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1.  Interference and Sensitivity Analysis 
Causal inference with interference is a rapidly growing area. The literature has begun to relax the “no-interference” assumption that the treatment received by one individual does not affect the outcomes of other individuals. In this paper we briefly review the literature on causal inference in the presence of interference when treatments have been randomized. We then consider settings in which causal effects in the presence of interference are not identified, either because randomization alone does not suffice for identification, or because treatment is not randomized and there may be unmeasured confounders of the treatment-outcome relationship. We develop sensitivity analysis techniques for these settings. We describe several sensitivity analysis techniques for the infectiousness effect which, in a vaccine trial, captures the effect of the vaccine of one person on protecting a second person from infection even if the first is infected. We also develop two sensitivity analysis techniques for causal effects in the presence of unmeasured confounding which generalize analogous techniques when interference is absent. These two techniques for unmeasured confounding are compared and contrasted.
PMCID: PMC4300555  PMID: 25620841
Causal inference; infectiousness effect; interference; sensitivity analysis; spillover effect; stable unit treatment value assumption; vaccine trial
2.  Does neighborhood collective efficacy for families change over time? The Boston Neighborhood Survey 
There is an increased interest in how neighborhood social processes, such as collective efficacy, may protect mental health. Yet little is known about how stable these neighborhood processes are over time, or how to change them to influence other downstream factors. We used a population-based, repeat cross-sectional study of adults (n=5135) to assess stability of collective efficacy for families in 38 Boston neighborhoods across 4 years (2006, 2008, 2010) (the Boston Neighborhood Survey). We test temporal stability of collective efficacy for families across and within neighborhoods using 2-level random effects linear regression, fixed effects linear regression, T-tests, and Wilcoxon rank tests. Across the different methods, neighborhood collective efficacy for families remained stable across 4 years, after adjustment for neighborhood composition. If neighborhood collective efficacy is measured within 4 years of the exposure period of interest, assuming temporal stability may be valid.
PMCID: PMC4066733  PMID: 24976653
Neighborhood; neighborhood effects; neighborhood change; collective efficacy; multilevel models
3.  A general regression framework for a secondary outcome in case–control studies 
Biostatistics (Oxford, England)  2013;15(1):117-128.
Modern case–control studies typically involve the collection of data on a large number of outcomes, often at considerable logistical and monetary expense. These data are of potentially great value to subsequent researchers, who, although not necessarily concerned with the disease that defined the case series in the original study, may want to use the available information for a regression analysis involving a secondary outcome. Because cases and controls are selected with unequal probability, regression analysis involving a secondary outcome generally must acknowledge the sampling design. In this paper, the author presents a new framework for the analysis of secondary outcomes in case–control studies. The approach is based on a careful re-parameterization of the conditional model for the secondary outcome given the case–control outcome and regression covariates, in terms of (a) the population regression of interest of the secondary outcome given covariates and (b) the population regression of the case–control outcome on covariates. The error distribution for the secondary outcome given covariates and case–control status is otherwise unrestricted. For a continuous outcome, the approach sometimes reduces to extending model (a) by including a residual of (b) as a covariate. However, the framework is general in the sense that models (a) and (b) can take any functional form, and the methodology allows for an identity, log or logit link function for model (a).
PMCID: PMC3983430  PMID: 24152770
Case–control studies; Generalized linear models; Statistical genetics; Secondary outcomes
4.  Why and When “Flawed” Social Network Analyses Still Yield Valid Tests of no Contagion 
Statistics, politics, and policy  2012;3(1):2151-1050.
Lyons (2011) offered several critiques of the social network analyses of Christakis and Fowler, including issues of confounding, model inconsistency, and statistical dependence in networks. Here we show that in some settings, social network analyses of the type employed by Christakis and Fowler will still yield valid tests of the null of no social contagion, even though estimates and confidence intervals may not be valid. In particular, we show that if the alter’s state is lagged by an additional period, then under the null of no contagion, the problems of model inconsistency and statistical dependence effectively disappear which allow for testing for contagion. Our results clarify the setting in which even “flawed” social network analyses are still useful for assessing social contagion and social influence.
PMCID: PMC4240520  PMID: 25419506
confounding; contagion; dependence; social influence; social networks
5.  Inverse Odds Ratio-Weighted Estimation for Causal Mediation Analysis 
Statistics in medicine  2013;32(26):4567-4580.
An important scientific goal of studies in the health and social sciences is increasingly to determine to what extent the total effect of a point exposure is mediated by an intermediate variable on the causal pathway between the exposure and the outcome. A causal framework has recently been proposed for mediation analysis, which gives rise to new definitions, formal identification results and novel estimators of direct and indirect effects. In the present paper, the author describes a new inverse odds ratio-weighted (IORW) approach to estimate so-called natural direct and indirect effects. The approach which uses as a weight, the inverse of an estimate of the odds ratio function relating the exposure and the mediator is universal in that it can be used to decompose total effects in a number of regression models commonly used in practice. Specifically, the approach may be used for effect decomposition in generalized linear models with a nonlinear link function, and in a number of other commonly used models such as the Cox proportional hazards regression for a survival outcome. The approach is simple and can be implemented in standard software provided a weight can be specified for each observation. An additional advantage of the method is that it easily incorporates multiple mediators of a categorical, discrete or continuous nature.
PMCID: PMC3954805  PMID: 23744517
Causal Mediation Analysis; Inverse odds ratio weighted estimation; natural direct and indirect effects; double robustness
6.  Blood pressure and cognition:Factors that may account for their inconsistent association 
Epidemiology (Cambridge, Mass.)  2013;24(6):10.1097/EDE.0b013e3182a7121c.
Studies of hypertension and cognition variously report adverse, null and protective associations. We evaluated evidence supporting three potential explanations for this variation: an effect of hypertension duration, an effect of age at hypertension initiation, and selection bias due to dependent censoring.
The Normative Aging Study is a prospective cohort study of men in the greater Boston area. Participants completed study visits, including hypertension assessment, every 3-5 years starting in 1961. 758 of 1284 men eligible at baseline completed cognitive assessment between 1992 and 2005; we used the mean age-adjusted cognitive test z-score from their first assessment to quantify cognition. We estimated how becoming hypertensive and increasing age at onset and duration since hypertension initiation affect cognition. We used inverse probability of censoring weights to reduce and quantify selection bias.
A history of hypertension diagnosis predicted lower cognition. Increasing duration since hypertension initiation predicted lower mean cognitive z-score (-0.02 standard units per year increase [95% confidence interval= -0.04 to -0.001]), independent of age at onset. Comparing participants with and without hypertension, we observed noteworthy differences in mean cognitive score only for those with a long duration since hypertension initiation, regardless of age at onset. Age at onset was not associated with cognition independent of duration. Analyses designed to quantify selection bias suggested upward bias.
Previous findings of null or protective associations between hypertension and cognition likely reflect the study of persons with short duration since hypertension initiation. Selection bias may also contribute to cross-study heterogeneity.
PMCID: PMC3818218  PMID: 24030502
7.  A Note on formulae for causal mediation analysis in an odds ratiocontext 
Epidemiologic methods  2014;2(1):21-31.
In a recent manuscript, VanderWeele and Vansteelandt (American Journal of Epidemiology, 2010,172:1339–1348) (hereafter VWV) build on results due to Judea Pearl on causal mediation analysis and derive simple closed-form expressions for so-called natural direct and indirect effects in an odds ratio context for a binary outcome and a continuous mediator. The expressions obtained by VWV make two key simplifying assumptions: The mediator is normally distributed with constant variance,The binary outcome is rare. Assumption A may not be appropriate in settings where, as can happen in routine epidemiologic applications, the distribution of the mediator variable is highly skew. However, in this note, the author establishes that under a key assumption of “no mediator-exposure interaction” in the logistic regression model for the outcome, the simple formulae of VWV continue to hold even when the normality assumption of the mediator is dropped. The author further shows that when the “no interaction” assumption is relaxed, the formula of VWV for the natural indirect effect in this setting continues to apply when assumption A is also dropped. However, an alternative formula to that of VWV for the natural direct effect is required in this context and is provided in an appendix. When the disease is not rare, the author replaces assumptions A and B with an assumption C that the mediator follows a so-called Bridge distribution in which case simple closed-form formulae are again obtained for the natural direct and indirect effects.
PMCID: PMC4193811  PMID: 25309848
8.  Bachelors, Divorcees, and Widowers: Does Marriage Protect Men from Type 2 Diabetes? 
PLoS ONE  2014;9(9):e106720.
While research has suggested that being married may confer a health advantage, few studies to date have investigated the role of marital status in the development of type 2 diabetes. We examined whether men who are not married have increased risk of incident type 2 diabetes in the Health Professionals Follow-up Study. Men (n = 41,378) who were free of T2D in 1986, were followed for ≤22 years with biennial reports of T2D, marital status and covariates. Cox proportional hazard models were used to compare risk of incident T2D by marital status (married vs unmarried and married vs never married, divorced/separated, or widowed). There were 2,952 cases of incident T2D. Compared to married men, unmarried men had a 16% higher risk of developing T2D (95%CI:1.04,1.30), adjusting for age, family history of diabetes, ethnicity, lifestyle and body mass index (BMI). Relative risks (RR) for developing T2D differed for divorced/separated (1.09 [95%CI: 0.94,1.27]), widowed (1.29 [95%CI:1.06,1.57]), and never married (1.17 [95%CI:0.91,1.52]) after adjusting for age, family history of diabetes and ethnicity. Adjusting for lifestyle and BMI, the RR for T2D associated with widowhood was no longer significant (RR:1.16 [95%CI:0.95,1.41]). When allowing for a 2-year lag period between marital status and disease, RRs of T2D for widowers were augmented and borderline significant (RR:1.24 [95%CI:1.00,1.54]) after full adjustment. In conclusion, not being married, and more specifically, widowhood was more consistently associated with an increased risk of type 2 diabetes in men and this may be mediated, in part, through unfavorable changes in lifestyle, diet and adiposity.
PMCID: PMC4167705  PMID: 25229473
9.  Validation of a polygenic risk score for dementia in black and white individuals 
Brain and Behavior  2014;4(5):687-697.
To determine whether a polygenic risk score for Alzheimer's disease (AD) predicts dementia probability and memory functioning in non-Hispanic black (NHB) and non-Hispanic white (NHW) participants from a sample not used in previous genome-wide association studies.
Non-Hispanic white and NHB Health and Retirement Study (HRS) participants provided genetic information and either a composite memory score (n = 10,401) or a dementia probability score (n = 7690). Dementia probability score was estimated for participants' age 65+ from 2006 to 2010, while memory score was available for participants age 50+. We calculated AD genetic risk scores (AD-GRS) based on 10 polymorphisms confirmed to predict AD, weighting alleles by beta coefficients reported in AlzGene meta-analyses. We used pooled logistic regression to estimate the association of the AD-GRS with dementia probability and generalized linear models to estimate its effect on memory score.
Each 0.10 unit change in the AD-GRS was associated with larger relative effects on dementia among NHW aged 65+ (OR = 2.22; 95% CI: 1.79, 2.74; P < 0.001) than NHB (OR=1.33; 95% CI: 1.00, 1.77; P = 0.047), although additive effect estimates were similar. Each 0.10 unit change in the AD-GRS was associated with a −0.07 (95% CI: −0.09, −0.05; P < 0.001) SD difference in memory score among NHW aged 50+, but no significant differences among NHB (β = −0.01; 95% CI: −0.04, 0.01; P = 0.546). [Correction added on 29 July 2014, after first online publication: confidence intervalshave been amended.] The estimated effect of the GRS was significantly smaller among NHB than NHW (P < 0.05) for both outcomes.
This analysis provides evidence for differential relative effects of the GRS on dementia probability and memory score among NHW and NHB in a new, national data set.
PMCID: PMC4107377  PMID: 25328845
Dementia; genetics; race
10.  Adjustment for Missing Data in Complex Surveys Using Doubly Robust Estimation 
Epidemiology (Cambridge, Mass.)  2010;21(6):863-871.
The Demographic and Health Survey program routinely collects nationally representative information on HIV-related risk behaviors in many countries, using face-to-face interviews and a complex sampling scheme. If respondents skip questions about behaviors perceived as socially undesirable, such interviews may introduce bias. We sought to implement a doubly robust estimator to correct for dependent missing data in this context.
We applied 3 methods of adjustment for nonresponse on self-reported commercial sexual contact data from the 2005–2006 India Demographic Health Survey to estimate the prevalence of sexual contact between sexually active men and female sex workers. These methods were inverse-probability weighted regression, outcome regression, and doubly robust estimation—a recently-described approach that is more robust to model misspecification.
Compared with an unadjusted prevalence of 0.9% for commercial sexual contact prevalence (95% confidence interval = 0.8%–1.0%), adjustment for nonresponse using doubly robust estimation yielded a prevalence of 1.1% (1.0%–1.2%). We found similar estimates with adjustment by outcome regression and inverse-probability weighting. Marital status was strongly associated with item nonresponse, and correction for nonresponse led to a nearly 80% increase in the prevalence of commercial sexual contact among unmarried men (from 6.9% to 12.1%–12.4%).
Failure to correct for nonresponse produced a bias in self-reported commercial sexual contact. To facilitate the application of these methods (including the doubly robust estimator) to complex survey data settings, we provide analytical variance estimators and the corresponding SAS and MATLAB code. These variance estimators remain valid regardless of whether the modeling assumptions are correct.
PMCID: PMC4122332  PMID: 20881599
11.  Validation of a polygenic risk score for dementia in black and white individuals 
Brain and Behavior  2014;10.1002/brb3.248.
To determine whether a polygenic risk score for Alzheimer's disease (AD) predicts dementia probability and memory functioning in non‐Hispanic black (NHB) and non‐Hispanic white (NHW) participants from a sample not used in previous genome‐wide association studies.
Non‐Hispanic white and NHB Health and Retirement Study (HRS) participants provided genetic information and either a composite memory score (n = 10,401) or a dementia probability score (n = 7690). Dementia probability score was estimated for participants' age 65+ from 2006 to 2010, while memory score was available for participants age 50+. We calculated AD genetic risk scores (AD‐GRS) based on 10 polymorphisms confirmed to predict AD, weighting alleles by beta coefficients reported in AlzGene meta‐analyses. We used pooled logistic regression to estimate the association of the AD‐GRS with dementia probability and generalized linear models to estimate its effect on memory score.
Each 0.10 unit change in the AD‐GRS was associated with larger relative effects on dementia among NHW aged 65+ (OR = 2.22; 95% CI: 1.79, 2.74; P < 0.001) than NHB (OR=1.33; 95% CI: 1.00, 1.77; P = 0.047), although additive effect estimates were similar. Each 0.10 unit change in the AD‐GRS was associated with a −0.07 (95% CI: −0.09, −0.06; P < 0.001) SD difference in memory score among NHW aged 50+, but no significant differences among NHB (β = −0.01; 95% CI: −0.03, 0.02; P = 0.546). The estimated effect of the GRS was significantly smaller among NHB than NHW (P < 0.05) for both outcomes.
This analysis provides evidence for differential relative effects of the GRS on dementia probability and memory score among NHW and NHB in a new, national data set.
PMCID: PMC4107377
Dementia; genetics; race
12.  On a Closed-Form Doubly Robust Estimator of the Adjusted Odds Ratio for a Binary Exposure 
American Journal of Epidemiology  2013;177(11):1314-1316.
Epidemiologic studies often aim to estimate the odds ratio for the association between a binary exposure and a binary disease outcome. Because confounding bias is of serious concern in observational studies, investigators typically estimate the adjusted odds ratio in a multivariate logistic regression which conditions on a large number of potential confounders. It is well known that modeling error in specification of the confounders can lead to substantial bias in the adjusted odds ratio for exposure. As a remedy, Tchetgen Tchetgen et al. (Biometrika. 2010;97(1):171–180) recently developed so-called doubly robust estimators of an adjusted odds ratio by carefully combining standard logistic regression with reverse regression analysis, in which exposure is the dependent variable and both the outcome and the confounders are the independent variables. Double robustness implies that only one of the 2 modeling strategies needs to be correct in order to make valid inferences about the odds ratio parameter. In this paper, I aim to introduce this recent methodology into the epidemiologic literature by presenting a simple closed-form doubly robust estimator of the adjusted odds ratio for a binary exposure. A SAS macro (SAS Institute Inc., Cary, North Carolina) is given in an online appendix to facilitate use of the approach in routine epidemiologic practice, and a simulated data example is also provided for the purpose of illustration.
PMCID: PMC3664333  PMID: 23558352
case-control sampling; doubly robust estimator; logistic regression; odds ratio; SAS macro
The annals of applied statistics  2013;7(4):2106-2137.
The primary goal of randomized trials is to compare the effects of different interventions on some outcome of interest. In addition to the treatment assignment and outcome, data on baseline covariates, such as demographic characteristics or biomarker measurements, are typically collected. Incorporating such auxiliary co-variates in the analysis of randomized trials can increase power, but questions remain about how to preserve type I error when incorporating such covariates in a flexible way, particularly when the number of randomized units is small. Using the Young Citizens study, a cluster randomized trial of an educational intervention to promote HIV awareness, we compare several methods to evaluate intervention effects when baseline covariates are incorporated adaptively. To ascertain the validity of the methods shown in small samples, extensive simulation studies were conducted. We demonstrate that randomization inference preserves type I error under model selection while tests based on asymptotic theory may yield invalid results. We also demonstrate that covariate adjustment generally increases power, except at extremely small sample sizes using liberal selection procedures. Although shown within the context of HIV prevention research, our conclusions have important implications for maximizing efficiency and robustness in randomized trials with small samples across disciplines.
PMCID: PMC3935423  PMID: 24587845
randomized trials; exact tests; covariate adjustment; model selection
15.  How Does Sex Trafficking Increase the Risk of HIV Infection? An Observational Study From Southern India 
American Journal of Epidemiology  2013;177(3):232-241.
Studies have documented the substantial risk of human immunodeficiency virus (HIV) infection endured by sex-trafficked women, but it remains unclear how exposure to trafficking puts its victims at risk. We assessed whether the association between sex trafficking and HIV could be explained by self-reported forced prostitution or young age at entry into prostitution using cross-sectional data collected from 1,814 adult female sex workers in Karnataka, India, between August 2005 and August 2006. Marginal structural logistic regression was used to estimate adjusted odds ratios for HIV infection. Overall, 372 (21%) women met 1 or both criteria used to define sex trafficking: 278 (16%) began sex work before age 18 years, and 107 (5%) reported being forcibly prostituted. Thirteen (0.7%) met both criteria. Forcibly prostituted women were more likely to be HIV-infected than were women who joined the industry voluntarily, independent of age at entering prostitution (odds ratio = 2.30, 95% confidence interval: 1.08, 4.90). Conversely, after adjustment for forced prostitution and other confounders, no association between age at entry into prostitution and HIV was observed. The association between forced prostitution and HIV infection became stronger in the presence of sexual violence (odds ratio = 11.13, 95% confidence interval: 2.41, 51.40). These findings indicate that forced prostitution coupled with sexual violence probably explains the association between sex trafficking and HIV.
PMCID: PMC3626049  PMID: 23324332
female sex workers; HIV; human immunodeficiency virus; India; marginal structural models; sex trafficking; sexual violence
16.  Performance of Polygenic Scores for Predicting Phobic Anxiety 
PLoS ONE  2013;8(11):e80326.
Anxiety disorders are common, with a lifetime prevalence of 20% in the U.S., and are responsible for substantial burdens of disability, missed work days and health care utilization. To date, no causal genetic variants have been identified for anxiety, anxiety disorders, or related traits.
To investigate whether a phobic anxiety symptom score was associated with 3 alternative polygenic risk scores, derived from external genome-wide association studies of anxiety, an internally estimated agnostic polygenic score, or previously identified candidate genes.
Longitudinal follow-up study. Using linear and logistic regression we investigated whether phobic anxiety was associated with polygenic risk scores derived from internal, leave-one out genome-wide association studies, from 31 candidate genes, and from out-of-sample genome-wide association weights previously shown to predict depression and anxiety in another cohort.
Setting and Participants
Study participants (n = 11,127) were individuals from the Nurses' Health Study and Health Professionals Follow-up Study.
Main Outcome Measure
Anxiety symptoms were assessed via the 8-item phobic anxiety scale of the Crown Crisp Index at two time points, from which a continuous phenotype score was derived.
We found no genome-wide significant associations with phobic anxiety. Phobic anxiety was also not associated with a polygenic risk score derived from the genome-wide association study beta weights using liberal p-value thresholds; with a previously published genome-wide polygenic score; or with a candidate gene risk score based on 31 genes previously hypothesized to predict anxiety.
There is a substantial gap between twin-study heritability estimates of anxiety disorders ranging between 20–40% and heritability explained by genome-wide association results. New approaches such as improved genome imputations, application of gene expression and biological pathways information, and incorporating social or environmental modifiers of genetic risks may be necessary to identify significant genetic predictors of anxiety.
PMCID: PMC3835914  PMID: 24278274
17.  Bounding the Infectiousness Effect in Vaccine Trials 
Epidemiology (Cambridge, Mass.)  2011;22(5):686-693.
In vaccine trials, the vaccination of one person might prevent the infection of another; a distinction can be drawn between the ways such a protective effect might arise. Consider a setting with 2 persons per household in which one of the 2 is vaccinated. Vaccinating the first person may protect the second person by preventing the first from being infected and passing the infection on to the second. Alternatively, vaccinating the first person may protect the second by rendering the infection less contagious even if the first is infected. This latter mechanism is sometimes referred to as an “infectiousness effect” of the vaccine. Crude estimators for the infectiousness effect will be subject to selection bias due to stratification on a postvaccination event, namely the infection status of the first person. We use theory concerning causal inference under interference along with a principal-stratification framework to show that, although the crude estimator is biased, it is, under plausible assumptions, conservative for what one might define as a causal infectiousness effect. This applies to bias from selection due to the persons in the comparison, and also to selection due to pathogen virulence. We illustrate our results with an example from the literature.
PMCID: PMC3792580  PMID: 21753730
18.  Components of the indirect effect in vaccine trials: identification of contagion and infectiousness effects 
Epidemiology (Cambridge, Mass.)  2012;23(5):751-761.
Vaccination of one person may prevent the infection of another either because the vaccine prevents the first from being infected and from infecting the second, or because, even if the first person is infected, the vaccine may render the infection less infectious. We might refer to the first of these mechanisms as a contagion effect and the second as an infectiousness effect. In the simple setting of a randomized vaccine trial with households of size two, we use counterfactual theory under interference to provide formal definitions of a contagion effect and an unconditional infectiousness effect. Using ideas analogous to mediation analysis, we show that the indirect effect (the effect of one person’s vaccine on another’s outcome) can be decomposed into a contagion effect and an unconditional infectiousness effect on the risk-difference, risk-ratio, odds-ratio and vaccine-efficacy scales. We provide identification assumptions for such contagion and unconditional infectiousness effects, and describe a simple statistical technique to estimate these effects when they are identified. We also give a sensitivity-analysis technique to assess how inferences would change under violations of the identification assumptions. The concepts and results of this paper are illustrated with hypothetical vaccine-trial data.
PMCID: PMC3415570  PMID: 22828661
19.  Gender and Crime Victimization Modify Neighborhood Effects on Adolescent Mental Health 
Pediatrics  2012;130(3):472-481.
Leverage an experimental study to determine whether gender or recent crime victimization modify the mental health effects of moving to low-poverty neighborhoods.
The Moving to Opportunity (MTO) study randomized low-income families in public housing to an intervention arm receiving vouchers to subsidize rental housing in lower-poverty neighborhoods or to controls receiving no voucher. We examined 3 outcomes 4 to 7 years after randomization, among youth aged 5 to 16 years at baseline (n = 2829): lifetime major depressive disorder (MDD), psychological distress (K6), and Behavior Problems Index (BPI). Treatment effect modification by gender and family’s baseline report of recent violent crime victimization was tested via interactions in covariate-adjusted intent-to-treat and instrumental variable adherence-adjusted regression models.
Gender and crime victimization significantly modified treatment effects on distress and BPI (P < .10). Female adolescents in families without crime victimization benefited from MTO treatment, for all outcomes (Distress B = –0.19, P = .008; BPI B = –0.13, P = .06; MDD B = –0.036, P = .03). Male adolescents in intervention families experiencing crime victimization had worse distress (B = 0.24, P = .004), more behavior problems (B = 0.30, P < .001), and nonsignificantly higher MDD (B = 0.022, P = .16) versus controls. Other subgroups experienced no effect of MTO treatment. Instrumental variable estimates were similar but larger.
Girls from families experiencing recent violent crime victimization were significantly less likely to achieve mental health benefits, and boys were harmed, by MTO, suggesting need for cross-sectoral program supports to offset multiple stressors.
PMCID: PMC3428753  PMID: 22908105
mental health; depression; adolescent behavior; randomized controlled trial; housing; public housing; adolescent; victimization; urban health
20.  Genetic Variants on 15q25.1, Smoking, and Lung Cancer: An Assessment of Mediation and Interaction 
American Journal of Epidemiology  2012;175(10):1013-1020.
Genome-wide association studies have identified variants on chromosome 15q25.1 that increase the risks of both lung cancer and nicotine dependence and associated smoking behavior. However, there remains debate as to whether the association with lung cancer is direct or is mediated by pathways related to smoking behavior. Here, the authors apply a novel method for mediation analysis, allowing for gene-environment interaction, to a lung cancer case-control study (1992–2004) conducted at Massachusetts General Hospital using 2 single nucleotide polymorphisms, rs8034191 and rs1051730, on 15q25.1. The results are validated using data from 3 other lung cancer studies. Tests for additive interaction (P = 2 × 10−10 and P = 1 × 10−9) and multiplicative interaction (P = 0.01 and P = 0.01) were significant. Pooled analyses yielded a direct-effect odds ratio of 1.26 (95% confidence interval (CI): 1.19, 1.33; P = 2 × 10−15) for rs8034191 and an indirect-effect odds ratio of 1.01 (95% CI: 1.00, 1.01; P = 0.09); the proportion of increased risk mediated by smoking was 3.2%. For rs1051730, direct- and indirect-effect odds ratios were 1.26 (95% CI: 1.19, 1.33; P = 1 × 10−15) and 1.00 (95% CI: 0.99, 1.01; P = 0.22), respectively, with a proportion mediated of 2.3%. Adjustment for measurement error in smoking behavior allowing up to 75% measurement error increased the proportions mediated to 12.5% and 9.2%, respectively. These analyses indicate that the association of the variants with lung cancer operates primarily through other pathways.
PMCID: PMC3353137  PMID: 22306564
gene-environment interaction; lung neoplasms; mediation; pathway analysis; smoking
21.  Credible Mendelian Randomization Studies: Approaches for Evaluating the Instrumental Variable Assumptions 
American Journal of Epidemiology  2012;175(4):332-339.
As with other instrumental variable (IV) analyses, Mendelian randomization (MR) studies rest on strong assumptions. These assumptions are not routinely systematically evaluated in MR applications, although such evaluation could add to the credibility of MR analyses. In this article, the authors present several methods that are useful for evaluating the validity of an MR study. They apply these methods to a recent MR study that used fat mass and obesity-associated (FTO) genotype as an IV to estimate the effect of obesity on mental disorder. These approaches to evaluating assumptions for valid IV analyses are not fail-safe, in that there are situations where the approaches might either fail to identify a biased IV or inappropriately suggest that a valid IV is biased. Therefore, the authors describe the assumptions upon which the IV assessments rely. The methods they describe are relevant to any IV analysis, regardless of whether it is based on a genetic IV or other possible sources of exogenous variation. Methods that assess the IV assumptions are generally not conclusive, but routinely applying such methods is nonetheless likely to improve the scientific contributions of MR studies.
PMCID: PMC3366596  PMID: 22247045
causality; confounding factors; epidemiologic methods; instrumental variables; Mendelian randomization analysis
22.  Gene-Environment Interactions in Genome-Wide Association Studies: A Comparative Study of Tests Applied to Empirical Studies of Type 2 Diabetes 
American Journal of Epidemiology  2011;175(3):191-202.
The question of which statistical approach is the most effective for investigating gene-environment (G-E) interactions in the context of genome-wide association studies (GWAS) remains unresolved. By using 2 case-control GWAS (the Nurses’ Health Study, 1976–2006, and the Health Professionals Follow-up Study, 1986–2006) of type 2 diabetes, the authors compared 5 tests for interactions: standard logistic regression-based case-control; case-only; semiparametric maximum-likelihood estimation of an empirical-Bayes shrinkage estimator; and 2-stage tests. The authors also compared 2 joint tests of genetic main effects and G-E interaction. Elevated body mass index was the exposure of interest and was modeled as a binary trait to avoid an inflated type I error rate that the authors observed when the main effect of continuous body mass index was misspecified. Although both the case-only and the semiparametric maximum-likelihood estimation approaches assume that the tested markers are independent of exposure in the general population, the authors did not observe any evidence of inflated type I error for these tests in their studies with 2,199 cases and 3,044 controls. Both joint tests detected markers with known marginal effects. Loci with the most significant G-E interactions using the standard, empirical-Bayes, and 2-stage tests were strongly correlated with the exposure among controls. Study findings suggest that methods exploiting G-E independence can be efficient and valid options for investigating G-E interactions in GWAS.
PMCID: PMC3261439  PMID: 22199026
case-control studies; case study; diabetes mellitus, type 2; epidemiologic methods; genome-wide association study; genotype-environment interaction
23.  Accounting for bias due to selective attrition: The example of smoking and cognitive decline 
Epidemiology (Cambridge, Mass.)  2012;23(1):119-128.
Selective attrition may introduce bias into analyses of the determinants of cognitive decline. This is a concern especially for risk factors, such as smoking, that strongly influence mortality and drop-out. Using inverse-probability-of-attrition weights (IPAWs), we examined the influence of selective attrition on the estimated association of current smoking (versus never smoking) with cognitive decline.
Chicago Health and Aging Project participants (n=3,713), aged 65–109, who were current smokers or never-smokers underwent cognitive assessments up to 5 times at 3-year intervals. We used pooled logistic regression to fit predictive models of attrition due to death or study drop-out across the follow-up waves. With these models, we computed inverse-probability-of-attrition weights for each observation. We fit unweighted and weighted, multivariable-adjusted generalized-estimating-equation models, contrasting rates of change in cognitive scores in current versus never-smokers. Estimates are expressed as rates of change in z-score per decade.
Over the 12 years of follow-up, smokers had higher mortality than never-smokers (hazard ratio= 1.93 [95% confidence interval= 1.67 to 2.23]). Higher previous cognitive score was associated with increased likelihood of survival and continued participation. In unweighted analyses, current smokers’ cognitive scores declined 0.11 standard units per decade more rapidly than never-smokers’ (95% CI= −0.20 to −0.02). Weighting to account for attrition yielded estimates that were 56%–86% larger, with smokers’ estimated 10-year rate of decline up to 0.20 units faster than never smokers’ (95% CI= −0.36 to −0.04).
Estimates of smoking’s effects on cognitive decline may be underestimated due to differential attrition. Analyses that weight for the inverse probability of attrition help - for this attrition.
PMCID: PMC3237815  PMID: 21989136
24.  On Causal Mediation Analysis with a Survival Outcome 
Suppose that having established a marginal total effect of a point exposure on a time-to-event outcome, an investigator wishes to decompose this effect into its direct and indirect pathways, also known as natural direct and indirect effects, mediated by a variable known to occur after the exposure and prior to the outcome. This paper proposes a theory of estimation of natural direct and indirect effects in two important semiparametric models for a failure time outcome. The underlying survival model for the marginal total effect and thus for the direct and indirect effects, can either be a marginal structural Cox proportional hazards model, or a marginal structural additive hazards model. The proposed theory delivers new estimators for mediation analysis in each of these models, with appealing robustness properties. Specifically, in order to guarantee ignorability with respect to the exposure and mediator variables, the approach, which is multiply robust, allows the investigator to use several flexible working models to adjust for confounding by a large number of pre-exposure variables. Multiple robustness is appealing because it only requires a subset of working models to be correct for consistency; furthermore, the analyst need not know which subset of working models is in fact correct to report valid inferences. Finally, a novel semiparametric sensitivity analysis technique is developed for each of these models, to assess the impact on inference, of a violation of the assumption of ignorability of the mediator.
PMCID: PMC3204669  PMID: 22049268
natural direct effect; natural indirect effect; Cox proportional hazards model; additive hazards model; multiple robustness
25.  Effect partitioning under interference in two-stage randomized vaccine trials 
Statistics & probability letters  2011;81(7):861-869.
In the presence of interference, the exposure of one individual may affect the outcomes of others. We provide new effect partitioning results under interferences that express the overall effect as a sum of (i) the indirect (or spillover) effect and (ii) a contrast between two direct effects.
PMCID: PMC3084013  PMID: 21532912
Causal inference; counterfactual; interference; SUTVA; randomized experiments; spillover effects; vaccine trials

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