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One way to quantify exposure to air pollution and its constituents in epidemiologic studies is to use an individual's nearest monitor. This strategy results in potential inaccuracy in the actual personal exposure, introducing bias in estimating the health effects of air pollution and its constituents, especially when evaluating the causal effects of correlated multi-pollutant constituents measured with correlated error. This paper addresses estimation and inference for the causal effect of one constituent in the presence of other PM2.5 constituents, accounting for measurement error and correlations. We used a linear regression calibration model, fitted with generalized estimating equations in an external validation study, and extended a double/debiased machine learning (DML) approach to correct for measurement error and estimate the effect of interest in the main study. We demonstrated that the DML estimator with regression calibration is consistent and derived its asymptotic variance. Simulations showed that the proposed estimator reduced bias and attained nominal coverage probability across most simulation settings. We applied this method to assess the causal effects of PM2.5 constituents on cognitive function in the Nurses' Health Study and identified two PM2.5 constituents, Br and Mn, that showed a negative causal effect on cognitive function after measurement error correction.

In environmental health research, it is of interest to understand the effect of the neighborhood environment on health. Researchers have shown a protective association between green space around a person's residential address and depression outcomes. In measuring exposure to green space, distance buffers are often used. However, buffer distances differ across studies. Typically, the buffer distance is determined by researchers a priori. It is unclear how to identify an appropriate buffer distance for exposure assessment. To address geographic uncertainty problem for exposure assessment, we present a domain selection algorithm based on the penalized functional linear Cox regression model. The theoretical properties of our proposed method are studied and simulation studies are conducted to evaluate finite sample performances of our method. The proposed method is illustrated in a study of associations of green space exposure with depression and/or antidepressant use in the Nurses' Health Study., Comment: 27 pages, 5 figures

In this paper, we identify the criteria for the selection of the minimal and most efficient covariate adjustment sets for the regression calibration method developed by Carroll, Rupert and Stefanski (CRS, 1992), used to correct bias due to continuous exposure measurement error. We utilize directed acyclic graphs to illustrate how subject matter knowledge can aid in the selection of such adjustment sets. Valid measurement error correction requires the collection of data on any (1) common causes of true exposure and outcome and (2) common causes of measurement error and outcome, in both the main study and validation study. For the CRS regression calibration method to be valid, researchers need to minimally adjust for covariate set (1) in both the measurement error model (MEM) and the outcome model and adjust for covariate set (2) at least in the MEM. In practice, we recommend including the minimal covariate adjustment set in both the MEM and the outcome model. In contrast with the regression calibration method developed by Rosner, Spiegelman and Willet, it is valid and more efficient to adjust for correlates of the true exposure or of measurement error that are not risk factors in the MEM only under CRS method. We applied the proposed covariate selection approach to the Health Professional Follow-up Study, examining the effect of fiber intake on cardiovascular incidence. In this study, we demonstrated potential issues with a data-driven approach to building the MEM that is agnostic to the structural assumptions. We extend the originally proposed estimators to settings where effect modification by a covariate is allowed. Finally, we caution against the use of the regression calibration method to calibrate the true nutrition intake using biomarkers., Comment: 11 pages, 4 tables, 3 figures. arXiv admin note: text overlap with arXiv:2212.00795

To leverage peer influence and increase population behavioral changes, behavioral interventions often rely on peer-based strategies. A common study design that assesses such strategies is the egocentric-network randomized trial (ENRT), in which those receiving the intervention are encouraged to disseminate information to their peers. The Average Spillover Effect (ASpE) measures the impact of the intervention on participants who do not receive it, but whose outcomes may be affected by others who do. The assessment of the ASpE relies on assumptions about, and correct measurement of, interference sets within which individuals may influence one another's outcomes. It can be challenging to properly specify interference sets, such as networks in ENRTs, and when mismeasured, intervention effects estimated by existing methods will be biased. In HIV prevention studies where social networks play an important role in disease transmission, correcting ASpE estimates for bias due to network misclassification is critical for accurately evaluating the full impact of interventions. We combined measurement error and causal inference methods to bias-correct the ASpE estimate for network misclassification in ENRTs, when surrogate networks are recorded in place of true ones, and validation data that relate the misclassified to the true networks are available. We investigated finite sample properties of our methods in an extensive simulation study, and illustrated our methods in the HIV Prevention Trials Network (HPTN) 037 study.

Many public health interventions are conducted in settings where individuals are connected to one another and the intervention assigned to randomly selected individuals may spill over to other individuals they are connected to. In these spillover settings, the effects of such interventions can be quantified in several ways. The average individual effect measures the intervention effect among those directly treated, while the spillover effect measures the effect among those connected to those directly treated. In addition, the overall effect measures the average intervention effect across the study population, over those directly treated along with those to whom the intervention spills over but who are not directly treated. Here, we develop methods for study design with the aim of estimating individual, spillover, and overall effects. In particular, we consider an egocentric network-based randomized design in which a set of index participants is recruited from the population and randomly assigned to treatment, while data are also collected from their untreated network members. We use the potential outcomes framework to define two clustered regression modeling approaches and clarify the underlying assumptions required to identify and estimate causal effects. We then develop sample size formulas for detecting individual, spillover, and overall effects. We investigate the roles of the intra-class correlation coefficient and the probability of treatment allocation on the required number of egocentric networks with a fixed number of network members for each egocentric network and vice-versa., Comment: 30 pages for main text including figures and tables, 5 figures and 3 tables

It is well known that changing the intervention package while a trial is ongoing does not lead to valid inference using standard statistical methods. However, it is often necessary to adapt, tailor, or tweak a complex intervention package in public health implementation trials, especially when the intervention package does not have the desired effect. This article presents conditions under which the resulting analyses remain valid even when the intervention package is adapted while a trial is ongoing. Our results on such Learn-As-you-GO (LAGO) studies extend the theory of LAGO for binary outcomes following a logistic regression model (Nevo, Lok and Spiegelman, 2021) to LAGO for continuous outcomes under flexible conditional mean model. We derive point and interval estimators of the intervention effects and ensure the validity of hypothesis tests for an overall intervention effect. We develop a confidence set for the optimal intervention package, which achieves a pre-specified mean outcome while minimizing cost, and confidence bands for the mean outcome under all intervention package compositions. This work will be useful for the design and analysis of large-scale intervention trials where the intervention package is adapted, tailored, or tweaked while the trial is ongoing., Comment: 65 pages, 15 tables

Mediation analysis is widely used in health science research to evaluate the extent to which an intermediate variable explains an observed exposure-outcome relationship. However, the validity of analysis can be compromised when the exposure is measured with error. Motivated by the Health Professionals Follow-up Study (HPFS), we investigate the impact of exposure measurement error on assessing mediation with a survival outcome, based on the Cox proportional hazards outcome model. When the outcome is rare and there is no exposure-mediator interaction, we show that the uncorrected estimators of the natural indirect and direct effects can be biased into either direction, but the uncorrected estimator of the mediation proportion is approximately unbiased as long as the measurement error is not large or the mediator-exposure association is not strong. We develop ordinary regression calibration and risk set regression calibration approaches to correct the exposure measurement error-induced bias when estimating mediation effects and allowing for an exposure-mediator interaction in the Cox outcome model. The proposed approaches require a validation study to characterize the measurement error process. We apply the proposed approaches to the HPFS (1986-2016) to evaluate extent to which reduced body mass index mediates the protective effect of vigorous physical activity on the risk of cardiovascular diseases, and compare the finite-sample properties of the proposed estimators via simulations.

Regression calibration as developed by Rosner, Spiegelman and Willet is used to correct the bias in effect estimates due to measurement error in continuous exposures. The method involves two models: a measurement error model (MEM) relating the mismeasured exposure to the true exposure and an outcome model relating the mismeasured exposure to outcome. However, no comprehensive guidance exists for determining which covariates should be included in each model. In this paper, we investigate the selection of the minimal and most efficient covariate adjustment sets under a causal inference framework. We show that in order to correct for the measurement error, researchers must adjust for, in both MEM and outcome model, any common causes (1) of true exposure and the outcome and (2) of measurement error and the outcome. When such variable(s) are only available in the main study, researchers should still adjust for them in the outcome model to reduce bias, provided that these covariates are at most weakly associated with measurement error. We also show that adjusting for so called prognostic variables that are independent of true exposure and measurement error in outcome model, may increase efficiency, while adjusting for any covariates that are associated only with true exposure generally results in efficiency loss in realistic settings. We apply the proposed covariate selection approach to the Health Professional Follow-up Study dataset to study the effect of fiber intake on cardiovascular disease. Finally, we extend the originally proposed estimators to a non-parametric setting where effect modification by covariates is allowed., Comment: 11 pages, 3 figures

This paper considers the design of observational longitudinal studies with a continuous response and a binary time-invariant exposure, where, typically, the exposure is unbalanced, the mean response in the two groups differs at baseline and the measurement times might not be the same for all participants. We consider group differences that are constant and those that increase linearly with time. We study power, number of study participants (N) and number of repeated measures (r), and provide formulas for each quantity when the other two are fixed, for compound symmetry, damped exponential and random intercepts and slopes covariances. When both N and r can be chosen by the investigator, we study the optimal combination for maximizing power subject to a cost constraint and minimizing cost for fixed power. Intuitive parameterizations are used for all quantities. All calculations are implemented in freely available software.

The estimation of the potential impact fraction (including the population attributable fraction) with continuous exposure data frequently relies on strong distributional assumptions. However, these assumptions are often violated if the underlying exposure distribution is unknown or if the same distribution is assumed across time or space. Nonparametric methods to estimate the potential impact fraction are available for cohort data, but no alternatives exist for cross-sectional data. In this article, we discuss the impact of distributional assumptions in the estimation of the population impact fraction, showing that under an infinite set of possibilities, distributional violations lead to biased estimates. We propose nonparametric methods to estimate the potential impact fraction for aggregated (mean and standard deviation) or individual data (e.g. observations from a cross-sectional population survey), and develop simulation scenarios to compare their performance against standard parametric procedures. We illustrate our methodology on an application of sugar-sweetened beverage consumption on incidence of type 2 diabetes. We also present an R package pifpaf to implement these methods.

Background: Although the missing covariate indicator method (MCIM) has been shown to be biased under extreme conditions, the degree and determinants of bias have not been formally assessed. Methods: We derived the formula for the relative bias in the MCIM and systematically investigated conditions under which bias arises. Results: We found that the extent of bias is independent of both the disease rate and the exposure-outcome association, but is a function of 5 parameters: exposure and covariate prevalences, covariate missingness proportion, and associations of covariate with exposure and outcome. The MCIM was unbiased when the missing covariate is a risk factor for the outcome but not a confounder. The average median relative bias was zero across each of the parameters over a wide range of values considered. When missingness was no greater than 50%, less than 5% of the scenarios considered had relative bias greater than 10%. In several analyses of the Harvard cohort studies, the MCIM produced materially the same results as the multiple imputation method. Conclusion: The MCIM is nearly valid almost always in settings typically encountered in epidemiology and its continued use is recommended, unless the covariate is missing in an extreme proportion or acts as a strong confounder.

The natural indirect effect (NIE) and mediation proportion (MP) are two measures of primary interest in mediation analysis. The standard approach for estimating NIE and MP is through the product method, which involves a model for the outcome conditional on the mediator and exposure and another model describing the exposure-mediator relationship. The purpose of this article is to comprehensively develop and investigate the finite-sample performance of NIE and MP estimators via the product method. With four common data types, we propose closed-form interval estimators via the theory of estimating equations and multivariate delta method, and evaluate its empirical performance relative to the bootstrap approach. In addition, we have observed that the rare outcome assumption is frequently invoked to approximate the NIE and MP with a binary outcome, although this approximation may lead to non-negligible bias when the outcome is common. We therefore introduce the exact expressions for NIE and MP with a binary outcome without the rare outcome assumption and compare its performance with the approximate estimators. Based upon these theoretical developments and empirical studies, we offer several practical recommendations to inform practice. An R package mediateP is developed to implement the methods for point and variance estimation discussed in this paper.

Background and objective: The stepped wedge cluster randomized trial is a study design increasingly used for public health intervention evaluations. Most previous literature focuses on power calculations for this particular type of cluster randomized trials for continuous outcomes, along with an approximation to this approach for binary outcomes. Although not accurate for binary outcomes, it has been widely used. To improve the approximation for binary outcomes, two new methods for stepped wedge designs (SWDs) of binary outcomes have recently been published. However, these new methods have not been implemented in publicly available software. The objective of this paper is to present power calculation software for SWDs in various settings for both continuous and binary outcomes. Methods: We have developed a SAS macro %swdpwr and an R package swdpwr for power calculation in SWDs. Different scenarios including cross-sectional and cohort designs, binary and continuous outcomes, marginal and conditional models, three link functions, with and without time effects are accommodated in this software. Results: swdpwr provides an efficient tool to support investigators in the design and analysis of stepped wedge cluster randomized trails. swdpwr addresses the implementation gap between newly proposed methodology and their application to obtain more accurate power calculations in SWDs. Conclusions: This user-friendly software makes the new methods more accessible and incorporates as many variations as currently available, which were not supported in other related packages. swdpwr is implemented under two platforms: SAS and R, satisfying the needs of investigators from various backgrounds., Comment: 29 pages, 4 figures

Some interventions may include important spillover or dissemination effects between study participants. For example, vaccines, cash transfers, and education programs may exert a causal effect on participants beyond those to whom individual treatment is assigned. In a recent paper, Buchanan et al. provide a causal definition of the "individual effect" of an intervention in networks of people who inject drugs. In this short note, we discuss the interpretation of the individual effect when a spillover or dissemination effect exists.

The standard Cox model in survival analysis assumes that the covariate effect is constant across the entire covariate domain. However, in many applications, there is interest in considering the possibility that the covariate of main interest is subject to a threshold effect: a change in the slope at a certain point within the covariate domain. Often, the value of this threshold is unknown and need to be estimated. In addition, often, the covariate of interest is not measured exactly, but rather is subject to some degree of measurement error. In this paper, we discuss estimation of the model parameters under an independent additive error model where the covariate of interesting is measured with error and the potential threshold value in this covariate is unknown. As in earlier work which discussed the case of konwn threshold, we study the performance of several bias correction methods: two versions of regression calibration (RC1 and RC2), two versions of the fitting a model for the induced relative risk (RR1 and RR2), maximum pseudo-partial likelihood estimator (MPPLE) and simulation-extrapolation (SIMEX). These correction methods are compared with the naive estimator. We develop the relevant theory, present a simulation study comparing the several correction methods, and illustrate the use of the bias correction methods in data from the Nurses Health Study (NHS) concerning the relationship between chronic air pollution exposure to particulate matter of diameter 10 $\mu$m or less (PM$_{10}$). The simulation results suggest that the best overall choice of bias correction method is either the RR2 method or the MPPLE method., Comment: 26 pages. arXiv admin note: text overlap with arXiv:1808.07662

The Cox regression model is a popular model for analyzing the relationship between a covariate and a survival endpoint. The standard Cox model assumes a constant covariate effect across the entire covariate domain. However, in many epidemiological and other applications, the covariate of main interest is subject to a threshold effect: a change in the slope at a certain point within the covariate domain. Often, the covariate of interest is subject to some degree of measurement error. In this paper, we study measurement error correction in the case where the threshold is known. Several bias correction methods are examined: two versions of regression calibration (RC1 and RC2, the latter of which is new), two methods based on the induced relative risk under a rare event assumption (RR1 and RR2, the latter of which is new), a maximum pseudo-partial likelihood estimator (MPPLE), and simulation-extrapolation (SIMEX). We develop the theory, present simulations comparing the methods, and illustrate their use on data concerning the relationship between chronic air pollution exposure to particulate matter PM10 and fatal myocardial infarction (Nurses Health Study (NHS)), and on data concerning the effect of a subject's long-term underlying systolic blood pressure level on the risk of cardiovascular disease death (Framingham Heart Study (FHS)). The simulations indicate that the best methods are RR2 and MPPLE.

In learn-as-you-go (LAGO) adaptive studies, the intervention is a complex package consisting of multiple components, and is adapted in stages during the study based on past outcome data. This design formalizes standard practice, and desires for practice, in public health intervention studies. An effective intervention package is sought, while minimizing intervention package cost. When analyzing data from a learn-as-you-go study, the interventions in later stages depend upon the outcomes in the previous stages, violating standard statistical theory. We develop methods for estimating the intervention effects in a LAGO study. We prove consistency and asymptotic normality using a novel coupling argument, ensuring the validity of the test for the hypothesis of no overall intervention effect. We develop a confidence set for the optimal intervention package and confidence bands for the success probabilities under alternative package compositions. We illustrate our methods in the BetterBirth Study, which aimed to improve maternal and neonatal outcomes among 157,689 births in Uttar Pradesh, India through a complex, multi-component intervention package.