Effect Of Misspecification Research Articles

Characterization of point-spread function specification error on Geometric Transfer Matrix partial volume correction in [11C]PiB amyloid imaging

PurposePartial-volume correction (PVC) using the Geometric Transfer Matrix (GTM) method is used in positron emission tomography (PET) to compensate for the effects of spatial resolution on quantitation. We evaluate the effect of misspecification of scanner point-spread function (PSF) on GTM results in amyloid imaging, including the effect on amyloid status classification (positive or negative).MethodsTwenty-nine subjects with Pittsburgh Compound B ([11C]PiB) PET and structural T1 MR imaging were analyzed. FreeSurfer 5.3 (FS) was used to parcellate MR images into regions-of-interest (ROIs) that were used to extract radioactivity concentration values from the PET images. GTM PVC was performed using our “standard” PSF parameterization [3D Gaussian, full-width at half-maximum (w) of approximately 5 mm]. Additional GTM PVC was performed with “incorrect” parameterizations, taken around the correct value. The result is a set of regional activity values for each of the GTM applications. For each case, activity values from various ROIs were combined and normalized to produce standardized uptake value ratios (SUVRs) for nine standard [11C]PiB quantitation ROIs and a global region. GTM operating-point characteristics were determined from the slope of apparent SUVR versus w curves.ResultsErrors in specification of w on the order of 1 mm (3D) mainly produce only modest errors of up to a few percent. An exception was the anterior ventral striatum in which fractional errors of up to 0.29 per millimeter (3D) of error in w were observed.ConclusionWhile this study does not address all the issues regarding the quantitative strengths and weakness of GTM PVC, we find that with reasonable caution, the unavoidable inaccuracies associated with PSF specification do not preclude its use in amyloid quantitation.

Power analyses for moderator effects with (non)randomly varying slopes in cluster randomized trials

Researchers often apply moderation analyses to examine whether the effects of an intervention differ conditional on individual or cluster moderator variables such as gender, pretest, or school size. This study develops formulas for power analyses to detect moderator effects in two-level cluster randomized trials (CRTs) using hierarchical linear models. We derive the formulas for estimating statistical power, minimum detectable effect size difference and 95% confidence intervals for cluster- and individual-level moderators. Our framework accommodates binary or continuous moderators, designs with or without covariates, and effects of individual-level moderators that vary randomly or nonrandomly across clusters. A small Monte Carlo simulation confirms the accuracy of our formulas. We also compare power between main effect analysis and moderation analysis, discuss the effects of mis-specification of the moderator slope (randomly vs. non-randomly varying), and conclude with directions for future research. We provide software for conducting a power analysis of moderator effects in CRTs.

The effect of random-effects misspecification on classification accuracy.

Mixed models are a useful way of analysing longitudinal data. Random effects terms allow modelling of patient specific deviations from the overall trend over time. Correlation between repeated measurements are captured by specifying a joint distribution for all random effects in a model. Typically, this joint distribution is assumed to be a multivariate normal distribution. For Gaussian outcomes misspecification of the random effects distribution usually has little impact. However, when the outcome is discrete (e.g. counts or binary outcomes) generalised linear mixed models (GLMMs) are used to analyse longitudinal trends. Opinion is divided about how robust GLMMs are to misspecification of the random effects. Previous work explored the impact of random effects misspecification on the bias of model parameters in single outcome GLMMs. Accepting that these model parameters may be biased, we investigate whether this affects our ability to classify patients into clinical groups using a longitudinal discriminant analysis. We also consider multiple outcomes, which can significantly increase the dimensions of the random effects distribution when modelled simultaneously. We show that when there is severe departure from normality, more flexible mixture distributions can give better classification accuracy. However, in many cases, wrongly assuming a single multivariate normal distribution has little impact on classification accuracy.

Online Ordinal Optimization under Model Misspecification

We consider an ordinal optimization problem, where a decision maker learns the statistical characteristics of a number of systems using sequential sampling in order to ultimately determine the best one (with high probability). In so doing, the decision maker postulates a parametric model which may not precisely represent the true underlying system structure. We show that this misspecification, if not managed properly, can lead to suboptimal performance in the ordinal optimization problem due to a phenomenon identified as sample-selection endogeneity. To address that, we propose online sampling strategies that judiciously learn the unknown model parameters on the fly, and at the same time eliminate the adverse effects of misspecification as the number of samples grows large. The proposed sampling strategies are oblivious to the model misspecification; are shown to have strong performance guarantees regardless of that knowledge; and are computationally tractable.

Economic design of repetitive group sampling plan based on truncated life test under Birnbaum–Saunders distribution

In this paper, we design the repetitive group sampling plan under Birnbaum–Saunders distribution, since this distribution is considered as an appropriate and flexible distribution to model different types of data particularly lifetime data. In this study, the Birnbaum–Saunders distributed mean lifetime of the product is considered as the quality characteristic where the shape parameter is assumed to be known. For different mean ratios, the design parameters such as sample size, conditional and unconditional acceptance numbers of the proposed repetitive group sampling plan are determined using the approach of two points on the operating characteristic curve. In order to select the optimal parameters, tables are constructed for different values of shape parameter of Birnbaum–Saunders distribution. We explain the implementation of the proposed repetitive group sampling plan with descriptive example as well as using real time data and the effect of misspecification of shape parameter on lot acceptance probability is investigated. In addition, the proposed repetitive group sampling plan is compared with single and double sampling plans in terms of discriminating power and average sample number. An economic design of the proposed repetitive group sampling plan is discussed and optimal plans are determined to satisfy both producer’s and consumer’s risks with minimum cost. Sensitivity of the proposed plan based on failure probability and cost parameters is analyzed in this paper.

The effects of misspecifying the random part of multilevel models

This paper examined the amount bias in standard errors for fixed effects when the random part of a multilevel model is misspecified. Study 1 examined the effects of misspecification for a model with one Level 1 predictor. Results indicated that misspecifying random slope variance as fixed had a moderate effect size on the standard errors of the fixed effects and had a greater effect than misspecifying fixed slopes as random. In Study 2, a second Level 1 predictor was added and allowed for the examination of the effects of misspecifying the slope variance of one predictor on the standard errors for the fixed effects of the other predictor. Results indicated that only the standard errors of coefficient relevant to that predictor were impacted and that the effect size for the bias could be considered moderate to large. These results suggest that researchers can use a piecemeal approach to testing multilevel models with random effects.

Detecting participant noncompliance across multiple time points by modeling a longitudinal biomarker.

Participant noncompliance, in which participants do not follow their assigned treatment protocol, has long complicated the interpretation of randomized clinical trials. No gold standard has been identified for detecting noncompliance, but in some trials participants' biomarkers can provide objective information that suggests exposure to non-study treatments. However, existing methods are limited to retrospectively detecting noncompliance at a single time point based on a single biomarker measurement. We propose a novel method that can leverage participants' full biomarker history to detect noncompliance across multiple time points. Conditional on longitudinal biomarker data, our method can estimate the probability of compliance at (1) a single time point of the trial, (2) all time points, and (3) a future time point. Across time points, we model the biomarker as a mixture density with (latent) components corresponding to longitudinal patterns of compliance. To estimate the mixture density, we fit mixed effects models for both compliance and the biomarker. We use the mixture density to derive compliance probabilities that condition on the longitudinal biomarker data. We evaluate our compliance probabilities by simulation and apply them to a trial in which current smokers were asked to only smoke low nicotine study cigarettes (Center for the Evaluation of Nicotine in Cigarettes Project 1 Study 2). In the simulation, we investigated three different effects of compliance on the biomarker, as well as the effect of misspecification of the covariance structures. We compared probability estimators (1) and (2) to those that ignore the longitudinal correlation in the data according to area under the receiver operating characteristic curve. We evaluated estimator (3) by plotting its calibration lines. For Center for the Evaluation of Nicotine in Cigarettes Project 1 Study 2, we compared estimators (1) and (3) to a probability estimator of compliance at the last time point that ignores the longitudinal correlation. In the simulation, for both compliance at the last time point and at all time points, conditioning on the longitudinal biomarker data uniformly raised area under the receiver operating characteristic curve across all three compliance effect scenarios. The gains in area under the receiver operating characteristic curve were smaller under misspecification. The calibration lines for the prediction of compliance closely followed 45°, though with additional variability under misspecification. For compliance at the last time point of Center for the Evaluation of Nicotine in Cigarettes Project 1 Study 2, conditioning on participants' full biomarker history boosted area under the receiver operating characteristic curve by three percentage points. The prediction probabilities somewhat accurately approximated the non-longitudinal compliance probabilities. Compared to existing methods that only use a single biomarker measurement, our method can account for the longitudinal correlation in the biomarker and compliance to more accurately identify noncompliant participants. Our method can also use participants' biomarker history to predict compliance at a future time point.

High dimensional nuisance parameters: an example from parametric survival analysis

Parametric statistical problems involving both large amounts of data and models with many parameters raise issues that are explicitly or implicitly differential geometric. When the number of nuisance parameters is comparable to the sample size, alternative approaches to inference on interest parameters treat the nuisance parameters either as random variables or as arbitrary constants. The two approaches are compared in the context of parametric survival analysis, with emphasis on the effects of misspecification of the random effects distribution. Notably, we derive a detailed expression for the precision of the maximum likelihood estimator of an interest parameter when the assumed random effects model is erroneous, recovering simply derived results based on the Fisher information in the correctly specified situation but otherwise illustrating complex dependence on other aspects. Methods of assessing model adequacy are given. The results are both directly applicable and illustrate general principles of inference when there is a high-dimensional nuisance parameter. Open problems with an information geometrical bearing are outlined.

The abatement of particulate matter 2.5 in Los Angeles County: a counterfactual evaluation

The ambient PM2.5 concentration in Los Angeles (LA) County has been on a decreasing trend since LA County was designated as a nonattainment area in 2005. However, whether the nonattainment assignment is the underlying cause of the county’s reductions in PM2.5 requires further empirical investigation. Traditional statistical approaches used to study the impact of nonattainment designation on air quality present problems involving indeterministic covariates, confoundedness, model misspecification, and undetected effects at the aggregate level. Our study successfully uses the Panel Data Approach for Program Evaluation (PAMPE) to compare the differences between the actual outcomes and counterfactual outcomes to reveal the treatment effects associated with nonattainment assignment without the burden associated with previous studies. Our results show that, at the monitor level, the air quality improvements obtained by the more-polluted areas were greater after LA County was designated as a nonattainment area. On average, the counterfactual reduction rates derived in our study range from − 0.01 to − 0.15%. Cases in which PM2.5 levels increased occurred at two monitors that were fully or partially compliant during the study period, suggesting the regulatory oversight is indeed spatially heterogeneous.

Semiparametric estimation for linear regression with symmetric errors

To avoid the effect of distributional misspecification in the model-based regression, we propose an essentially nonparametric symmetric error distribution and construct a so-called doubly smoothed (DS) likelihood function by applying the same amount of smoothing to both the model and given data. To compute the DS maximum likelihood estimator based on the DS likelihood, we propose an approximated DS likelihood which has the form of a semiparametric mixture likelihood and apply some existing algorithms in the nonparametric mixture literature. The consistency of the DS maximum likelihood estimator is also established with any fixed smoothing parameter. Through numerical studies, we demonstrate that the proposed regression coefficient estimator has relatively good performance in terms of efficiency across a wide range of error distributions and robustness against outliers.

English

The current interest in meta-analysis of count data in which some studies have zero events (sparse data) has led to re-assessment of commonly used meta-analysis methods to establish their validity in such scenarios. The general consensus is that methods which exclude studies with zero events should be avoided. In the family of parametric methods, random effects models come out highly recommended. While acknowledging the strength of this approach, one of its aspects with potentially undesirable impact on the results, is often overlooked. The random effects approach accounts for the variation in the effect measure across studies by using models with random slopes. It has been shown that parameters associated with a random structure risk being estimated with biased unless the distribution of the random effects is correctly specified. In meta-analysis the parameter of interest, average effect measure, is associated with a random structure (random slope). Information on how the effect measure point and precision estimates are affected by misspecification of random effects distribution is still lacking. To fill in the information gap, we used a simulation study to investigate the impact of misspecification of distribution of random effects in this context and provide guidelines in using the random effects approach. Our results indicated that relative bias in the estimated effect measure could be as high as 30% and 95% confidence interval coverage as low as 0%. These results send a clear message that possible effects of misspecification of the distribution of random effects should not be ignored. In light of these findings, we have proposed a sensitivity analysis that also establishes whether a random slope model is necessary.

Effect of misspecification of random effects distribution on the performance of parameters estimation methods in binary logistic mixed models

Nous avons compare, a l’aide de la simulation, une methode d’estimation Bayesienne (INLA) a trois methodes classiques d’estimation (PQL, HLM et AGHQ) sous six distributions des effets aleatoires dans le cadre des modeles logistiques binaires mixtes. Les resultats ont montre la superiorite de AGHQ et HLM sur les autres pour toutes les distributions considerees dans le cas des effets fixes. Pour les effets aleatoires, les methodes classiques ont montre les meilleures performances pour les distributions symetriques consideres. AGHQ, HLM et INLA ont donne de meilleurs resultats par rapport a PQL pour les distributions normale et uniforme pour tous les echantillons consideres.

Designing of Repetitive Group Sampling Plan under the Inverse Gaussian Distribution

This study investigates the attributes repetitive group sampling plans based on a truncated life test under the inverse Gaussian distribution with known shape parameter. The sample size and two acceptance numbers are the three design parameters determined for the proposed repetitive group sampling plans for different mean ratios. Tables are constructed to determine the optimal design parameters for different values of shape parameters of the inverse Gaussian model and the results are explained by with examples. Also the effect of misspecification of shape parameters is also discussed.

A New Statistical Method for Estimating Usual Intakes of Nearly-Daily Consumed Foods and Nutrients Through Use of Only One 24-hour Dietary Recall

BackgroundTo estimate usual intake distributions of dietary components, collection of nonconsecutive repeated 24-h dietary recalls is recommended, but resource limitations sometimes restrict data collection to single-day dietary data per person.ObjectivesWe developed a new statistical method, the NCI 1-d method, which uses single-day dietary data and an external within-person to between-person variance ratio to estimate population distributions of usual intake of nearly-daily consumed foods and nutrients.MethodsWe used NHANES 2011–2014 data for men (n = 4938 and n = 4293 for the first and second 24-h recalls) to compare nutrient intake distributions of vitamin A, magnesium, folate, and vitamin E generated by the 1-d method (with use of only the first recall per person) with those from the NCI amount-only method (with use of all days of dietary intake per person). The within-person to between-person variance ratio from the amount-only model was used as the unbiased “external” estimate for the 1-d method. We also examined the effect of mis-specification of variance ratios on usual intake distributions.ResultsThe amount-only and 1-d methods estimated statistically equivalent median (25p, 75p): 647 (459, 890) compared with 648 (461, 886) μg retinol activity equivalents/d, 338 (268, 420) compared with 334 (266, 417) mg magnesium/d, 595 (458, 762) compared with 589 (456, 758) μg dietary folate equivalents/d, and 9.7 (7.3, 12.6) compared with 9.6 (7.3, 12.7) mg vitamin E/d. As the external variance ratios increased from 25% to 200% of the unbiased ratios, the prevalence of inadequate intake ranged from 53% to 43% for vitamin A, 57% to 55% for magnesium, 16% to 2% for folate, and 70% to 73% for vitamin E.ConclusionsThe 1-d method is a viable statistical method for estimating usual intakes of nearly-daily consumed dietary components when the variance ratio is unbiased. Results are sensitive to variance ratio selection, so researchers should still collect replicate data where possible.

The Effects of Misspecification and Hierarchical Structure of Attributes in Q-Matrix on the Quality Level in Estimating Cognitive Diagnostic Model

The Effects of Misspecification and Hierarchical Structure of Attributes in Q-Matrix on the Quality Level in Estimating Cognitive Diagnostic Model

Robust designs for multinomial models

Model misspecification in generalized linear models (GLMs) occurs usually when the linear predictor and/or the link function assumed are incorrect. This article discusses the effect of such misspecification on design selection for multinomial GLMs and proposes the use of quantile dispersion graphs to select robust designs. Due to misspecification in the model, parameter estimates are usually biased and the designs are compared on the basis of their mean squared error of prediction. Several numerical examples including a real data set are presented to illustrate the proposed methodology.

Monotonicity and robustness in Wiener disorder detection

We study the problem of detecting a drift change of a Brownian motion under various extensions of the classical case. Specifically, we consider the case of a random post-change drift and examine monotonicity properties of the solution with respect to different model parameters. Moreover, robustness properties – effects of misspecification of the underlying model – are explored.

Inference in dynamic discrete choice problems under local misspecification

Single‐agent dynamic discrete choice models are typically estimated using heavily parametrized econometric frameworks, making them susceptible to model misspecification. This paper investigates how misspecification affects the results of inference in these models. Specifically, we consider a local misspecification framework in which specification errors are assumed to vanish at an arbitrary and unknown rate with the sample size. Relative to global misspecification, the local misspecification analysis has two important advantages. First, it yields tractable and general results. Second, it allows us to focus on parameters with structural interpretation, instead of “pseudo‐true” parameters.We consider a general class of two‐step estimators based on the K‐stage sequential policy function iteration algorithm, where K denotes the number of iterations employed in the estimation. This class includes Hotz and Miller (1993)'s conditional choice probability estimator, Aguirregabiria and Mira (2002)'s pseudo‐likelihood estimator, and Pesendorfer and Schmidt‐Dengler (2008)'s asymptotic least squares estimator.We show that local misspecification can affect the asymptotic distribution and even the rate of convergence of these estimators. In principle, one might expect that the effect of the local misspecification could change with the number of iterations K. One of our main findings is that this is not the case, that is, the effect of local misspecification is invariant to K. In practice, this means that researchers cannot eliminate or even alleviate problems of model misspecification by choosing K. Single‐agent dynamic discrete choice models estimation inference misspecification local misspecification C13 C61 C73

Determination of optimal quick switching system with varying sample size for assuring mean life under Weibull distribution

Conventional sampling plans are applied to dispose an individual lot or isolated lot that requires a large sample size. Consequently, the inspection time and cost needed to make a decision under conventional plans are high. In order to reduce the sample size and to inspect the series of lots with minimum cost and time, special purpose plans are utilized. In this article, we propose one of the special purpose plans, namely, a quick switching sampling system that is also known as a two-plan sampling system. Through this sampling system, the Weibull-distributed mean life of the product is ensured based on time-truncated life tests. The proposed system is designed with the intention of minimizing the average sample number using two points on the operating characteristic curve approach. The optimal parameters of the proposed system are determined for different combinations of producer’s risk and consumer’s risk. Implementation of the proposed system is also explained and the performance of the proposed system is compared with other existing plans. In addition, the effects of misspecification of shape parameters on optimal parameters and the probability of acceptance are discussed.

Prior Robustness for Bayesian Implementation of the Fault Tree Analysis

We propose a prior robustness approach for the Bayesian implementation of the fault tree analysis (FTA). FTA is often used to evaluate risk in large, safety critical systems but has limitations due to its static structure. Bayesian approaches have been proposed as a superior alternative to it, however, this involves prior elicitation, which is not straightforward. We show that minor misspecification of priors for elementary events can result in a significant prior misspecification for the top event. A large amount of data is required to correctly update a misspecified prior and such data may not be available for many complex, safety critical systems. In such cases, prior misspecification equals posterior misspecification. Therefore, there is a need to develop a robustness approach for FTA, which can quantify the effects of prior misspecification on the posterior analysis. Here, we propose the first prior robustness approach specifically developed for FTA. We not only prove a few important mathematical properties of this approach, but also develop easy to use Monte Carlo sampling algorithms to implement this approach on any given fault tree with and and/or or gates. We then implement this Bayesian robustness approach on two real-life examples: a spacecraft re-entry example and a feeding control system example. We also provide a step-by-step illustration of how this approach can be applied to a real-life problem.