Regression Calibration Approach Research Articles

Correcting for measurement error in assessing gestational age in a low-resource setting: a regression calibration approach.

Measurement error in gestational age (GA) may bias the association of GA with a health outcome. Ultrasound-based GA is considered the gold standard and is not readily available in low-resource settings. We corrected for measurement error in GA based on fundal height (FH) and date of last menstrual period (LMP) using ultrasound from the sub-cohort and adjusted for the bias in associating GA with neonatal mortality and low birth weight (< 2,500 grams, LBW). We used data collected from 01/2015 to 09/2019 from pregnant women enrolled at two public hospitals in Siaya county, Kenya (N = 2,750). We used regression calibration to correct for measurement error in FH- and LMP-based GA accounting for maternal and child characteristics. We applied logistic regression to associate GA with neonatal mortality and low birth weight, with and without calibrating FH- and LMP-based GA. Calibration improved the precision of LMP (correlation coefficient, from 0.48 to 0.57) and FH-based GA ( from 0.82 to 0.83). Calibrating FH/LMP-based GA eliminated the bias in the mean GA estimates. The log odds ratio that quantifies the association of GA with neonatal mortality increased by 29% (from -0.159 to -0.205) by calibrating FH-based GA and by more than twofold (from -0.158 to -0.471) by calibrating LMP-based GA. Calibrating FH/LMP-based GA improved the accuracy and precision of GA estimates and strengthened the association of GA with neonatal mortality/LBW. When assessing GA, neonatal public health and clinical interventions may benefit from calibration modeling in settings where ultrasound may not be fully available.

Exposure uncertainty effects on regression parameter values

Exposure uncertainty in community noise exposure-response investigations can bias the results of regression analyses, especially when the range of sound levels is limited, the standard deviation of sound level uncertainty is more than a decibel or two and the distribution of sound levels across the sample population deviates significantly from a uniform one. The bias is manifested in the solved values of the regression coefficients, leading to incorrect representations of both the slope and intercept. Methods are available to reduce the magnitude of such bias and this paper examines the regression calibration approach. A basic overview of regression calibration is provided as well as its implementation in a logistic regression analysis. The effectiveness and limitations of the procedure are discussed, as are the requisite additional field measurements necessary to quantify situational parameters required in the calibration process. While coefficient bias can be mitigated, coefficient uncertainty that might otherwise be due only to uncertainty in the predicted variable (fraction annoyed) increases with increasing exposure uncertainty. Such uncertainty impacts the ability to observe differences between sample populations in both scalar and categorical variables.

Raking and regression calibration: Methods to address bias from correlated covariate and time-to-event error.

Medical studies that depend on electronic health records (EHR) data are often subject to measurement error, as the data are not collected to support research questions under study. These data errors, if not accounted for in study analyses, can obscure or cause spurious associations between patient exposures and disease risk. Methodology to address covariate measurement error has been well developed; however, time-to-event error has also been shown to cause significant bias, but methods to address it are relatively underdeveloped. More generally, it is possible to observe errors in both the covariate and the time-to-event outcome that are correlated. We propose regression calibration (RC) estimators to simultaneously address correlated error in the covariates and the censored event time. Although RC can perform well in many settings with covariate measurement error, it is biased for nonlinear regression models, such as the Cox model. Thus, we additionally propose raking estimators which are consistent estimators of the parameter defined by the population estimating equation. Raking can improve upon RC in certain settings with failure-time data, require no explicit modeling of the error structure, and can be utilized under outcome-dependent sampling designs. We discuss features of the underlying estimation problem that affect the degree of improvement the raking estimator has over the RC approach. Detailed simulation studies are presented to examine the performance of the proposed estimators under varying levels of signal, error, and censoring. The methodology is illustrated on observational EHR data on HIV outcomes from the Vanderbilt Comprehensive Care Clinic.

A quantitative bias analysis to estimate measurement error-related attenuation of the association between self-reported physical activity and colorectal cancer risk.

Self-reported physical activity is inaccurate, yet few investigators attempt to adjust for measurement error when estimating risks for health outcomes. We estimated what the association between self-reported physical activity and colorectal cancer risk would be if physical activity had been assessed using accelerometry instead. We conducted a validation study in which 235 Australian adults completed a telephone-administered International Physical Activity Questionnaire (IPAQ), and wore an accelerometer (Actigraph GT3X+) for 7 days. Using accelerometer-assessed physical activity as the criterion measure, we calculated validity coefficients and attenuation factors using a structural equation model adjusted for age, sex, education and body mass index. We then used a regression calibration approach to apply the attenuation factors to data from the Melbourne Collaborative Cohort Study (MCCS) to compute bias-adjusted hazard ratios (HR) and 95% confidence intervals (CI). Average daily minutes of physical activity from the short form of the International Physical Activity Questionnaire (IPAQ-short) were substantially higher than accelerometer-measured duration (55 versus 32 min). The validity coefficient (0.32; 95% CI: 0.20, 0.43) and attenuation factor (0.20; 95% CI: 0.12, 0.28) were low. The HRs for colorectal cancer risk for high (75thpercentile; 411 min/week) versus low (25thpercentile; 62 min/week) levels of self-reported physical activity were 0.95 (95% CI: 0.87, 1.05) before and 0.78 (95% CI: 0.47, 1.28) after bias adjustment. Over-estimation of physical activity by the IPAQ-short substantially attenuates the association between physical activity and colorectal cancer risk, suggesting that the protective effect of physical activity has been previously underestimated.

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

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. Wageningen area, the Netherlands, 2011-2013. 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. Data of 236 individuals collected within the National Dietary Assessment Reference Database. 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. Our study highlights the potential of combining FFQ and 24hR data. Using RC and ERC resulted in less biased associations for protein and K.

Anticipating critical transitions of the housing market: new evidence from China

ABSTRACTWe introduce a novel quantitative methodology to detect real estate bubbles and forecast their critical end time, which we apply to the housing markets of China's metropolises. Building on the Log-Periodic Power Law Singularity (LPPLS) model of self-reinforcing feedback loops, we use the quantile regression calibration approach recently introduced by two of us to build confidence intervals and explore possible distinct scenarios. We propose to consolidate the quantile regressions into the arithmetic average of the quantile-based LPPLS Confidence indicator, which accounts for the robustness of the calibration with respect to bootstrapped residuals. We make three main contributions to the literature of real estate bubbles. First, we verify the validity of the arithmetic average of the quantile-based LPPLS Confidence indicator by studying the critical times of historical housing price bubbles in the U.S., Hong Kong, U.K. and Canada. Second, the LPPLS detection methods are applied to provide early warning signals of the housing markets in some metropolises in China. Third, we determine the possible turning points of the markets in Beijing, Shanghai, Shenzhen, Guangzhou, Tianjin and Chengdu and anticipate critical transitions of China's housing markets via our multi-scales and multi-quantiles analyses. Finally, given these projections performed in February 2017, the price trajectories from March 2017 to January 2018 that became available from the time of submission to the time of revision of the present article offer quite unique genuine out-of-sample tests of the performances of our indicators.

Ex-post risk premia estimation and asset pricing tests using large cross sections: The regression-calibration approach

We propose a modification of the two-pass cross-sectional regression approach for estimating ex-post risk premia in linear asset pricing models, suitable for the case of large cross sections and short time series. Employing the regression-calibration method, we provide a beta correction method, which deals with the error-in-variables problem, based on which we construct an N-consistent estimator of ex-post risk premia and develop associated novel asset pricing tests. Empirically, we reject the implications of the CAPM and the Fama–French three-factor and five-factor models but also offer new evidence on the relevance of the HML factor for pricing large cross sections of individual stocks.

Anticipating Critical Transitions of Chinese Housing Markets

We introduce a novel quantitative methodology to detect real estate bubbles and forecast their critical end time, which we apply to the housing markets of China's major cities. Building on the Log-Periodic Power Law Singular (LPPLS) model of self-reinforcing feedback loops, we use the quantile regression calibration approach recently introduced by two of us to build confidence intervals and explore possible distinct scenarios. We propose to consolidate the quantile regressions into the arithmetic average of the quantile-based DS LPPLS Confidence indicator, which accounts for the robustness of the calibration with respect to bootstrapped residuals. We make three main contributions to the literature of real estate bubbles. First, we verify the validity of the arithmetic average of the quantile-based DS LPPLS Confidence indicator by studying the critical times of historical housing price bubbles in the U.S., Hong Kong, U.K. and Canada. Second, the LPPLS detection methods are applied to provide early warning signals of the housing markets in China's major cities. Third, we determine the possible turning points of the markets in BeiJing, ShangHai, ShenZhen, GuangZhou, TianJin and ChengDu and forecast the future evolution of China's housing market via our multi-scales and multi-quantiles analyses.

Estimating relative risk of a log-transformed exposure measured in pools.

Pooling biospecimens prior to performing laboratory assays is a useful tool to reduce costs, achieve minimum volume requirements and mitigate assay measurement error. When estimating the risk of a continuous, pooled exposure on a binary outcome, specialized statistical techniques are required. Current methods include a regression calibration approach, where the expectation of the individual-level exposure is calculated by adjusting the observed pooled measurement with additional covariate data. While this method employs a linear regression calibration model, we propose an alternative model that can accommodate log-linear relationships between the exposure and predictive covariates. The proposed model permits direct estimation of the relative risk associated with a log-transformation of an exposure measured in pools. Published 2016. This article is a U.S. Government work and is in the public domain in the USA.

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.

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.

Bayesian generalized varying coefficient models for longitudinal proportional data with errors-in-covariates

This paper is motivated from a neurophysiological study of muscle fatigue, in which biomedical researchers are interested in understanding the time-dependent relationships of handgrip force and electromyography measures. A varying coefficient model is appealing here to investigate the dynamic pattern in the longitudinal data. The response variable in the study is continuous but bounded on the standard unit interval (0, 1) over time, while the longitudinal covariates are contaminated with measurement errors. We propose a generalization of varying coefficient models for the longitudinal proportional data with errors-in-covariates. We describe two estimation methods with penalized splines, which are formalized under a Bayesian inferential perspective. The first method is an adaptation of the popular regression calibration approach. The second method is based on a joint likelihood under the hierarchical Bayesian model. A simulation study is conducted to evaluate the efficacy of the proposed methods under different scenarios. The analysis of the neurophysiological data is presented to demonstrate the use of the methods.

Calibrating a cellular automata model for understanding rural–urban land conversion: a Pareto front-based multi-objective optimization approach

Cellular automata (CA) modeling is useful to assist in understanding rural–urban land conversion processes. Although CA calibration is essential to ensuring an accurate modeling outcome, it remains a significant challenge. This study aims to address that challenge by developing and evaluating a multi-objective optimization model that considers the objectives of minimizing minus maximum likelihood estimation (MLE) value and minimizing number of errors (NOE) when calibrating CA transition rules. A Pareto front-based heuristic search algorithm, the Non-dominated Sorting Genetic Algorithm-II (NSGA-II), is used to obtain optimal or near-optimal solutions. The proposed calibration approach is validated using a case study from New Castle County, Delaware, United States. A comparison of the NSGA-II-based calibration model, the generic Logit regression calibration approach (MLE-based Generic Genetic Algorithm (GGA) calibration approach), and the NOE-based GGA calibration approach demonstrates that the proposed calibration model can produce stable solutions with better simulation accuracy. Furthermore, it can generate a set of solutions with different preferences regarding the two objectives which can provide CA simulation with robust parameters options.

Non-Gaussian Berkson errors in bioassay

The experimental design plays an important role in every experimental study. However, if errors in the settings of the studied factors cannot be avoided, i.e. Berkson errors occur, the estimates of the model parameters may be biased and the variability in the study increased. Correction methods for the effect of Berkson errors are compared. The emphasis is on the study of correlated Berkson errors which follow non-Gaussian distribution as this appears to have been a neglected, yet important, area. It is shown that the regression calibration approach bias correction methods are useful when the Berkson errors are independent. However, when these errors are dependent, the newly proposed method B-SIMEX clearly outperforms the other methods.

Improved Regression Calibration

The likelihood for generalized linear models with covariate measurement error cannot in general be expressed in closed form, which makes maximum likelihood estimation taxing. A popular alternative is regression calibration which is computationally efficient at the cost of inconsistent estimation. We propose an improved regression calibration approach, a general pseudo maximum likelihood estimation method based on a conveniently decomposed form of the likelihood. It is both consistent and computationally efficient, and produces point estimates and estimated standard errors which are practically identical to those obtained by maximum likelihood. Simulations suggest that improved regression calibration, which is easy to implement in standard software, works well in a range of situations.

A conditional likelihood approach for regression analysis using biomarkers measured with batch‐specific error

Measurement error is common in epidemiological and biomedical studies. When biomarkers are measured in batches or groups, measurement error is potentially correlated within each batch or group. In regression analysis, most existing methods are not applicable in the presence of batch-specific measurement error in predictors. We propose a robust conditional likelihood approach to account for batch-specific error in predictors when batch effect is additive and the predominant source of error, which requires no assumptions on the distribution of measurement error. Although a regression model with batch as a categorical covariable yields the same parameter estimates as the proposed conditional likelihood approach for linear regression, this result does not hold in general for all generalized linear models, in particular, logistic regression. Our simulation studies show that the conditional likelihood approach achieves better finite sample performance than the regression calibration approach or a naive approach without adjustment for measurement error. In the case of logistic regression, our proposed approach is shown to also outperform the regression approach with batch as a categorical covariate. In addition, we also examine a 'hybrid' approach combining the conditional likelihood method and the regression calibration method, which is shown in simulations to achieve good performance in the presence of both batch-specific and measurement-specific errors. We illustrate our method by using data from a colorectal adenoma study.

Regression calibration with more surrogates than mismeasured variables

In a recent paper (Weller EA, Milton DK, Eisen EA, Spiegelman D. Regression calibration for logistic regression with multiple surrogates for one exposure. Journal of Statistical Planning and Inference 2007; 137: 449-461), the authors discussed fitting logistic regression models when a scalar main explanatory variable is measured with error by several surrogates, that is, a situation with more surrogates than variables measured with error. They compared two methods of adjusting for measurement error using a regression calibration approximate model as if it were exact. One is the standard regression calibration approach consisting of substituting an estimated conditional expectation of the true covariate given observed data in the logistic regression. The other is a novel two-stage approach when the logistic regression is fitted to multiple surrogates, and then a linear combination of estimated slopes is formed as the estimate of interest. Applying estimated asymptotic variances for both methods in a single data set with some sensitivity analysis, the authors asserted superiority of their two-stage approach. We investigate this claim in some detail. A troubling aspect of the proposed two-stage method is that, unlike standard regression calibration and a natural form of maximum likelihood, the resulting estimates are not invariant to reparameterization of nuisance parameters in the model. We show, however, that, under the regression calibration approximation, the two-stage method is asymptotically equivalent to a maximum likelihood formulation, and is therefore in theory superior to standard regression calibration. However, our extensive finite-sample simulations in the practically important parameter space where the regression calibration model provides a good approximation failed to uncover such superiority of the two-stage method. We also discuss extensions to different data structures.

Performance of bias‐correction methods for exposure measurement error using repeated measurements with and without missing data

It is known that measurement error leads to bias in assessing exposure effects, which can however, be corrected if independent replicates are available. For expensive replicates, two-stage (2S) studies that produce data 'missing by design', may be preferred over a single-stage (1S) study, because in the second stage, measurement of replicates is restricted to a sample of first-stage subjects. Motivated by an occupational study on the acute effect of carbon black exposure on respiratory morbidity, we compare the performance of several bias-correction methods for both designs in a simulation study: an instrumental variable method (EVROS IV) based on grouping strategies, which had been recommended especially when measurement error is large, the regression calibration and the simulation extrapolation methods. For the 2S design, either the problem of 'missing' data was ignored or the 'missing' data were imputed using multiple imputations. Both in 1S and 2S designs, in the case of small or moderate measurement error, regression calibration was shown to be the preferred approach in terms of root mean square error. For 2S designs, regression calibration as implemented by Stata software is not recommended in contrast to our implementation of this method; the 'problematic' implementation of regression calibration although substantially improved with use of multiple imputations. The EVROS IV method, under a good/fairly good grouping, outperforms the regression calibration approach in both design scenarios when exposure mismeasurement is severe. Both in 1S and 2S designs with moderate or large measurement error, simulation extrapolation severely failed to correct for bias.

Allowing for never and episodic consumers when correcting for error in food record measurements of dietary intake

Food records, including 24-hour recalls and diet diaries, are considered to provide generally superior measures of long-term dietary intake relative to questionnaire-based methods. Despite the expense of processing food records, they are increasingly used as the main dietary measurement in nutritional epidemiology, in particular in sub-studies nested within prospective cohorts. Food records are, however, subject to excess reports of zero intake. Measurement error is a serious problem in nutritional epidemiology because of the lack of gold standard measurements and results in biased estimated diet–disease associations. In this paper, a 3-part measurement error model, which we call the never and episodic consumers (NEC) model, is outlined for food records. It allows for both real zeros, due to never consumers, and excess zeros, due to episodic consumers (EC). Repeated measurements are required for some study participants to fit the model. Simulation studies are used to compare the results from using the proposed model to correct for measurement error with the results from 3 alternative approaches: a crude approach using the mean of repeated food record measurements as the exposure, a linear regression calibration (RC) approach, and an EC model which does not allow real zeros. The crude approach results in badly attenuated odds ratio estimates, except in the unlikely situation in which a large number of repeat measurements is available for all participants. Where repeat measurements are available for all participants, the 3 correction methods perform equally well. However, when only a subset of the study population has repeat measurements, the NEC model appears to provide the best method for correcting for measurement error, with the 2 alternative correction methods, in particular the linear RC approach, resulting in greater bias and loss of coverage. The NEC model is extended to include adjustment for measurements from food frequency questionnaires, enabling better estimation of the proportion of never consumers when the number of repeat measurements is small. The methods are applied to 7-day diary measurements of alcohol intake in the EPIC-Norfolk study.

On Estimating the Relationship between Longitudinal Measurements and Time‐to‐Event Data Using a Simple Two‐Stage Procedure

Ye, Lin, and Taylor (2008, Biometrics 64, 1238-1246) proposed a joint model for longitudinal measurements and time-to-event data in which the longitudinal measurements are modeled with a semiparametric mixed model to allow for the complex patterns in longitudinal biomarker data. They proposed a two-stage regression calibration approach that is simpler to implement than a joint modeling approach. In the first stage of their approach, the mixed model is fit without regard to the time-to-event data. In the second stage, the posterior expectation of an individual's random effects from the mixed-model are included as covariates in a Cox model. Although Ye et al. (2008) acknowledged that their regression calibration approach may cause a bias due to the problem of informative dropout and measurement error, they argued that the bias is small relative to alternative methods. In this article, we show that this bias may be substantial. We show how to alleviate much of this bias with an alternative regression calibration approach that can be applied for both discrete and continuous time-to-event data. Through simulations, the proposed approach is shown to have substantially less bias than the regression calibration approach proposed by Ye et al. (2008). In agreement with the methodology proposed by Ye et al. (2008), an advantage of our proposed approach over joint modeling is that it can be implemented with standard statistical software and does not require complex estimation techniques.