Regression calibration for models with two predictor variables measured with error and their interaction, using instrumental variables and longitudinal data

Addressing unmeasured confounders in cohort studies: Instrumental variable method for a time-fixed exposure on an outcome trajectory

Instrumental variable methods, which handle unmeasured confounding by targeting the part of the exposure explained by an exogenous variable not subject to confounding, have gained much interest in observational studies. We consider the very frequent setting of estimating the unconfounded effect of an exposure measured at baseline on the subsequent trajectory of an outcome repeatedly measured over time. We didactically explain how to apply the instrumental variable method in such setting by adapting the two-stage classical methodology with (1) the prediction of the exposure according to the instrumental variable, (2) its inclusion into a mixed model to quantify the exposure association with the subsequent outcome trajectory, and (3) the computation of the estimated total variance. A simulation study illustrates the consequences of unmeasured confounding in classical analyses and the usefulness of the instrumental variable approach. The methodology is then applied to 6224 participants of the 3C cohort to estimate the association of type-2 diabetes with subsequent cognitive trajectory, using 42 genetic polymorphisms as instrumental variables. This contribution shows how to handle endogeneity when interested in repeated outcomes, along with a R implementation. However, it should still be used with caution as it relies on instrumental variable assumptions hardly testable in practice.

Health effects of concurrent ambient and tobacco smoke-derived particle exposures at low concentrations in children with asthma

Exposure to particulate matter less than 2.5 microns from either ambient pollution (AMB-PM_2.5) or secondhand smoke (SHS-PM_2.5) have been associated with asthma worsening, but there is little information on effects and relative potency with concurrent exposures. We studied health effects of concurrent exposures to AMB-PM_2.5 and SHS-PM_2.5 over a 6-year period in schoolchildren with asthma. Regression calibration with instrumental variables (RCIV) was utilized to estimate effects of personal exposure to low-level SHS and AMB-PM_2.5 on daily albuterol usage and urinary leukotriene E4 (uLTE₄; a biomarker of asthma-related inflammation) using urine cotinine and concentrations from fixed and personal pollution monitors. Each IQR increase in SHS-PM_2.5 exposure was associated with a 6.7% increase (95% CI: 1.0-12.8%) in uLTE₄ on the same day and 9.4% increase (95% CI: -2.6 to 22.7%) in albuterol use the next day, when children were co-exposed to mean levels of AMB-PM_2.5. The dose-response relationship between health outcomes and one pollutant was higher at lower levels of the other pollutant. For example, at lower levels of predicted SHS-PM_2.5 exposure, increases in health outcomes per IQR increase in AMB-PM_2.5 ranged between 2 and 5%, but were negligible at higher SHS-PM_2.5 levels. Comparing at equivalent co-exposure levels, SHS-PM_2.5 was 1.6 times more potent than AMB-PM_2.5 for uLTE₄ (95% CI: 1.1-2.3); estimates for albuterol usage were similar but less significant. Effects at mean co-exposure levels were closer [SHS to AMB-PM_2.5 potency ratio = 1.2 (95% CI: 0.9-1.5) for uLTE₄ and 1.2 (95% CI: 0.7-1.9) for albuterol usage]. In summary, concurrent exposure to relatively low levels of SHS and AMB-PM_2.5 were associated with health outcomes in asthmatic schoolchildren. Dose responses varied with changes in the relative amounts of each pollutant; SHS-PM_2.5 was observed to be more potent than AMB-PM_2.5 when co-exposure levels were equivalent.

Multipollutant measurement error in air pollution epidemiology studies arising from predicting exposures with penalized regression splines

Air pollution epidemiology studies are trending towards a multi-pollutant approach. In these studies, exposures at subject locations are unobserved and must be predicted using observed exposures at misaligned monitoring locations. This induces measurement error, which can bias the estimated health effects and affect standard error estimates. We characterize this measurement error and develop an analytic bias correction when using penalized regression splines to predict exposure. Our simulations show bias from multi-pollutant measurement error can be severe, and in opposite directions or simultaneously positive or negative. Our analytic bias correction combined with a non-parametric bootstrap yields accurate coverage of 95% confidence intervals. We apply our methodology to analyze the association of systolic blood pressure with PM2.5 and NO2 in the NIEHS Sister Study. We find that NO2 confounds the association of systolic blood pressure with PM2.5 and vice versa. Elevated systolic blood pressure was significantly associated with increased PM2.5 and decreased NO2. Correcting for measurement error bias strengthened these associations and widened 95% confidence intervals.

The Orthogonally Partitioned EM Algorithm: Extending the EM Algorithm for Algorithmic Stability and Bias Correction Due to Imperfect Data

We propose an extension of the EM algorithm that exploits the common assumption of unique parameterization, corrects for biases due to missing data and measurement error, converges for the specified model when standard implementation of the EM algorithm has a low probability of convergence, and reduces a potentially complex algorithm into a sequence of smaller, simpler, self-contained EM algorithms. We use the theory surrounding the EM algorithm to derive the theoretical results of our proposal, showing that an optimal solution over the parameter space is obtained. A simulation study is used to explore the finite sample properties of the proposed extension when there is missing data and measurement error. We observe that partitioning the EM algorithm into simpler steps may provide better bias reduction in the estimation of model parameters. The ability to breakdown a complicated problem in to a series of simpler, more accessible problems will permit a broader implementation of the EM algorithm, permit the use of software packages that now implement and/or automate the EM algorithm, and make the EM algorithm more accessible to a wider and more general audience.

Regression calibration with instrumental variables for longitudinal models with interaction terms, and application to air pollution studies

In this paper, we derive forms of estimators and associated variances for regression calibration with instrumental variables in longitudinal models that include interaction terms between two unobservable predictors and interactions between these predictors and covariates not measured with error; the inclusion of the latter interactions generalize results we previously reported. The methods are applied to air pollution and health data collected on children with asthma. The new methods allow for the examination of how the relationship between health outcome leukotriene E4 (LTE₄, a biomarker of inflammation) and two unobservable pollutant exposures and their interaction are modified by the presence or absence of upper respiratory infections. The pollutant variables include secondhand smoke and ambient (outdoor) fine particulate matter. Simulations verify the accuracy of the proposed methods under various conditions.