Abstract Suppose that we are interested in the average causal effect of a binary treatment on an outcome when this relationship is confounded by a binary confounder. Suppose that the confounder is unobserved but a nondifferential proxy of it is observed. We show that, under certain monotonicity assumption that is empirically verifiable, adjusting for the proxy produces a measure of the effect that is between the unadjusted and the true measures.

While the HVTN 505 trial showed no overall efficacy of the tested vaccine to prevent HIV infection over placebo, markers measuring immune response to vaccination were strongly correlated with infection. This finding generated the hypothesis that some marker-defined vaccinated subgroups were partially protected whereas others had their risk increased. This hypothesis can be assessed using the principal stratification framework (Frangakis and Rubin, 2002) for studying treatment effect modification by an intermediate response variable, using methods in the sub-field of principal surrogate (PS) analysis that studies multiple principal strata. Unfortunately, available methods for PS analysis require an augmented study design not available in HVTN 505, and make untestable structural risk assumptions, motivating a need for more robust PS methods. Fortunately, another sub-field of principal stratification, survivor average causal effect (SACE) analysis (Rubin, 2006) - which studies effects in a single principal stratum - provides many methods not requiring an augmented design and making fewer assumptions. We show how, for a binary intermediate response variable, methods developed for SACE analysis can be adapted to PS analysis, providing new and more robust PS methods. Application to HVTN 505 supports that the vaccine partially protected individuals with vaccine-induced T-cells expressing certain combinations of functions.

Abstract We address the characterization of problems in which a consistent estimator exists in a union of two models, also termed as a doubly robust estimator. Such estimators are important in missing information, including causal inference problems. Existing characterizations, based on the semiparametric theory of projections, have seen sufficient progress, but can still leave one’s understanding less than satisfied as to when and especially why such estimation works. We explore here a different, explanatory characterization – an exegesis based on logical operators. We show that double robustness exists if and only if we can produce consistent estimators for each contributing model based on an “AND” estimator, i. e., an estimator whose consistency generally needs both models to be correct. We show how this characterization explains double robustness through falsifiability.

Abstract In the causal adjustment setting, variable selection techniques based only on the outcome or only on the treatment allocation model can result in the omission of confounders and hence may lead to bias, or the inclusion of spurious variables and hence cause variance inflation, in estimation of the treatment effect. We propose a variable selection method using a penalized objective function that is based on both the outcome and treatment assignment models. The proposed method facilitates confounder selection in high-dimensional settings. We show that under some mild conditions our method attains the oracle property. The selected variables are used to form a doubly robust regression estimator of the treatment effect. Using the proposed method we analyze a set of data on economic growth and study the effect of life expectancy as a measure of population health on the average growth rate of gross domestic product per capita.

Abstract We study a model where one target variableY$Y$is correlated with a vectorX:=(X1,…,Xd)$\textbf{X}:=(X_1,\dots,X_d)$of predictor variables being potential causes ofY$Y$. We describe a method that infers to what extent the statistical dependences betweenX$\textbf{X}$andY$Y$are due to the influence ofX$\textbf{X}$onY$Y$and to what extent due to a hidden common cause (confounder) ofX$\textbf{X}$andY$Y$. The method relies on concentration of measure results for large dimensionsd$d$and an independence assumption stating that, in the absence of confounding, the vector of regression coefficients describing the influence of eachX$\textbf{X}$onY$Y$typically has ‘generic orientation’ relative to the eigenspaces of the covariance matrix ofX$\textbf{X}$. For the special case of a scalar confounder we show that confounding typically spoils this generic orientation in a characteristic way that can be used to quantitatively estimate the amount of confounding (subject to our idealized model assumptions).

In this paper, we study the effect of a time-varying exposure mediated by a time-varying intermediate variable. We consider general longitudinal settings, including survival outcomes. At a given time point, the exposure and mediator of interest are influenced by past covariates, mediators and exposures, and affect future covariates, mediators and exposures. Right censoring, if present, occurs in response to past history. To address the challenges in mediation analysis that are unique to these settings, we propose a formulation in terms of random interventions based on conditional distributions for the mediator. This formulation, in particular, allows for well-defined natural direct and indirect effects in the survival setting, and natural decomposition of the standard total effect. Upon establishing identifiability and the corresponding statistical estimands, we derive the efficient influence curves and establish their robustness properties. Applying Targeted Maximum Likelihood Estimation, we use these efficient influence curves to construct multiply robust and efficient estimators. We also present an inverse probability weighted estimator and a nested non-targeted substitution estimator for these parameters.

Abstract We address several questions relating to the use of standard regression and Structural Nested Mean Model (SNMM) approach (e. g., Ten Have et al. 2007) to analyze post-randomization effect modifiers of the intent-to-treat effect of a randomized intervention on a subsequent outcome, which has not been well examined. We show through simulations that the SNMM performs better with respect to bias of estimates of the intervention and interaction effects than does the corresponding standard interaction approach when the baseline intervention is randomized and the post-randomization factors are subject to confounding, and even when there is no association between the intervention and effect modifier. However, causal inference under the SNMM makes untestable assumptions that the causal contrasts do not vary across observed levels of the intervention and post-randomization factor. In addition, the precision of the SNMM-based estimators depends on the effect of the randomized intervention on the post-randomization factor varying across baseline covariate combinations. These issues and methods are illustrated with the application of the standard and causal methods to a randomized cognitive therapy (CT) trial, for which there is a conceptual model of negative cognitive styles or distortions impacted by CT but then in turn modifying the effect of CT on subsequent suicide ideation and social problem solving outcomes.

While child and adolescent obesity is a serious public health concern, few studies have utilized parameters based on the causal inference literature to examine the potential impacts of early intervention. The purpose of this analysis was to estimate the causal effects of early interventions to improve physical activity and diet during adolescence on body mass index (BMI), a measure of adiposity, using improved techniques. The most widespread statistical method in studies of child and adolescent obesity is multi-variable regression, with the parameter of interest being the coefficient on the variable of interest. This approach does not appropriately adjust for time-dependent confounding, and the modeling assumptions may not always be met. An alternative parameter to estimate is one motivated by the causal inference literature, which can be interpreted as the mean change in the outcome under interventions to set the exposure of interest. The underlying data-generating distribution, upon which the estimator is based, can be estimated via a parametric or semi-parametric approach. Using data from the National Heart, Lung, and Blood Institute Growth and Health Study, a 10-year prospective cohort study of adolescent girls, we estimated the longitudinal impact of physical activity and diet interventions on 10-year BMI z-scores via a parameter motivated by the causal inference literature, using both parametric and semi-parametric estimation approaches. The parameters of interest were estimated with a recently released R package, ltmle, for estimating means based upon general longitudinal treatment regimes. We found that early, sustained intervention on total calories had a greater impact than a physical activity intervention or non-sustained interventions. Multivariable linear regression yielded inflated effect estimates compared to estimates based on targeted maximum-likelihood estimation and data-adaptive super learning. Our analysis demonstrates that sophisticated, optimal semiparametric estimation of longitudinal treatment-specific means via ltmle provides an incredibly powerful, yet easy-to-use tool, removing impediments for putting theory into practice.

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