The impact of imprecisely measured covariates on estimating gene-environment interactions

BACKGROUND The effects of measurement error in epidemiological exposures and confounders on estimated effects of exposure are well described, but the effects on estimates for gene-environment interactions has received rather less attention. In particular, the effects of confounder measurement error on gene-environment interactions are unknown. METHODS We investigate these effects using simulated data and illustrate our results with a practical example in nutrition epidemiology. RESULTS We show that the interaction regression coefficient is unchanged by confounder measurement error under certain conditions, but biased by exposure measurement error. We also confirm that confounder measurement error can lead to estimated effects of exposure biased either towards or away from the null, depending on the correlation structure, with associated effects on type II errors. CONCLUSION Whilst measurement error in confounders does not lead to bias in interaction coefficients, it may still lead to bias in the estimated effects of exposure. There may still be cost implications for epidemiological studies that need to calibrate all error-prone covariates against a valid reference, in addition to the exposure, to reduce the effects of confounder measurement erro

The role of dwelling type when estimating the effect of magnetic fields on childhood leukemia in the California Power Line Study (CAPS).

PurposeThe type of dwelling where a child lives is an important factor when considering residential exposure to environmental agents. In this paper, we explore its role when estimating the potential effects of magnetic fields (MF) on leukemia using data from the California Power Line Study (CAPS). In this context, dwelling type could be a risk factor, a proxy for other risk factors, a cause of MF exposure, a confounder, an effect-measure modifier, or some combination.MethodsWe obtained information on type of dwelling at birth on over 2,000 subjects. Using multivariable-adjusted logistic regression, we assessed whether dwelling type was a risk factor for childhood leukemia, which covariates and MF exposures were associated with dwelling type, and whether dwelling type was a potential confounder or an effect-measure modifier in the MF-leukemia relationship under the assumption of no-uncontrolled confounding.ResultsA majority of children lived in single-family homes or duplexes (70%). Dwelling type was associated with race/ethnicity and socioeconomic status but not with childhood leukemia risk, after other adjustments, and did not alter the MF-leukemia relationship upon adjustment as a potential confounder. Stratification revealed potential effect-measure modification by dwelling type on the multiplicative scale.ConclusionDwelling type does not appear to play a significant role in the MF-leukemia relationship in the CAPS dataset as a leukemia risk factor or confounder. Future research should explore the role of dwelling as an effect-measure modifier of the MF-leukemia association

Detecting confounding in multivariate linear models via spectral analysis

We study a model where one target variable Y is correlated with a vector X:=(X_1,...,X_d) of predictor variables being potential causes of Y. We describe a method that infers to what extent the statistical dependences between X and Y are due to the influence of X on Y and to what extent due to a hidden common cause (confounder) of X and Y. The method relies on concentration of measure results for large dimensions d and an independence assumption stating that, in the absence of confounding, the vector of regression coefficients describing the influence of each X on Y typically has `generic orientation' relative to the eigenspaces of the covariance matrix of 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.Comment: 27 pages, 16 figure

Robust and Flexible Estimation of Stochastic Mediation Effects: A Proposed Method and Example in a Randomized Trial Setting

Causal mediation analysis can improve understanding of the mechanisms underlying epidemiologic associations. However, the utility of natural direct and indirect effect estimation has been limited by the assumption of no confounder of the mediator-outcome relationship that is affected by prior exposure---an assumption frequently violated in practice. We build on recent work that identified alternative estimands that do not require this assumption and propose a flexible and double robust semiparametric targeted minimum loss-based estimator for data-dependent stochastic direct and indirect effects. The proposed method treats the intermediate confounder affected by prior exposure as a time-varying confounder and intervenes stochastically on the mediator using a distribution which conditions on baseline covariates and marginalizes over the intermediate confounder. In addition, we assume the stochastic intervention is given, conditional on observed data, which results in a simpler estimator and weaker identification assumptions. We demonstrate the estimator's finite sample and robustness properties in a simple simulation study. We apply the method to an example from the Moving to Opportunity experiment. In this application, randomization to receive a housing voucher is the treatment/instrument that influenced moving to a low-poverty neighborhood, which is the intermediate confounder. We estimate the data-dependent stochastic direct effect of randomization to the voucher group on adolescent marijuana use not mediated by change in school district and the stochastic indirect effect mediated by change in school district. We find no evidence of mediation. Our estimator is easy to implement in standard statistical software, and we provide annotated R code to further lower implementation barriers.Comment: 24 pages, 2 tables, 2 figure

On the Nondifferential Misclassification of a Binary Confounder

Abstract Consider a study with binary exposure, outcome, and confounder, where the confounder is nondifferentially misclassified. Epidemiologists have long accepted the unproven but oft-cited result that, if the confounder is binary, odds ratios, risk ratios, and risk differences which control for the mismeasured confounder will lie between the crude and the true measures. In this paper the authors provide an analytic proof of the result in the absence of a qualitative interaction between treatment and confounder, and demonstrate via counterexample that the result need not hold when there is a qualitative interaction between treatment and confounder. They also present an analytic proof of the result for the effect of treatment amount the treated, and describe extensions to measures conditional on or standardized over other covariates

Data-Driven Confounder Selection via Markov and Bayesian Networks

To unbiasedly estimate a causal effect on an outcome unconfoundedness is often assumed. If there is sufficient knowledge on the underlying causal structure then existing confounder selection criteria can be used to select subsets of the observed pretreatment covariates, $X$, sufficient for unconfoundedness, if such subsets exist. Here, estimation of these target subsets is considered when the underlying causal structure is unknown. The proposed method is to model the causal structure by a probabilistic graphical model, e.g., a Markov or Bayesian network, estimate this graph from observed data and select the target subsets given the estimated graph. The approach is evaluated by simulation both in a high-dimensional setting where unconfoundedness holds given $X$ and in a setting where unconfoundedness only holds given subsets of $X$. Several common target subsets are investigated and the selected subsets are compared with respect to accuracy in estimating the average causal effect. The proposed method is implemented with existing software that can easily handle high-dimensional data, in terms of large samples and large number of covariates. The results from the simulation study show that, if unconfoundedness holds given $X$, this approach is very successful in selecting the target subsets, outperforming alternative approaches based on random forests and LASSO, and that the subset estimating the target subset containing all causes of outcome yields smallest MSE in the average causal effect estimation.Comment: To appear in Biometric