Simulation Extrapolation Research Articles

Variable selection and estimation for recurrent event model with covariates subject to measurement error

This article focuses on variable selection in the Andersen–Gill model for recurrent event analysis, particularly when covariates are subject to measurement errors. We propose a comprehensive three-stage procedure that incorporates simulation–extrapolation with various penalty functions. This approach allows for the simultaneous selection of significant covariates, estimation of regression parameters, and adjustment for measurement errors. Through extensive simulation studies, we demonstrate that our method outperforms approaches that fail to account for measurement errors or the need for variable selection. Specifically, our procedure excels in removing unimportant error-prone covariates and accurately estimating the coefficients of important variables. The results also reveal that the magnitude of measurement error has a substantial negative impact on variable selection outcomes. Additionally, we apply our method to a real-world dataset, further illustrating its practical effectiveness and robustness.

SIMEX-Based and Analytical Bias Corrections in Stocking–Lord Linking

Stocking–Lord (SL) linking is a popular linking method for group comparisons based on dichotomous item responses. This article proposes a bias correction technique based on the simulation extrapolation (SIMEX) method for SL linking in the 2PL model in the presence of uniform differential item functioning (DIF). The SIMEX-based method is compared to the analytical bias correction methods of SL linking. It turned out in a simulation study that SIMEX-based SL linking performed best, is easy to implement, and can be adapted to other linking methods straightforwardly.

Dose error correction using simulation extrapolation for community noise dose-response modeling

The objective of this work is to provide a framework to account and correct for dose error in dose-response modeling due to measurement uncertainty. Error in noise measurements, especially in the case of limited monitoring locations in a community, can lead to an attenuation or misestimation of parameters in dose-response models. This error can result in overpredicted annoyance at lower doses and underpredicted annoyance at higher doses. Simulated data in the present work are based on previous NASA community studies and incorporate a notional design for future studies with the X-59 aircraft. Several populations of different annoyance response sensitivities are included. Simulation extrapolation (SIMEX) is used to correct for the dose error in a simple, fully pooled logistic regression. Results indicate the negative impact of attenuation is greatly diminished for all amounts of dose error considered, regardless of a population’s annoyance sensitivity. Therefore, SIMEX can help produce a more accurate dose-response relationship.

Adjusting for bias due to measurement error in functional quantile regression models with error-prone functional and scalar covariates

Wearable devices enable the continuous monitoring of physical activity (PA) but generate complex functional data with poorly characterized errors. Most work on functional data views the data as smooth, latent curves obtained at discrete time intervals with some random noise with mean zero and constant variance. Viewing this noise as homoscedastic and independent ignores potential serial correlations. Our preliminary studies indicate that failing to account for these serial correlations can bias estimations. In dietary assessments, epidemiologists often use self-reported measures based on food frequency questionnaires that are prone to recall bias. With the increased availability of complex, high-dimensional functional, and scalar biomedical data potentially prone to measurement errors, it is necessary to adjust for biases induced by these errors to permit accurate analyzes in various regression settings. However, there has been limited work to address measurement errors in functional and scalar covariates in the context of quantile regression. Therefore, we developed new statistical methods based on simulation extrapolation (SIMEX) and mixed effects regression with repeated measures to correct for measurement error biases in this context. We conducted simulation studies to establish the finite sample properties of our new methods. The methods are illustrated through application to a real data set.

Estimation for single-index spatial autoregressive model with covariate measurement errors

This paper explores the estimators of parameters for a spatial data single-index model which has measurement errors of covariates in the nonparametric part. The related estimations are considered to combine a local-linear smoother based simulation-extrapolation (SIMEX) algorithm, the estimation equation and the estimation method for profile maximum likelihood. Under regular conditions, asymptotic properties of the link function and uncertain estimators are derived. As verified in simulations, the performance of the estimators is satisfactory. Finally, an application to a real dataset is illustrated.

Nonparametric estimation of a survival function in the presence of measurement errors on the failure time of interest

AbstractThis article discusses nonparametric estimation of a survival function in the presence of measurement errors on the observation of the failure time of interest. One situation where such issues arise would be clinical studies of chronic diseases where the observation on the time to the failure event of interest such as the onset of the disease relies on patient recall or chart review of electronic medical records. It is easy to see that both situations can be subject to measurement errors. To resolve this problem, we propose a simulation extrapolation approach to correct the bias induced by the measurement error. To overcome potential computational difficulties, we use spline regression to approximate the unspecified extrapolated coefficient function of time, and establish the asymptotic properties of our proposed estimator. The proposed method is applied to nonparametric estimation based on interval‐censored data. Extensive numerical experiments involving both simulated and actual study datasets demonstrate the feasibility of this proposed estimation procedure.

SIMEX Estimation of Partially Linear Multiplicative Regression Model with Mismeasured Covariates

In many practical applications, such as the studies of financial and biomedical data, the response variable usually is positive, and the commonly used criteria are based on absolute errors, which is not desirable. Rather, the relative errors are more of concern. We consider statistical inference for a partially linear multiplicative regression model when covariates in the linear part are measured with error. The simulation–extrapolation (SIMEX) estimators of parameters of interest are proposed based on the least product relative error criterion and B-spline approximation, where two kinds of relative errors are both introduced and the symmetry emerges in the loss function. Extensive simulation studies are conducted and the results show that the proposed method can effectively eliminate the bias caused by the measurement errors. Under some mild conditions, the asymptotic normality of the proposed estimator is established. Finally, a real example is analyzed to illustrate the practical use of our proposed method.

Causal relationship between addictive behaviors and epilepsy risk: A mendelian randomization study

BackgroundPrevious studies have reported inconsistent results regarding the potential relationships between addictive behaviors and the risk of epilepsy. ObjectiveTo assess whether genetically predicted addictive behaviors are causally associated with the risk of epilepsy outcomes. MethodsThe causation between five addictive behaviors (including cigarettes per day, alcoholic drinks per week, tea intake, coffee intake, and lifetime cannabis use) and epilepsy was evaluated by using a two-sample Mendelian Randomization (MR) analysis. The inverse-variance weighted (IVW) method was used as the primary outcome. The other MR analysis methods (MR Egger, weighted median, simulation extrapolation corrected MR-Egger, and Mendelian Randomization Pleiotropy Residual Sum and Outlier (MR-PRESSO)) were performed to complement IVW. In addition, the robustness of the MR analysis results was assessed by leave-one-out analysis. ResultsThe IVW analysis method indicated an approximately 20% increased risk of epilepsy per standard deviation increase in lifetime cannabis use (odds ratio [OR], 1.20; 95% confidence interval [CI]), 1.02–1.42, P = 0.028). However, there is no causal association between the other four addictive behaviors and the risk of epilepsy (cigarettes per day: OR, 1.04; 95% CI, 0.92–1.18, P = 0.53; alcoholic drinks per week: OR, 1.31; 95% CI, 0.93–1.84, P = 0.13; tea intake: OR, 1.15; 95% CI, 0.84–1.56, P = 0.39; coffee intake: OR, 0.86; 95% CI, 0.59–1.23, P = 0.41). The other MR analysis methods and further leave-one-out sensitivity analysis suggested the results were robust. ConclusionThis MR study indicated a potential genetically predicted causal association between lifetime cannabis use and higher risk of epilepsy. As for the other four addictive behaviors, no evidence of a causal relationship with the risk of epilepsy was found in this study.

Mendelian randomization shows depression increases the risk of type 2 diabetes.

Introduction: Type 2 diabetes (T2D) is associated with severe mental illnesses (SMIs), such as schizophrenia, bipolar disorder, and depression. However, causal relationships between SMIs and T2D remain unclear owing to potential bias in observational studies. We aimed to characterize the causal effect of SMI liability on T2D using two-sample Mendelian randomization (MR). Methods: The causality between liability to SMI and T2D was investigated using the inverse-variance weighted (IVW), MREgger, MR-Egger with a simulation extrapolation, weighted median, and the MR pleiotropy residual sum and outlier method. Similarly, we performed additional MR which can detect the reverse causation effect by switching exposure and outcome for T2D liability for SMI. To further consider pleiotropic effects between SMIs, multivariable MR analysis was performed after accounting for the other traits. Results: In the univariable IVW method, depression showed a causal effect on T2D (odds ratio [OR]: 1.128, 95% confidence interval [CI]: 1.024-1.245, p = 0.014). Multinomial MR more strongly supported these results (IVW OR: 1.197, 95% CI: 1.069, 1.340, p = 0.002; MR-Egger OR: 1.198, 95% CI: 1.062, 1.349, p = 0.003). Bidirectional MR showed absence of reversecausality between depression and T2D. However, causal relationship of bipolar and schizophrenia on T2D was not detected. Discussion: Careful attention is needed for patients with depression regarding T2D prevention and treatment.

Using stochastic frontier analysis instead of data envelopment analysis in modelling investment performance

AbstractWe introduce methods to apply stochastic frontier analysis (SFA) to financial assets as an alternative to data envelopment analysis, because SFA allows us to fit a frontier with noisy data. In contrast to conventional SFA, we wish to deal with estimation risk, heteroscedasticity in noise and inefficiency terms. We investigate measurement error in the risk and return measures using a simulation–extrapolation method and develop residual plots to test model fit. We find that shrinkage estimators for estimation risk makes a striking difference to model fit, dealing with measurement error only improves confidence in the model, and the residual plots are vital for establishing model fit. The methods are important because they allow us to fit a frontier under the assumption that the risks and returns are not known exactly.

Nonparametric simulation extrapolation for measurement‐error models

AbstractThe presence of measurement error is a widespread issue, which, when ignored, can render the results of an analysis unreliable. Numerous corrections for the effects of measurement error have been proposed and studied, often under the assumption of a normally distributed, additive measurement‐error model. In many situations, observed data are nonsymmetric, heavy‐tailed, or otherwise highly non‐normal. In these settings, correction techniques relying on the assumption of normality are undesirable. We propose an extension of simulation extrapolation that is nonparametric in the sense that no specific distributional assumptions are required on the error terms. The technique can be implemented when either validation data or replicate measurements are available, and is designed to be immediately accessible to those familiar with simulation extrapolation.

Extrapolation estimation for nonparametric regression with measurement error

AbstractFor the nonparametric regression models with covariates contaminated with the normal measurement errors, this paper proposes an extrapolation algorithm to estimate the regression functions. By applying the conditional expectation directly to the kernel‐weighted least squares of the deviations between the local linear approximation and the observed responses, the proposed algorithm successfully bypasses the simulation step in the classical simulation extrapolation, thus significantly reducing the computational time. It is noted that the proposed method also provides an exact form of the extrapolation function, although the extrapolation estimate generally cannot be obtained by simply setting the extrapolation variable to negative one in the fitted extrapolation function, if the bandwidth is less than the SD of the measurement error. Large sample properties of the proposed estimation procedure are discussed, as well as simulation studies and a real data example being conducted to illustrate its applications.

Technology advancement is driving electric vehicle adoption

Electric vehicle sales have been growing rapidly in the United States and around the world. This study explores the drivers of demand for electric vehicles, examining whether this trend is primarily a result of technology improvements or changes in consumer preferences for the technology over time. We conduct a discrete choice experiment of new vehicle consumers in the United States, weighted to be representative of the population. Results suggest that improved technology has been the stronger force. Estimates of consumer willingness to pay for vehicle attributes show that when consumers compare a gasoline vehicle to its battery electric vehicle (BEV) counterpart, the improved operating cost, acceleration, and fast-charging capabilities of today's BEVs mostly or entirely compensate for their perceived disadvantages, particularly for longer-range BEVs. Moreover, forecasted improvements of BEV range and price suggest that consumer valuation of many BEVs is expected to equal or exceed their gasoline counterparts by 2030. A suggestive market-wide simulation extrapolation indicates that if every gasoline vehicle had a BEV option in 2030, the majority of new car and near-majority of new sport-utility vehicle choice shares could be electric in that year due to projected technology improvements alone.

Sensitivity of the SIMulation-EXtrapolation (SIMEX) methodology to mis-specification of the statistical properties of the measurement errors

Sensitivity of the SIMulation-EXtrapolation (SIMEX) methodology to mis-specification of the statistical properties of the measurement errors

Misclassification simulation extrapolation method for a Weibull accelerated failure time model.

The problem of misclassification in covariates is ubiquitous in survival data and often leads to biased estimates. The misclassification simulation extrapolation method is a popular method to correct this bias. However, its impact on Weibull accelerated failure time models has not been studied. In this paper, we study the bias caused by misclassification in one or more binary covariates in Weibull accelerated failure time models and explore the use of the misclassification simulation extrapolation in correcting for this bias, along with its asymptotic properties. Simulation studies are carried out to investigate the numerical properties of the resulting estimator for finite samples. The proposed method is then applied to colon cancer data obtained from the cancer registry at Memorial Sloan Kettering Cancer Center.

Clinical biostatistics in the 2020s

Clinical biostatistics in the 2020s

Extrapolation in parametric models with Laplace measurement error

For general parametric statistical models with some variables being contaminated with the Laplace measurement error, we propose an extrapolation algorithm to estimate the unknown parameters. By applying the conditional expectation directly to the target function, either the function to be optimized or an estimation equation, the proposed algorithm successfully bypasses the simulation step in the classical simulation extrapolation procedure and thus provides a viable alternative to the classical simulation extrapolation algorithm. Large sample properties of the resulting estimator are discussed. Finite sample performance of the proposed extrapolation estimation procedure is demonstrated by examples and numerical simulation studies.

Adapting SIMEX to correct for bias due to interval-censored outcomes in survival analysis with time-varying exposure.

Many clinical and epidemiological applications of survival analysis focus on interval-censored events that can be ascertained only at discrete times of clinic visits. This implies that the values of time-varying covariates are not correctly aligned with the true, unknown event times, inducing a bias in the estimated associations. To address this issue, we adapted the simulation-extrapolation (SIMEX) methodology, based on assessing how the estimates change with the artificially increased time between clinic visits. We propose diagnostics to choose the extrapolating function. In simulations, the SIMEX-corrected estimates reduced considerably the bias to the null and generally yielded a better bias/variance trade-off than conventional estimates. In a real-life pharmacoepidemiological application, the proposed method increased by 27% the excess hazard of the estimated association between a time-varying exposure, representing the 2-year cumulative duration of past use of a hypertensive medication, and the hazard of nonmelanoma skin cancer (interval-censored events). These simulation-based and real-life results suggest that the proposed SIMEX-based correction may help improve the accuracy of estimated associations between time-varying exposures and the hazard of interval-censored events in large cohort studies where the events are recorded only at relatively sparse times of clinic visits/assessments. However, these advantages may be less certain for smaller studies and/or weak associations.

Parameter estimation of structural equation models with misclassification: The MC-SIMEX approach

The random errors in the measurement process, called measurement error or misclassification, are inevitable and cause bias and inconsistent parameter estimates. Misclassification Simulation Extrapolation (MC-SIMEX) is a simulation based measurement error estimation method to obtain reduced parameter bias under misclassification. The main purpose of this study is an adaptation of MC-SIMEX method on Structural Equation Modeling (SEM). The effects of misclassification on the parameter estimates of a binary explanatory variables in SEM and the performance of MC-SIMEX method investigated with both Monte Carlo and an empirical study. According to the main results, finding the best extrapolant function is just as important as estimating the misclassification matrix although MC-SIMEX corrected a part of the bias.

Estimation of sparse functional quantile regression with measurement error: a SIMEX approach.

Quantile regression is a semiparametric method for modeling associations between variables. It is most helpful when the covariates have complex relationships with the location, scale, and shape of the outcome distribution. Despite the method's robustness to distributional assumptions and outliers in the outcome, regression quantiles may be biased in the presence of measurement error in the covariates. The impact of function-valued covariates contaminated with heteroscedastic error has not yet been examined previously; although, studies have investigated the case of scalar-valued covariates. We present a two-stage strategy to consistently fit linear quantile regression models with a function-valued covariate that may be measured with error. In the first stage, an instrumental variable is used to estimate the covariance matrix associated with the measurement error. In the second stage, simulation extrapolation (SIMEX) is used to correct for measurement error in the function-valued covariate. Point-wise standard errors are estimated by means of nonparametric bootstrap. We present simulation studies to assess the robustness of the measurement error corrected for functional quantile regression. Our methods are applied to National Health and Examination Survey data to assess the relationship between physical activity and body mass index among adults in the United States.