Measurement Error in Nonlinear Models

Carroll, Raymond J.; Ruppert, David; Stefanski, Leonard A.; Crainiceanu, Ciprian M.

doi:10.1201/9781420010138

Cited by 2,162 publications

(2,419 citation statements)

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“…1b, e.g., the Lagergren plot for the FO equation (AkmilBasar et al 2005;Marczewski 2010): ln(a t -a eq ) versus t and t/a t versus t for the SO equation where at stands for adsorption at time t and a eq for the amount adsorbed in equilibrium. However, such a method requires data transformation, which may lead to further transformation of data deviation (Draper and Smith 1998;Carroll et al 2006;Chatterjee and Simonoff 2013). Therefore, in this study, fitting data to linear forms of FO and SO was done only to evaluate the equilibrium adsorption value used in further analysis with a multiexponentional equation (to calculate the adsorption progress precisely).…”

Section: Adsorption Kineticsmentioning

confidence: 99%

Revision of adsorption models of xyloglucan on microcrystalline cellulose

et al. 2016

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Interactions among cellulose, hemicellulose and pectins are important for plant cell wall assembly and properties and also for industrial applications of these polysaccharides. Therefore, binding of pectin and xyloglucan on microcrystalline cellulose was investigated in this experiment by adsorption isotherms, zeta potential and scanning electron microscopy (SEM). Analysis of three isotherm models (Langmuir, Freundlich and Fowler-Guggenheim isotherms) showed that the experimental adsorption isotherm was well described via the Fowler-Guggenheim model, which includes lateral interaction between the adsorbate. The adsorption isotherm and zeta potential measurement showed that at temperature 25°C only xyloglucan adsorbed on the microcrystalline cellulose. In case of xyloglucan on cellulose, the equilibrium was reached in about 3-4 h, and the kinetics of adsorption were well described by the multiexponential equation. Analysis of the model suggests that two steps can be distinguished: diffusion and reconformation in an adsorbed layer. No adsorption of pectin was observed in this study. SEM study showed that xyloglucan may prevent cellulose from aggregation.

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Section: Adsorption Kineticsmentioning

confidence: 99%

Revision of adsorption models of xyloglucan on microcrystalline cellulose

et al. 2016

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“…Although there is an extensive literature on covariate measurement errors and censoring, 4,5 to our knowledge, none seems to have considered NLME models for time-dependent covariates with censoring and measurement errors. Bernhardt et al 5 considered censored covariates in a survival model based on a multiple imputation method and an empirical model for generating imputations.…”

Section: Introductionmentioning

confidence: 99%

A mechanistic nonlinear model for censored and mismeasured covariates in longitudinal models, with application in AIDS studies

Zhang

Wong

2017

Statistics in Medicine

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When modeling longitudinal data, the true values of time-varying covariates may be unknown because of detection-limit censoring or measurement error.A common approach in the literature is to empirically model the covariate process based on observed data and then predict the censored values or mismeasured values based on this empirical model. Such an empirical model can be misleading, especially for censored values since the (unobserved) censored values may behave very differently than observed values due to the underlying data-generation mechanisms or disease status. In this paper, we propose a mechanistic nonlinear covariate model based on the underlying data-generation mechanisms to address censored values and mismeasured values. Such a mechanistic model is based on solid scientific or biological arguments, so the predicted censored or mismeasured values are more reasonable. We use a Monte Carlo EM algorithm for likelihood inference and apply the methods to an AIDS dataset, where viral load is censored by a lower detection limit. Simulation results confirm that the proposed models and methods offer substantial advantages over existing empirical covariate models for censored and mismeasured covariates.

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“…Instead, we seek an observable function such that (2) In the case of discrete error-prone covariates, a satisfying (2) may be constructed by a simple device we define (3) where k(i, t) is as defined previously and is the (k, l) element of the matrix B (i,t) =[A (i,t) ] −1 . We then have (4) so that (2) is indeed satisfied.…”

Section: The Key Ideamentioning

confidence: 99%

“…For nonlinear models, theory has been developing over the past 25 or so years. Carroll et al [2] provide a comprehensive summary of the development to date; currently, the covariate error problem for nonlinear models remains an active research area. In particular, beginning with Prentice [3], a growing literature has developed on the Cox [4] proportional hazards survival regression model when some covariates are measured with error.…”

Section: Introductionmentioning

confidence: 99%

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Corrected score estimation in the proportional hazards model with misclassified discrete covariates

Zucker

Spiegelman

2008

Statistics in Medicine

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SUMMARYWe consider Cox proportional hazards regression when the covariate vector includes error-prone discrete covariates along with error-free covariates, which may be discrete or continuous. The misclassification in the discrete error-prone covariates is allowed to be of any specified form. Building on the work of Nakamura and his colleagues, we present a corrected score method for this setting. The method can handle all three major study designs (internal validation design, external validation design, and replicate measures design), both functional and structural error models, and time-dependent covariates satisfying a certain 'localized error' condition. We derive the asymptotic properties of the method and indicate how to adjust the covariance matrix of the regression coefficient estimates to account for estimation of the misclassification matrix. We present the results of a finite-sample simulation study under Weibull survival with a single binary covariate having known misclassification rates. The performance of the method described here was similar to that of related methods we have examined in previous works. Specifically, our new estimator performed as well as or, in a few cases, better than the full Weibull maximum likelihood estimator. We also present simulation results for our method for the case where the misclassification probabilities are estimated from an external replicate measures study. Our method generally performed well in these simulations. The new estimator has a broader range of applicability than many other estimators proposed in the literature, including those described in our own earlier work, in that it can handle time-dependent covariates with an arbitrary misclassification structure. We illustrate the method on data from a study of the relationship between dietary calcium intake and distal colon cancer.

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Measurement Error in Nonlinear Models

Cited by 2,162 publications

References 0 publications

Revision of adsorption models of xyloglucan on microcrystalline cellulose

Revision of adsorption models of xyloglucan on microcrystalline cellulose

A mechanistic nonlinear model for censored and mismeasured covariates in longitudinal models, with application in AIDS studies

Corrected score estimation in the proportional hazards model with misclassified discrete covariates

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