Covariate measurement error correction methods in mediation analysis with failure time data

Mediation analysis in the presence of continuous exposure measurement error

The difference method is used in mediation analysis to quantify the extent to which a mediator explains the mechanisms underlying the pathway between an exposure and an outcome. In many health science studies, the exposures are almost never measured without error, which can result in biased effect estimates. This article investigates methods for mediation analysis when a continuous exposure is mismeasured. Under a linear exposure measurement error model, we prove that the bias of indirect effect and mediation proportion can go in either direction but the mediation proportion is usually be less biased when the associations between the exposure and its error-prone counterpart are similar with and without adjustment for the mediator. We further propose methods to adjust for exposure measurement error with continuous and binary outcomes. The proposed approaches require a main study/validation study design where in the validation study, data are available for characterizing the relationship between the true exposure and its error-prone counterpart. The proposed approaches are then applied to the Health Professional Follow-up Study, 1986-2016, to investigate the impact of body mass index (BMI) as a mediator for mediating the effect of physical activity on the risk of cardiovascular diseases. Our results reveal that physical activity is significantly associated with a lower risk of cardiovascular disease incidence, and approximately half of the total effect of physical activity is mediated by BMI after accounting for exposure measurement error. Extensive simulation studies are conducted to demonstrate the validity and efficiency of the proposed approaches in finite samples.

Consistent inverse probability of treatment weighted estimation of the average treatment effect with mismeasured time-dependent confounders

In longitudinal studies, the inverse probability of treatment weighted (IPTW) method is commonly employed to estimate the effect of time-dependent treatments on an outcome of interest. However, it has been documented that when the confounders are subject to measurement error, the naive IPTW method which simply ignores measurement error leads to biased treatment effect estimation. In the existing literature, there is a lack of measurement error correction methods that fully remove measurement error effect and produce consistent treatment effect estimation. In this article, we develop a novel consistent IPTW estimation procedure for longitudinal studies. The key step of the proposed method is to use the observed data to construct a corrected function that is unbiased of the unknown IPTW function. Simulation studies reveal that the proposed method outperforms the existing consistent and approximate measurement error correction methods for IPTW estimation of the average treatment effect. Finally, we apply the proposed method to analyze a real dataset.

Analysis of noisy survival data with graphical proportional hazards measurement error models

In survival data analysis, the Cox proportional hazards (PH) model is perhaps the most widely used model to feature the dependence of survival times on covariates. While many inference methods have been developed under such a model or its variants, those models are not adequate for handling data with complex structured covariates. High-dimensional survival data often entail several features: (1) many covariates are inactive in explaining the survival information, (2) active covariates are associated in a network structure, and (3) some covariates are error-contaminated. To hand such kinds of survival data, we propose graphical PH measurement error models and develop inferential procedures for the parameters of interest. Our proposed models significantly enlarge the scope of the usual Cox PH model and have great flexibility in characterizing survival data. Theoretical results are established to justify the proposed methods. Numerical studies are conducted to assess the performance of the proposed methods.

Low-fat dietary pattern and cardiovascular disease: results from the Women's Health Initiative randomized controlled trial

Background: The influence of a low-fat dietary pattern on the cardiovascular health of postmenopausal women continues to be of public health interest.Objective: This report evaluates low-fat dietary pattern influences on cardiovascular disease (CVD) incidence and mortality during the intervention and postintervention phases of the Women's Health Initiative Dietary Modification Trial.Design: Participants comprised 48,835 postmenopausal women aged 50-79 y; 40% were randomly assigned to a low-fat dietary pattern intervention (target of 20% of energy from fat), and 60% were randomly assigned to a usual diet comparison group. The 8.3-y intervention period ended in March 2005, after which >80% of surviving participants consented to additional active follow-up through September 2010; all participants were followed for mortality through 2013. Breast and colorectal cancer were the primary trial outcomes, and coronary heart disease (CHD) and overall CVD were additional designated outcomes.Results: Incidence rates for CHD and total CVD did not differ between the intervention and comparison groups in either the intervention or postintervention period. However, CHD HRs comparing these groups varied strongly with baseline CVD and hypertension status. Participants without prior CVD had an intervention period CHD HR of 0.70 (95% CI: 0.56, 0.87) or 1.04 (95% CI: 0.90, 1.19) if they were normotensive or hypertensive, respectively (P-interaction = 0.003). The CHD benefit among healthy normotensive women was partially offset by an increase in ischemic stroke risk. Corresponding HRs in the postintervention period were close to null. Participants with CVD at baseline (3.4%) had CHD HRs of 1.47 (95% CI: 1.12, 1.93) and 1.61 (95% CI: 1.02, 2.55) in the intervention and postintervention periods, respectively. However, various lines of evidence suggest that results in women with CVD or hypertension at baseline are confounded by postrandomization use of cholesterol-lowering medications.Conclusions: CVD risk in postmenopausal women appears to be sensitive to a change to a low-fat dietary pattern and, among healthy women, includes both CHD benefit and stroke risk. This trial was registered at clinicaltrials.gov as NCT00000611.

Survival analysis with functions of mismeasured covariate histories: the case of chronic air pollution exposure in relation to mortality in the nurses' health study

Environmental epidemiologists are often interested in estimating the effect of functions of time-varying exposure histories, such as the 12-month moving average, in relation to chronic disease incidence or mortality. The individual exposure measurements that comprise such an exposure history are usually mis-measured, at least moderately, and, often, more substantially. To obtain unbiased estimates of Cox model hazard ratios for these complex mis-measured exposure functions, an extended risk set regression calibration method for Cox models is developed and applied to a study of long-term exposure to the fine particulate matter (PM_2.5) component of air pollution in relation to all-cause mortality in the Nurses' Health Study. Simulation studies under several realistic assumptions about the measurement error model and about the correlation structure of the repeated exposure measurements were conducted to assess the finite sample properties of this new method, and found that the method has good performance in terms of finite sample bias reduction and nominal confidence interval coverage.

Estimating and testing high-dimensional mediation effects in epigenetic studies

MOTIVATION

High-dimensional DNA methylation markers may mediate pathways linking environmental exposures with health outcomes. However, there is a lack of analytical methods to identify significant mediators for high-dimensional mediation analysis.

RESULTS

Based on sure independent screening and minimax concave penalty techniques, we use a joint significance test for mediation effect. We demonstrate its practical performance using Monte Carlo simulation studies and apply this method to investigate the extent to which DNA methylation markers mediate the causal pathway from smoking to reduced lung function in the Normative Aging Study. We identify 2 CpGs with significant mediation effects.

AVAILABILITY AND IMPLEMENTATION

R package, source code, and simulation study are available at https://github.com/YinanZheng/HIMA CONTACT: lei.liu@northwestern.edu.

Evaluation of a two-part regression calibration to adjust for dietary exposure measurement error in the Cox proportional hazards model: A simulation study

Dietary questionnaires are prone to measurement error, which bias the perceived association between dietary intake and risk of disease. Short-term measurements are required to adjust for the bias in the association. For foods that are not consumed daily, the short-term measurements are often characterized by excess zeroes. Via a simulation study, the performance of a two-part calibration model that was developed for a single-replicate study design was assessed by mimicking leafy vegetable intake reports from the multicenter European Prospective Investigation into Cancer and Nutrition (EPIC) study. In part I of the fitted two-part calibration model, a logistic distribution was assumed; in part II, a gamma distribution was assumed. The model was assessed with respect to the magnitude of the correlation between the consumption probability and the consumed amount (hereafter, cross-part correlation), the number and form of covariates in the calibration model, the percentage of zero response values, and the magnitude of the measurement error in the dietary intake. From the simulation study results, transforming the dietary variable in the regression calibration to an appropriate scale was found to be the most important factor for the model performance. Reducing the number of covariates in the model could be beneficial, but was not critical in large-sample studies. The performance was remarkably robust when fitting a one-part rather than a two-part model. The model performance was minimally affected by the cross-part correlation.

A bivariate measurement error model for semicontinuous and continuous variables: Application to nutritional epidemiology

Semicontinuous data in the form of a mixture of a large portion of zero values and continuously distributed positive values frequently arise in many areas of biostatistics. This article is motivated by the analysis of relationships between disease outcomes and intakes of episodically consumed dietary components. An important aspect of studies in nutritional epidemiology is that true diet is unobservable and commonly evaluated by food frequency questionnaires with substantial measurement error. Following the regression calibration approach for measurement error correction, unknown individual intakes in the risk model are replaced by their conditional expectations given mismeasured intakes and other model covariates. Those regression calibration predictors are estimated using short-term unbiased reference measurements in a calibration substudy. Since dietary intakes are often "energy-adjusted," e.g., by using ratios of the intake of interest to total energy intake, the correct estimation of the regression calibration predictor for each energy-adjusted episodically consumed dietary component requires modeling short-term reference measurements of the component (a semicontinuous variable), and energy (a continuous variable) simultaneously in a bivariate model. In this article, we develop such a bivariate model, together with its application to regression calibration. We illustrate the new methodology using data from the NIH-AARP Diet and Health Study (Schatzkin et al., 2001, American Journal of Epidemiology 154, 1119-1125), and also evaluate its performance in a simulation study.