%-63%) than in an uncolonized host. Fitness components (carriage duration, acquisition rate, lack of susceptibility to competition) were positively correlated with each other and with baseline prevalence, and were associated with biologic properties previously shown to associate with serotype. Duration of carriage declined with age for most serotypes.

CONCLUSIONS

Common S. pneumoniae serotypes appear superior in many dimensions of fitness. Differences in rate of immune clearance are attenuated as children age and become capable of more rapid clearance of the longest-lived serotypes. These findings provide information for comparison after introduction of pneumococcal conjugate vaccine.

Higher Order Inference On A Treatment Effect Under Low Regularity Conditions

We describe a novel approach to nonparametric point and interval estimation of a treatment effect in the presence of many continuous confounders. We show the problem can be reduced to that of point and interval estimation of the expected conditional covariance between treatment and response given the confounders. Our estimators are higher order U-statistics. The approach applies equally to the regular case where the expected conditional covariance is root-n estimable and to the irregular case where slower non-parametric rates prevail.

Semiparametric Minimax Rates

We consider the minimax rate of testing (or estimation) of non-linear functionals defined on semiparametric models. Existing methods appear not capable of determining a lower bound on the minimax rate of testing (or estimation) for certain functionals of interest. In particular, if the semiparametric model is indexed by several infinite-dimensional parameters. To cover these examples we extend the approach of [1], which is based on comparing a "true distribution" to a convex mixture of perturbed distributions to a comparison of two convex mixtures. The first mixture is obtained by perturbing a first parameter of the model, and the second by perturbing in addition a second parameter. We apply the new result to two examples of semiparametric functionals:the estimation of a mean response when response data are missing at random, and the estimation of an expected conditional covariance functional.