Eric J. Tchetgen Tchetgen

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 con- founder, 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.

Missing data is a common occurrence in epidemiologic research. In this paper, 3 data sets with induced missing values from the Collaborative Perinatal Project, a multisite US study conducted from 1959 to 1974, are provided as examples of prototypical epidemiologic studies with missing data. Our goal was to estimate the association of maternal smoking behavior with spontaneous abortion while adjusting for numerous confounders. At the same time, we did not necessarily wish to evaluate the joint distribution among potentially unobserved covariates, which is seldom the subject of substantive scientific interest. The inverse probability weighting (IPW) approach preserves the semiparametric structure of the underlying model of substantive interest and clearly separates the model of substantive interest from the model used to account for the missing data. However, IPW often will not result in valid inference if the missing-data pattern is nonmonotone, even if the data are missing at random. We describe a recently proposed approach to modeling nonmonotone missing-data mechanisms under missingness at random to use in constructing the weights in IPW complete-case estimation, and we illustrate the approach using 3 data sets described in a companion article (Am J Epidemiol. 2018;187(3):568–575).

Mendelian randomization (MR) is a popular instrumental variable (IV) approach, in which one or several genetic markers serve as IVs that can be leveraged to recover under certain conditions, valid inferences about a given exposure-outcome causal association subject to unmeasured confounding. A key IV identification condition known as the exclusion restriction states that the IV has no direct effect on the outcome that is not mediated by the exposure in view. In MR studies, such an assumption requires an unrealistic level of knowledge and understanding of the mechanism by which the genetic markers causally affect the outcome, particularly when a large number of genetic variants are considered as IVs. As a result, possible violation of the exclusion restriction can seldom be ruled out in such MR studies, and if present, such violation can invalidate IVbased inferences even if unbeknownst to the analyst, confounding is either negligible or absent. To address this concern, we introduce a new class of IV estimators which are robust to violation of the exclusion restriction under a large collection of data generating mechanisms consistent with parametric models commonly assumed in the MR literature. Our approach which we have named “MR G-Estimation under No Interaction with Unmeasured Selection” (MR GENIUS) may in fact be viewed as a modification to Robins’ G-estimation approach that is robust to both additive unmeasured confounding and violation of the exclusion restriction assumption. We also establish that estimation with MR GENIUS may also be viewed as a robust generalization of the well-known Lewbel estimator for a triangular system of structural equations with endogeneity. Specifically, we show that unlike Lewbel estimation, MR GENIUS is under fairly weak conditions also robust to unmeasured confounding of the effects of the genetic IVs on both the exposure and the outcome, another possible violation of a key IV Identification condition. Furthermore, while Lewbel estimation involves specification of linear models both for the outcome and the exposure, MR GENIUS generally does not require specification of a structural model for the direct effect of invalid IVs on the outcome, therefore allowing the latter model to be unrestricted. Finally, unlike Lewbel estimation, MR GENIUS is shown to equally apply for binary, discrete or continuous exposure and outcome variables and can be used under prospective sampling, or retrospective sampling such as in a case-control study, as well as for right censored time-to-event outcomes under an additive hazards model.

When a risk factor affects certain categories of a multinomial outcome but not others, outcome heterogeneity is said to be present. A standard epidemiologic approach for modeling risk factors of a categorical outcome typically entails fitting a polytomous logistic regression via maximum likelihood estimation. In this paper, we show that standard polytomous regression is ill equipped to detect outcome heterogeneity and will generally understate the degree to which such heterogeneity may be present. Specifically, nonsaturated polytomous regression will often a priori rule out the possibility of outcome heterogeneity from its parameter space. As a remedy, we propose to model each category of the outcome as a separate binary regression. For full efficiency, we propose to estimate the collection of regression parameters jointly using a constrained Bayesian approach that ensures that one remains within the multinomial model. The approach is straightforward to implement in standard software for Bayesian estimation.

Summary: The use of instrumental variables for estimating the effect of an exposure on an outcome is popular in econometrics, and increasingly so in epidemiology. This increasing popularity may be attributed to the natural occurrence of instrumental variables in observational studies that incorporate elements of randomization, either by design or by nature (e.g., random inheritance of genes). Instrumental variables estimation of exposure effects is well established for continuous outcomes and to some extent for binary outcomes. It is, however, largely lacking for time-to-event outcomes because of complications due to censoring and survivorship bias. In this article, we make a novel proposal under a class of structural cumulative survival models which parameterize time-varying effects of a point exposure directly on the scale of the survival function; these models are essentially equivalent with a semi-parametric variant of the instrumental variables additive hazards model. We propose a class of recursive instrumental variable estimators for these exposure effects, and derive their large sample properties along with inferential tools. We examine the performance of the proposed method in simulation studies and illustrate it in a Mendelian randomization study to evaluate the effect of diabetes on mortality using data from the Health and Retirement Study. We further use the proposed method to investigate potential benefit from breast cancer screening on subsequent breast cancer mortality based on the HIP-study.

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.

Case-control studies are designed towards studying associations between risk factors and a single, primary outcome. Information about additional, secondary outcomes is also collected, but association studies targeting such secondary outcomes should account for the case-control sampling scheme, or otherwise results may be biased. Often, one uses inverse probability weighted (IPW) estimators to estimate population effects in such studies. IPW estimators are robust, as they only require correct specification of the mean regression model of the secondary outcome on covariates, and knowledge of the disease prevalence. However, IPW estimators are inefficient relative to estimators that make additional assumptions about the data generating mechanism. We propose a class of estimators for the effect of risk factors on a secondary outcome in case-control studies that combine IPW with an additional modeling assumption: specification of the disease outcome probability model. We incorporate this model via a mean zero control function. We derive the class of all regular and asymptotically linear estimators corresponding to our modeling assumption, when the secondary outcome mean is modeled using either the identity or the log link. We find the efficient estimator in our class of estimators and show that it reduces to standard IPW when the model for the primary disease outcome is unrestricted, and is more efficient than standard IPW when the model is either parametric or semiparametric.

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.