Measurement error correction for ambient PM2.5 exposure using stratified regression calibration: Effects on all-cause mortality

BACKGROUND

Previous studies on the impact of measurement error for PM2.5 were mostly simulation studies, did not control for other pollutants, or used a single regression calibration model to correct for measurement error. However, the relationship between actual and error-prone PM2.5 concentration may vary by time and region. We aim to correct the measurement error of PM2.5 predictions using stratified regression calibration and investigate how the measurement error biases the association between PM2.5 and mortality in the Medicare Cohort.

METHODS

The "gold-standard" measurements of PM2.5 were defined as daily monitoring data. We regressed daily monitoring PM2.5 on modeled PM2.5 using the simple linear regression by strata of season, elevation, census division and time period. Calibrated PM2.5 was calculated with stratum-specific calibration parameters β0 (intercept) and β1 (slope) for each strata and aggregated to annual level. Associations between calibrated and error-prone annual PM2.5 and all-cause mortality among Medicare beneficiaries were estimated with Quasi-Poisson regression models.

RESULTS

Across 208 strata, the median of β0 and β1 were 0.62 (25% 0.0.20, 75% 1.06) and 0.93 (25% 0.87, 75% 0.99). From calibrated and error-prone PM2.5 data, we estimated that each 10 μg/m3 increase in PM2.5 was respectively associated with 4.9% (95%CI 4.6-5.2) and 4.6% (95%CI 4.4-4.9) increases in the mortality rate among Medicare beneficiaries, conditional on confounders.

CONCLUSIONS

Regression calibration parameters of PM2.5 varied by time and region. Using error-prone measures of PM2.5 underestimated the association between PM2.5 and all-cause mortality. Modern exposure models produce relatively small bias.

Sensitivity analysis for random measurement error using regression calibration and simulation-extrapolation

Objective

Sensitivity analysis for random measurement error can be applied in the absence of validation data by means of regression calibration and simulation-extrapolation. These have not been compared for this purpose.

Study design and setting

A simulation study was conducted comparing the performance of regression calibration and simulation-extrapolation for linear and logistic regression. The performance of the two methods was evaluated in terms of bias, mean squared error (MSE) and confidence interval coverage, for various values of reliability of the error-prone measurement (0.05-0.91), sample size (125-4000), number of replicates (2-10), and R-squared (0.03-0.75). It was assumed that no validation data were available about the error-free measures, while correct information about the measurement error variance was available.

Results

Regression calibration was unbiased while simulation-extrapolation was biased: median bias was 0.8% (interquartile range (IQR): -0.6;1.7%), and -19.0% (IQR: -46.4;-12.4%), respectively. A small gain in efficiency was observed for simulation-extrapolation (median MSE: 0.005, IQR: 0.004;0.006) versus regression calibration (median MSE: 0.006, IQR: 0.005;0.009). Confidence interval coverage was at the nominal level of 95% for regression calibration, and smaller than 95% for simulation-extrapolation (median coverage: 85%, IQR: 73;93%). The application of regression calibration and simulation-extrapolation for a sensitivity analysis was illustrated using an example of blood pressure and kidney function.

Conclusion

Our results support the use of regression calibration over simulation-extrapolation for sensitivity analysis for random measurement error.

Mecor: An R package for measurement error correction in linear regression models with a continuous outcome

Measurement error in a covariate or the outcome of regression models is common, but is often ignored, even though measurement error can lead to substantial bias in the estimated covariate-outcome association. While several texts on measurement error correction methods are available, these methods remain seldomly applied. To improve the use of measurement error correction methodology, we developed mecor, an R package that implements measurement error correction methods for regression models with a continuous outcome. Measurement error correction requires information about the measurement error model and its parameters. This information can be obtained from four types of studies, used to estimate the parameters of the measurement error model: an internal validation study, a replicates study, a calibration study and an external validation study. In the package mecor, regression calibration methods and a maximum likelihood method are implemented to correct for measurement error in a continuous covariate in regression analyses. Additionally, methods of moments methods are implemented to correct for measurement error in the continuous outcome in regression analyses. Variance estimation of the corrected estimators is provided in closed form and using the bootstrap.

Analysis in case-control sequencing association studies with different sequencing depths

With the advent of next-generation sequencing, investigators have access to higher quality sequencing data. However, to sequence all samples in a study using next generation sequencing can still be prohibitively expensive. One potential remedy could be to combine next generation sequencing data from cases with publicly available sequencing data for controls, but there could be a systematic difference in quality of sequenced data, such as sequencing depths, between sequenced study cases and publicly available controls. We propose a regression calibration (RC)-based method and a maximum-likelihood method for conducting an association study with such a combined sample by accounting for differential sequencing errors between cases and controls. The methods allow for adjusting for covariates, such as population stratification as confounders. Both methods control type I error and have comparable power to analysis conducted using the true genotype with sufficiently high but different sequencing depths. We show that the RC method allows for analysis using naive variance estimate (closely approximates true variance in practice) and standard software under certain circumstances. We evaluate the performance of the proposed methods using simulation studies and apply our methods to a combined data set of exome sequenced acute lung injury cases and healthy controls from the 1000 Genomes project.

Calibration of the Active Australia questionnaire and application to a logistic regression model

OBJECTIVES

To estimate the extent of measurement error in the Active Australia questionnaire, and to examine the impact of measurement error on the association of moderate-vigorous physical activity (MVPA) with obesity.

DESIGN

Accelerometer Validation Study, cross-sectional; data from the third wave of a prospective cohort (Australian Diabetes, Obesity, and Lifestyle (AusDiab) Study)).

METHODS

Self-reported physical activity data were obtained from 4005 participants of the third wave of the AusDiab study via the Active Australia questionnaire. Accelerometer-derived physical activity data were obtained from a subsample of 670 participants. Validity coefficients and attenuation factors were estimated from a measurement error model. A regression calibration method was applied to a logistic regression model examining the association between self-reported MVPA and obesity to adjust observed odds ratios (OR) for measurement error.

RESULTS

The validity coefficient was 0.35 (0.28, 0.43) and the attenuation factor was 0.16 (0.13, 0.20) in models adjusted for age and sex. The uncorrected OR for obesity for 210min/week of MVPA (50th percentile) relative to 80min/week (25th percentile) was 0.87 (0.85, 0.90). The attenuation factor was used to adjust this OR for measurement error, giving a corrected OR of 0.43 (0.32, 0.55).

CONCLUSIONS

Substantial measurement error (relative to accelerometry) was evident in the Active Australia questionnaire, leading to attenuation of the association of MVPA with obesity. A regression-calibration method can be used to adjust risk estimates for associations between self-reported MVPA and health-related outcomes for measurement error specific to self-report. These corrected risk estimates reflect associations that would be expected if MVPA were measured by accelerometry.

Approaches to addressing missing values, measurement error, and confounding in epidemiologic studies

OBJECTIVES

Epidemiologic studies often suffer from incomplete data, measurement error (or misclassification), and confounding. Each of these can cause bias and imprecision in estimates of exposure-outcome relations. We describe and compare statistical approaches that aim to control all three sources of bias simultaneously.

STUDY DESIGN AND SETTING

We illustrate four statistical approaches that address all three sources of bias, namely, multiple imputation for missing data and measurement error, multiple imputation combined with regression calibration, full information maximum likelihood within a structural equation modeling framework, and a Bayesian model. In a simulation study, we assess the performance of the four approaches compared with more commonly used approaches that do not account for measurement error, missing values, or confounding.

RESULTS

The results demonstrate that the four approaches consistently outperform the alternative approaches on all performance metrics (bias, mean squared error, and confidence interval coverage). Even in simulated data of 100 subjects, these approaches perform well.

CONCLUSION

There can be a large benefit of addressing measurement error, missing values, and confounding to improve the estimation of exposure-outcome relations, even when the available sample size is relatively small.

Immune correlates analysis using vaccinees from test negative designs

Determining the effect of vaccine-induced immune response on disease risk is an important goal of vaccinology. Typically, immune correlates analyses are conducted prospectively with immune response measured shortly after vaccination and subsequent disease status regressed on immune response. In outbreaks and rare disease settings, collecting samples from all vaccinees is not feasible. The test negative design is a retrospective design used to measure vaccine efficacy where symptomatic individuals who present at a clinic are assessed for relevant disease (cases) or some other disease (controls) and vaccination status ascertained. This article proposes that test negative vaccinees have immune response to vaccine assessed both for relevant (e.g., Ebola) and irrelevant (e.g., vector) proteins. If the latter immune response is unaffected by active (Ebola) infection, and is correlated with the relevant immune response, it can serve as a proxy for the immune response of interest proximal to infection. We show that logistic regression using imputed immune response as the covariate and case disease as outcome can estimate the prospective immune response slope and detail the assumptions needed for unbiased inference. The method is evaluated by simulation under various scenarios including constant and decaying immune response. A simulated dataset motivated by ring vaccination for an ongoing Ebola outbreak is analyzed.

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.

Relying on repeated biospecimens to reduce the effects of classical-type exposure measurement error in studies linking the exposome to health

The exposome calls for assessing numerous exposures, typically using biomarkers with varying amounts of measurement error, which can be assumed to be of classical type. We evaluated the impact of classical-type measurement error on the performance of exposome-health studies, and the efficiency of two measurement error correction methods relying on the collection of repeated biospecimens: within-subject biospecimens pooling and regression calibration. In a simulation study, we generated 237 exposures from a realistic correlation matrix, with various amounts of classical-type measurement error, and a continuous health outcome linearly influenced by exposures. Measurement error decreased the sensitivity to identify exposures influencing health from a value of 75% down to 46%, increased false discovery proportion from 26% to 49% and increased attenuation bias in the slope of true predictors from 45% to 66%. Assuming that repeated biospecimens were available, within-subject pooling and regression calibration improved sensitivity (which increased to 63%), false discovery proportion (down to 37%) and bias (down to 49%) compared to an error-prone study with a single biospecimen per subject. Performances were poorer for the exposures with the largest amount of measurement error, and increased with the number of available biospecimens. Relying on repeated biospecimens only for the exposures with the largest amount of measurement error provided similar performance improvement. Exposome studies relying on spot exposure biospecimens suffer from decreased performances if some biomarkers suffer from measurement error due to their temporal variability; performances can be improved by collecting repeated biospecimens per subject, in particular for non persistent chemicals.

Using enhanced regression calibration to combine dietary intake estimates from 24 h recall and FFQ reduces bias in diet-disease associations

OBJECTIVE

To illustrate the impact of combining 24 h recall (24hR) and FFQ estimates using regression calibration (RC) and enhanced regression calibration (ERC) on diet-disease associations.

SETTING

Wageningen area, the Netherlands, 2011-2013.

DESIGN

Five approaches for obtaining self-reported dietary intake estimates of protein and K were compared: (i) uncorrected FFQ intakes (FFQ); (ii) uncorrected average of two 24hR ( $\overline {\rm R}$ ); (iii) average of FFQ and $\overline {\rm R}$ ( ${\overline {\rm F}}\,\overline {\rm R}}$ ); (iv) RC from regression of 24hR v. FFQ; and (v) ERC by adding individual random effects to the RC approach. Empirical attenuation factors (AF) were derived by regression of urinary biomarker measurements v. the resulting intake estimates.

PARTICIPANTS

Data of 236 individuals collected within the National Dietary Assessment Reference Database.

RESULTS

Both FFQ and 24hR dietary intake estimates were measured with substantial error. Using statistical techniques to correct for measurement error (i.e. RC and ERC) reduced bias in diet-disease associations as indicated by their AF approaching 1 (RC 1·14, ERC 0·95 for protein; RC 1·28, ERC 1·34 for K). The larger sd and narrower 95% CI of AF obtained with ERC compared with RC indicated that using ERC has more power than using RC. However, the difference in AF between RC and ERC was not statistically significant, indicating no significantly better de-attenuation by using ERC compared with RC. AF larger than 1, observed for the ERC for K, indicated possible overcorrection.

CONCLUSIONS

Our study highlights the potential of combining FFQ and 24hR data. Using RC and ERC resulted in less biased associations for protein and K.

Methods to account for uncertainties in exposure assessment in studies of environmental exposures

BACKGROUND

Accurate exposure estimation in environmental epidemiological studies is crucial for health risk assessment. Failure to account for uncertainties in exposure estimation could lead to biased results in exposure-response analyses. Assessment of the effects of uncertainties in exposure estimation on risk estimates received a lot of attention in radiation epidemiology and in several studies of diet and air pollution. The objective of this narrative review is to examine the commonly used statistical approaches to account for exposure estimation errors in risk analyses and to suggest how each could be applied in environmental epidemiological studies.

MAIN TEXT

We review two main error types in estimating exposures in epidemiological studies: shared and unshared errors and their subtypes. We describe the four main statistical approaches to adjust for exposure estimation uncertainties (regression calibration, simulation-extrapolation, Monte Carlo maximum likelihood and Bayesian model averaging) along with examples to give readers better understanding of their advantages and limitations. We also explain the advantages of using a 2-dimensional Monte-Carlo (2DMC) simulation method to quantify the effect of uncertainties in exposure estimates using full-likelihood methods. For exposures that are estimated independently between subjects and are more likely to introduce unshared errors, regression calibration and SIMEX methods are able to adequately account for exposure uncertainties in risk analyses. When an uncalibrated measuring device is used or estimation parameters with uncertain mean values are applied to a group of people, shared errors could potentially be large. In this case, Monte Carlo maximum likelihood and Bayesian model averaging methods based on estimates of exposure from the 2DMC simulations would work well. The majority of reviewed studies show relatively moderate changes (within 100%) in risk estimates after accounting for uncertainties in exposure estimates, except for the two studies which doubled/tripled naïve estimates.

CONCLUSIONS

In this paper, we demonstrate various statistical methods to account for uncertain exposure estimates in risk analyses. The differences in the results of various adjustment methods could be due to various error structures in datasets and whether or not a proper statistical method was applied. Epidemiological studies of environmental exposures should include exposure-response analyses accounting for uncertainties in exposure estimates.

Impact of exposure to phenols during early pregnancy on birth weight in two Canadian cohort studies subject to measurement errors

BACKGROUND

It is of interest to know whether early pregnancy exposure to phenols such as bisphenol-A (BPA) or triclosan (TCS) negatively impacts birth weight outcomes. Exposure to these chemicals is widespread in the Canadian population but obtaining accurate measurements of average exposure is difficult because these chemicals are rapidly excreted from the body, causing body levels to fluctuate both within and between days, as observed in a recent Canadian study (P4). This measurement error can attenuate the estimated effects of exposures.

METHODS

Data from two Canadian cohort studies, the Plastics and Personal-care Products use in Pregnancy (P4) Study and the Maternal-Infant Research on Environmental Chemicals (MIREC) Study, such that all participants with complete BPA or TCS exposure and outcome data were used (MIREC n = 1822, P4 n = 68). We used regression calibration to correct for the attenuating effects of exposure measurement error when modeling the effect of first trimester BPA or TCS exposure on four birth weight outcomes: birth weight (BW), low birth weight (LBW), small for gestational age (SGA) and large for gestational age (LGA). Specific gravity, time of day, and time since last urine void were also controlled in the analysis.

RESULTS

TCS exposure has a marginally significant association with SGA only with odds ratio 0.87 and 95% confidence interval (0.74, 1.00). It also has a marginally significant association with LGA in male offspring with odds ratio 1.11 and 95% confidence interval (1.00, 1.25). The effects of BPA on the four birth outcomes were insignificant.

CONCLUSIONS

Increased TCS exposure during pregnancy is marginally associated with decreased odds of having SGA offspring. It is possibly associated with decreased BW in males and decreased odds of LBW, though these associations were not present in measurement error corrected models. TCS is possibly associated with increased odds in male offspring of being LGA, though this relationship was not present in models not corrected for measurement error. The study finds no significant effects of BPA on birth weight outcomes, which may be due to more severe measurement error in a single observation of BPA.

MALDI-TOF peptidomic analysis of serum and post-prostatic massage urine specimens to identify prostate cancer biomarkers

Background

Lower urinary tract symptoms (LUTS) and prostate specific antigen-based parameters seem to have only a limited utility for the differential diagnosis of prostate cancer (PCa). MALDI-TOF/MS peptidomic profiling could be a useful diagnostic tool for biomarker discovery, although reproducibility issues have limited its applicability until now. The current study aimed to evaluate a new MALDI-TOF/MS candidate biomarker.

Methods

Within- and between-subject variability of MALDI-TOF/MS-based peptidomic urine and serum analyses were evaluated in 20 and 15 healthy donors, respectively. Normalizations and approaches for accounting below limit of detection (LOD) values were utilized to enhance reproducibility, while Monte Carlo experiments were performed to verify whether measurement error can be dealt with LOD data. Post-prostatic massage urine and serum samples from 148 LUTS patients were analysed using MALDI-TOF/MS. Regression-calibration and simulation and extrapolation methods were used to derive the unbiased association between peptidomic features and PCa.

Results

Although the median normalized peptidomic variability was 24.9%, the within- and between-subject variability showed that median normalization, LOD adjustment, and log₂ data transformation were the best combination in terms of reliability; in measurement error conditions, intraclass correlation coefficient was a reliable estimate when the LOD/2 was substituted for below LOD values. In the patients studied, 43 peptides were shared by the urine and serum, and several features were found to be associated with PCa. Only few serum features, however, show statistical significance after the multiple testing procedures were completed. Two serum fragmentation patterns corresponded to the complement C4-A.

Conclusions

MALDI-TOF/MS serum peptidome profiling was more efficacious with respect to post-prostatic massage urine analysis in discriminating PCa.

Electronic supplementary material

The online version of this article (10.1186/s12014-018-9199-8) contains supplementary material, which is available to authorized users.

Incorporating Measurement Error from Modeled Air Pollution Exposures into Epidemiological Analyses

PURPOSE OF REVIEW

Outdoor air pollution exposures used in epidemiological studies are commonly predicted from spatiotemporal models incorporating limited measurements, temporal factors, geographic information system variables, and/or satellite data. Measurement error in these exposure estimates leads to imprecise estimation of health effects and their standard errors. We reviewed methods for measurement error correction that have been applied in epidemiological studies that use model-derived air pollution data.

RECENT FINDINGS

We identified seven cohort studies and one panel study that have employed measurement error correction methods. These methods included regression calibration, risk set regression calibration, regression calibration with instrumental variables, the simulation extrapolation approach (SIMEX), and methods under the non-parametric or parameter bootstrap. Corrections resulted in small increases in the absolute magnitude of the health effect estimate and its standard error under most scenarios. Limited application of measurement error correction methods in air pollution studies may be attributed to the absence of exposure validation data and the methodological complexity of the proposed methods. Future epidemiological studies should consider in their design phase the requirements for the measurement error correction method to be later applied, while methodological advances are needed under the multi-pollutants setting.

A zero-augmented generalized gamma regression calibration to adjust for covariate measurement error: A case of an episodically consumed dietary intake

Measurement error in exposure variables is a serious impediment in epidemiological studies that relate exposures to health outcomes. In nutritional studies, interest could be in the association between long-term dietary intake and disease occurrence. Long-term intake is usually assessed with food frequency questionnaire (FFQ), which is prone to recall bias. Measurement error in FFQ-reported intakes leads to bias in parameter estimate that quantifies the association. To adjust for bias in the association, a calibration study is required to obtain unbiased intake measurements using a short-term instrument such as 24-hour recall (24HR). The 24HR intakes are used as response in regression calibration to adjust for bias in the association. For foods not consumed daily, 24HR-reported intakes are usually characterized by excess zeroes, right skewness, and heteroscedasticity posing serious challenge in regression calibration modeling. We proposed a zero-augmented calibration model to adjust for measurement error in reported intake, while handling excess zeroes, skewness, and heteroscedasticity simultaneously without transforming 24HR intake values. We compared the proposed calibration method with the standard method and with methods that ignore measurement error by estimating long-term intake with 24HR and FFQ-reported intakes. The comparison was done in real and simulated datasets. With the 24HR, the mean increase in mercury level per ounce fish intake was about 0.4; with the FFQ intake, the increase was about 1.2. With both calibration methods, the mean increase was about 2.0. Similar trend was observed in the simulation study. In conclusion, the proposed calibration method performs at least as good as the standard method.

Spatial regression with covariate measurement error: A semiparametric approach

Spatial data have become increasingly common in epidemiology and public health research thanks to advances in GIS (Geographic Information Systems) technology. In health research, for example, it is common for epidemiologists to incorporate geographically indexed data into their studies. In practice, however, the spatially defined covariates are often measured with error. Naive estimators of regression coefficients are attenuated if measurement error is ignored. Moreover, the classical measurement error theory is inapplicable in the context of spatial modeling because of the presence of spatial correlation among the observations. We propose a semiparametric regression approach to obtain bias-corrected estimates of regression parameters and derive their large sample properties. We evaluate the performance of the proposed method through simulation studies and illustrate using data on Ischemic Heart Disease (IHD). Both simulation and practical application demonstrate that the proposed method can be effective in practice.

Analysis of error-prone survival data under additive hazards models: measurement error effects and adjustments

Covariate measurement error occurs commonly in survival analysis. Under the proportional hazards model, measurement error effects have been well studied, and various inference methods have been developed to correct for error effects under such a model. In contrast, error-contaminated survival data under the additive hazards model have received relatively less attention. In this paper, we investigate this problem by exploring measurement error effects on parameter estimation and the change of the hazard function. New insights of measurement error effects are revealed, as opposed to well-documented results for the Cox proportional hazards model. We propose a class of bias correction estimators that embraces certain existing estimators as special cases. In addition, we exploit the regression calibration method to reduce measurement error effects. Theoretical results for the developed methods are established, and numerical assessments are conducted to illustrate the finite sample performance of our methods.

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.

Estimation in closed capture-recapture models when covariates are missing at random

Individual covariates are commonly used in capture-recapture models as they can provide important information for population size estimation. However, in practice, one or more covariates may be missing at random for some individuals, which can lead to unreliable inference if records with missing data are treated as missing completely at random. We show that, in general, such a naive complete-case analysis in closed capture-recapture models with some covariates missing at random underestimates the population size. We develop methods for estimating regression parameters and population size using regression calibration, inverse probability weighting, and multiple imputation without any distributional assumptions about the covariates. We show that the inverse probability weighting and multiple imputation approaches are asymptotically equivalent. We present a simulation study to investigate the effects of missing covariates and to evaluate the performance of the proposed methods. We also illustrate an analysis using data on the bird species yellow-bellied prinia collected in Hong Kong.

Estimation of radiation risk in presence of classical additive and Berkson multiplicative errors in exposure doses

In this paper, the influence of measurement errors in exposure doses in a regression model with binary response is studied. Recently, it has been recognized that uncertainty in exposure dose is characterized by errors of two types: classical additive errors and Berkson multiplicative errors. The combination of classical additive and Berkson multiplicative errors has not been considered in the literature previously. In a simulation study based on data from radio-epidemiological research of thyroid cancer in Ukraine caused by the Chornobyl accident, it is shown that ignoring measurement errors in doses leads to overestimation of background prevalence and underestimation of excess relative risk. In the work, several methods to reduce these biases are proposed. They are new regression calibration, an additive version of efficient SIMEX, and novel corrected score methods.

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.

Functional and Structural Methods with Mixed Measurement Error and Misclassification in Covariates

Covariate measurement imprecision or errors arise frequently in many areas. It is well known that ignoring such errors can substantially degrade the quality of inference or even yield erroneous results. Although in practice both covariates subject to measurement error and covariates subject to misclassification can occur, research attention in the literature has mainly focused on addressing either one of these problems separately. To fill this gap, we develop estimation and inference methods that accommodate both characteristics simultaneously. Specifically, we consider measurement error and misclassification in generalized linear models under the scenario that an external validation study is available, and systematically develop a number of effective functional and structural methods. Our methods can be applied to different situations to meet various objectives.

Calibrating abundance indices with population size estimators of red back salamanders (Plethodon cinereus) in a New England forest

Herpetologists and conservation biologists frequently use convenient and cost-effective, but less accurate, abundance indices (e.g., number of individuals collected under artificial cover boards or during natural objects surveys) in lieu of more accurate, but costly and destructive, population size estimators to detect and monitor size, state, and trends of amphibian populations. Although there are advantages and disadvantages to each approach, reliable use of abundance indices requires that they be calibrated with accurate population estimators. Such calibrations, however, are rare. The red back salamander, Plethodon cinereus, is an ecologically useful indicator species of forest dynamics, and accurate calibration of indices of salamander abundance could increase the reliability of abundance indices used in monitoring programs. We calibrated abundance indices derived from surveys of P. cinereus under artificial cover boards or natural objects with a more accurate estimator of their population size in a New England forest. Average densities/m² and capture probabilities of P. cinereus under natural objects or cover boards in independent, replicate sites at the Harvard Forest (Petersham, Massachusetts, USA) were similar in stands dominated by Tsuga canadensis (eastern hemlock) and deciduous hardwood species (predominantly Quercus rubra [red oak] and Acer rubrum [red maple]). The abundance index based on salamanders surveyed under natural objects was significantly associated with density estimates of P. cinereus derived from depletion (removal) surveys, but underestimated true density by 50%. In contrast, the abundance index based on cover-board surveys overestimated true density by a factor of 8 and the association between the cover-board index and the density estimates was not statistically significant. We conclude that when calibrated and used appropriately, some abundance indices may provide cost-effective and reliable measures of P. cinereus abundance that could be used in conservation assessments and long-term monitoring at Harvard Forest and other northeastern USA forests.

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

Mediation analysis is important for understanding the mechanisms whereby one variable causes changes in another. Measurement error could obscure the ability of the potential mediator to explain such changes. This article focuses on developing correction methods for measurement error in the mediator with failure time outcomes. We consider a broad definition of measurement error, including technical error, and error associated with temporal variation. The underlying model with the "true" mediator is assumed to be of the Cox proportional hazards model form. The induced hazard ratio for the observed mediator no longer has a simple form independent of the baseline hazard function, due to the conditioning event. We propose a mean-variance regression calibration approach and a follow-up time regression calibration approach, to approximate the partial likelihood for the induced hazard function. Both methods demonstrate value in assessing mediation effects in simulation studies. These methods are generalized to multiple biomarkers and to both case-cohort and nested case-control sampling designs. We apply these correction methods to the Women's Health Initiative hormone therapy trials to understand the mediation effect of several serum sex hormone measures on the relationship between postmenopausal hormone therapy and breast cancer risk.

Moment Adjusted Imputation for Multivariate Measurement Error Data with Applications to Logistic Regression

In clinical studies, covariates are often measured with error due to biological fluctuations, device error and other sources. Summary statistics and regression models that are based on mismeasured data will differ from the corresponding analysis based on the "true" covariate. Statistical analysis can be adjusted for measurement error, however various methods exhibit a tradeo between convenience and performance. Moment Adjusted Imputation (MAI) is method for measurement error in a scalar latent variable that is easy to implement and performs well in a variety of settings. In practice, multiple covariates may be similarly influenced by biological fluctuastions, inducing correlated multivariate measurement error. The extension of MAI to the setting of multivariate latent variables involves unique challenges. Alternative strategies are described, including a computationally feasible option that is shown to perform well.