Instrumental variable approach to estimating the scalar-on-function regression model with measurement error with application to energy expenditure assessment in childhood obesity.
ABSTRACT: Wearable device technology allows continuous monitoring of biological markers and thereby enables study of time-dependent relationships. For example, in this paper, we are interested in the impact of daily energy expenditure over a period of time on subsequent progression toward obesity among children. Data from these devices appear as either sparsely or densely observed functional data and methods of functional regression are often used for their statistical analyses. We study the scalar-on-function regression model with imprecisely measured values of the predictor function. In this setting, we have a scalar-valued response and a function-valued covariate that are both collected at a single time period. We propose a generalized method of moments-based approach for estimation, while an instrumental variable belonging in the same time space as the imprecisely measured covariate is used for model identification. Additionally, no distributional assumptions regarding the measurement errors are assumed, while complex covariance structures are allowed for the measurement errors in the implementation of our proposed methods. We demonstrate that our proposed estimator is L2 consistent and enjoys the optimal rate of convergence for univariate nonparametric functions. In a simulation study, we illustrate that ignoring measurement error leads to biased estimations of the functional coefficient. The simulation studies also confirm our ability to consistently estimate the function-valued coefficient when compared to approaches that ignore potential measurement errors. Our proposed methods are applied to our motivating example to assess the impact of baseline levels of energy expenditure on body mass index among elementary school-aged children.
Project description:Joint models are formulated to investigate the association between a primary endpoint and features of multiple longitudinal processes. In particular, the subject-specific random effects in a multivariate linear random-effects model for multiple longitudinal processes are predictors in a generalized linear model for primary endpoints. Li, Zhang, and Davidian (2004, Biometrics60, 1-7) proposed an estimation procedure that makes no distributional assumption on the random effects but assumes independent within-subject measurement errors in the longitudinal covariate process. Based on an asymptotic bias analysis, we found that their estimators can be biased when random effects do not fully explain the within-subject correlations among longitudinal covariate measurements. Specifically, the existing procedure is fairly sensitive to the independent measurement error assumption. To overcome this limitation, we propose new estimation procedures that require neither a distributional or covariance structural assumption on covariate random effects nor an independence assumption on within-subject measurement errors. These new procedures are more flexible, readily cover scenarios that have multivariate longitudinal covariate processes, and can be implemented using available software. Through simulations and an analysis of data from a hypertension study, we evaluate and illustrate the numerical performances of the new estimators.
Project description:We take a semiparametric approach in fitting a linear transformation model to a right censored data when predictive variables are subject to measurement errors. We construct consistent estimating equations when repeated measurements of a surrogate of the unobserved true predictor are available. The proposed approach applies under minimal assumptions on the distributions of the true covariate or the measurement errors. We derive the asymptotic properties of the estimator and illustrate the characteristics of the estimator in finite sample performance via simulation studies. We apply the method to analyze an AIDS clinical trial data set that motivated the work.
Project description:We consider the problem of multivariate density deconvolution when interest lies in estimating the distribution of a vector valued random variable X but precise measurements on X are not available, observations being contaminated by measurement errors U. The existing sparse literature on the problem assumes the density of the measurement errors to be completely known. We propose robust Bayesian semiparametric multivariate deconvolution approaches when the measurement error density of U is not known but replicated proxies are available for at least some individuals. Additionally, we allow the variability of U to depend on the associated unobserved values of X through unknown relationships, which also automatically includes the case of multivariate multiplicative measurement errors. Basic properties of finite mixture models, multivariate normal kernels and exchangeable priors are exploited in novel ways to meet modeling and computational challenges. Theoretical results showing the flexibility of the proposed methods in capturing a wide variety of data generating processes are provided. We illustrate the efficiency of the proposed methods in recovering the density of X through simulation experiments. The methodology is applied to estimate the joint consumption pattern of different dietary components from contaminated 24 hour recalls. Supplementary Material presents substantive additional details.
Project description:The main purpose of this paper is to establish the Milloux inequality of E-valued meromorphic function from the complex plane ℂ to an infinite dimensional complex Banach space E with a Schauder basis. As an application, we study the Borel exceptional values of an E-valued meromorphic function and those of its derivatives; results are obtained to extend some related results for meromorphic scalar-valued function of Singh, Gopalakrishna, and Bhoosnurmath.
Project description:The angular distribution of [Formula: see text] ([Formula: see text]) depends on two parameters, the lepton forward-backward asymmetry, [Formula: see text], and the flat term, [Formula: see text]. Both are strongly suppressed in the standard model and constitute sensitive probes of tensor and scalar contributions. We use the latest experimental results for [Formula: see text] in combination with the branching ratio of [Formula: see text] to derive the strongest model-independent bounds on tensor and scalar effective couplings to date. The measurement of [Formula: see text] provides a complementary constraint to that of the branching ratio of [Formula: see text] and allows us - for the first time - to constrain all complex-valued (pseudo-)scalar couplings and their chirality-flipped counterparts in one fit. Based on Bayesian fits of various scenarios, we find that our bounds even become tighter when vector couplings are allowed to deviate from the standard model and that specific combinations of angular observables in [Formula: see text] are still allowed to be up to two orders of magnitude larger than in the standard model, which would place them in the region of LHCb's sensitivity.
Project description:For time-to-event outcomes, a rich literature exists on the bias introduced by covariate measurement error in regression models, such as the Cox model, and methods of analysis to address this bias. By comparison, less attention has been given to understanding the impact or addressing errors in the failure time outcome. For many diseases, the timing of an event of interest (such as progression-free survival or time to AIDS progression) can be difficult to assess or reliant on self-report and therefore prone to measurement error. For linear models, it is well known that random errors in the outcome variable do not bias regression estimates. With nonlinear models, however, even random error or misclassification can introduce bias into estimated parameters. We compare the performance of 2 common regression models, the Cox and Weibull models, in the setting of measurement error in the failure time outcome. We introduce an extension of the SIMEX method to correct for bias in hazard ratio estimates from the Cox model and discuss other analysis options to address measurement error in the response. A formula to estimate the bias induced into the hazard ratio by classical measurement error in the event time for a log-linear survival model is presented. Detailed numerical studies are presented to examine the performance of the proposed SIMEX method under varying levels and parametric forms of the error in the outcome. We further illustrate the method with observational data on HIV outcomes from the Vanderbilt Comprehensive Care Clinic.
Project description:Recurrent event data arise frequently in many longitudinal follow-up studies. Hence, evaluating covariate effects on the rates of occurrence of such events is commonly of interest. Examples include repeated hospitalizations, recurrent infections of HIV, and tumor recurrences. In this article, we consider semiparametric regression methods for the occurrence rate function of recurrent events when the covariates may be measured with errors. In contrast to the existing works, in our case the conventional assumption of independent censoring is violated since the recurrent event process is interrupted by some correlated events, which is called informative drop-out. Further, some covariates may be measured with errors. To accommodate for both informative censoring and measurement error, the occurrence of recurrent events is modelled through an unspecified frailty distribution and accompanied with a classical measurement error model. We propose two corrected approaches based on different ideas, and we show that they are numerically identical when estimating the regression parameters. The asymptotic properties of the proposed estimators are established, and the finite sample performance is examined via simulations. The proposed methods are applied to the Nutritional Prevention of Cancer trial for assessing the effect of the plasma selenium treatment on the recurrence of squamous cell carcinoma.
Project description:Multistate Markov regression models used for quantifying the effect size of state-specific covariates pertaining to the dynamics of multistate outcomes have gained popularity. However, the measurements of multistate outcome are prone to the errors of classification, particularly when a population-based survey/research is involved with proxy measurements of outcome due to cost consideration. Such a misclassification may affect the effect size of relevant covariates such as odds ratio used in the field of epidemiology. We proposed a Bayesian measurement-error-driven hidden Markov regression model for calibrating these biased estimates with and without a 2-stage validation design. A simulation algorithm was developed to assess various scenarios of underestimation and overestimation given nondifferential misclassification (independent of covariates) and differential misclassification (dependent on covariates). We applied our proposed method to the community-based survey of androgenetic alopecia and found that the effect size of the majority of covariate was inflated after calibration regardless of which type of misclassification. Our proposed Bayesian measurement-error-driven hidden Markov regression model is practicable and effective in calibrating the effects of covariates on multistate outcome, but the prior distribution on measurement errors accrued from 2-stage validation design is strongly recommended.
Project description:Despite obesity being highly prevalent in persons with spinal cord injury (SCI), our current understanding of the interactions between energy balance components, which may contribute to this, is limited. The primary aim of this study is to identify the intra-individual variability of physical activity dimensions across days and suggest an appropriate monitoring time frame for these constructs in adults with SCI. The secondary aim is to examine these parameters with regard to energy intake and dietary macronutrient composition.Participants [33 men and women with chronic (> 1 year post injury) paraplegia; age = 44 ± 9 years (mean ± S.D.] wore an Actiheart™ PA monitor and completed a weighed food diary for 7 consecutive days. Spearman-Brown Prophecy Formulae, based on Intraclass Correlations of .80 (acceptable reliability), were used to predict the number of days required to measure energy balance components. Linear mixed-effects analyses and magnitude-based inferences were performed for all energy intake, expenditure and physical activity dimensions. Adjustments were made for age, injury level, wear time, sex, day of the week and measurement order as fixed effects.To reliably measure energy expenditure components; 1 day [total energy expenditure (TEE)], 2 days [physical activity energy expenditure (PAEE), light-intensity activity, moderate-to-vigorous PA (MVPA)], 3 days [physical activity level (PAL)] and 4 days (sedentary behaviour) are necessary. Device wear time (P < 0.02), injury level (P < 0.04) and sex (P < 0.001) were covariates for energy expenditure components. Four and ?24 days are required to reliably measure total energy intake (kcal) and diet macronutrient composition (%), respectively. Measurement order (from day 1-7) was a covariate for total energy intake (P = 0.01).This is the first study to demonstrate the variability of energy intake and expenditure components in free-living persons with chronic (> 1 year) paraplegia and propose suitable measurement durations to achieve acceptable reliability in outcome measures. Device wear time and measurement order play a role in the quality of energy expenditure and intake data, respectively, and should be considered when designing and analysing studies of energy balance components in persons with SCI.N/A.
Project description:It is a common practice to analyze complex longitudinal data using semiparametric nonlinear mixed-effects (SNLME) models with a normal distribution. Normality assumption of model errors may unrealistically obscure important features of subject variations. To partially explain between- and within-subject variations, covariates are usually introduced in such models, but some covariates may often be measured with substantial errors. Moreover, the responses may be missing and the missingness may be nonignorable. Inferential procedures can be complicated dramatically when data with skewness, missing values, and measurement error are observed. In the literature, there has been considerable interest in accommodating either skewness, incompleteness or covariate measurement error in such models, but there has been relatively little study concerning all three features simultaneously. In this article, our objective is to address the simultaneous impact of skewness, missingness, and covariate measurement error by jointly modeling the response and covariate processes based on a flexible Bayesian SNLME model. The method is illustrated using a real AIDS data set to compare potential models with various scenarios and different distribution specifications.