scholarly journals Calibration of surgical tools using multilevel modeling with LINEX loss function: Theory and experiment

2021 ◽  
pp. 096228022110036
Author(s):  
Parisa Azimaee ◽  
Mohammad Jafari Jozani ◽  
Yaser Maddahi
Keyword(s):  
Maximum Likelihood ◽  
Multilevel Modeling ◽  
Loss Function ◽  
Multilevel Models ◽  
Confidence Bounds ◽  
Nonparametric Bootstrap ◽  
Surgical Tools ◽  
Modeling Methodology ◽  
Surgical Tool ◽  
Applied Forces

Quantifying the tool–tissue interaction forces in surgery can be used in the training process of novice surgeons to help them better handle surgical tools and avoid exerting excessive forces. A significant challenge concerns the development of proper statistical learning techniques to model the relationship between the true force exerted on the tissue and several outputs read from sensors mounted on the surgical tools. We propose a nonparametric bootstrap technique and a Bayesian multilevel modeling methodology to estimate the true forces. We use the linear exponential loss function to asymmetrically penalize the over and underestimation of the applied forces to the tissue. We incorporate the direction of the force as a group factor in our analysis. A weighted approach is used to account for the nonhomogeneity of read voltages from the surgical tool. Our proposed Bayesian multilevel models provide estimates that are more accurate than those under the maximum likelihood and restricted maximum likelihood approaches. Moreover, confidence bounds are much narrower and the biases and root mean squared errors are significantly smaller in our multilevel models with the linear exponential loss function.

Large-sample confidence intervals of information-theoretic measures in linguistics

2020 ◽  
Vol 6 (1) ◽  
pp. 19-54
Author(s):  
Ryan Ka Yau Lai ◽  
Youngah Do
Keyword(s):  
Maximum Likelihood ◽  
Corpus Linguistics ◽  
Delta Method ◽  
Confidence Bounds ◽  
Likelihood Estimator ◽  
Information Theoretic ◽  
Leibler Divergence ◽  
Information Theoretic Measures ◽  
Data Points ◽  
Measure Of Uncertainty

This article explores a method of creating confidence bounds for information-theoretic measures in linguistics, such as entropy, Kullback-Leibler Divergence (KLD), and mutual information. We show that a useful measure of uncertainty can be derived from simple statistical principles, namely the asymptotic distribution of the maximum likelihood estimator (MLE) and the delta method. Three case studies from phonology and corpus linguistics are used to demonstrate how to apply it and examine its robustness against common violations of its assumptions in linguistics, such as insufficient sample size and non-independence of data points.

scholarly journals 87. Impact of State of Residence on Adult Vaccination Uptake: A Multilevel Modeling Approach

2020 ◽  
Vol 7 (Supplement_1) ◽  
pp. S175-S175
Author(s):  
Shannon Hunter ◽  
Diana Garbinsky ◽  
Elizabeth M La ◽  
Sara Poston ◽  
Cosmina Hogea
Keyword(s):  
Multilevel Modeling ◽  
Vaccination Coverage ◽  
Multilevel Models ◽  
State Level ◽  
Childhood Vaccination ◽  
Material Support ◽  
Adult Vaccination ◽  
Direct Compensation ◽  
Cluster Variation ◽  
Coverage Rates

Abstract Background Previous studies on adult vaccination coverage found inter-state variability that persists after adjusting for individual demographic factors. Assessing the impact of state-level factors may help improve uptake strategies. This study aimed to: • Update previous estimates of state-level, model-adjusted coverage rates for influenza; pneumococcal; tetanus, diphtheria, and acellular pertussis (Tdap); and herpes zoster (HZ) vaccines (individually and in compliance with all age-appropriate recommended vaccinations) • Evaluate effects of individual and state-level factors on adult vaccination coverage using a multilevel modeling framework. Methods Behavioral Risk Factor Surveillance System (BRFSS) survey data (2015–2017) were retrospectively analyzed. Multivariable logistic regression models estimated state vaccination coverage and compliance using predicted marginal proportions. BRFSS data were then combined with external state-level data to estimate multilevel models evaluating effects of state-level factors on coverage. Weighted odds ratios and measures of cluster variation were estimated. Results Adult vaccination coverage and compliance varied by state, even after adjusting for individual characteristics, with coverage ranging as follows: • Influenza (2017): 35.1–48.1% • Pneumococcal (2017): 68.2–80.8% • Tdap (2016): 21.9–46.5% • HZ (2017): 30.5–50.9% Few state-level variables were retained in final multilevel models, and measures of cluster variation suggested substantial residual variation unexplained by individual and state-level variables. Key state-level variables positively associated with vaccination included health insurance coverage rates (influenza/HZ), pharmacists’ vaccination authority (HZ), presence of childhood vaccination exemptions (pneumococcal/Tdap), and adult immunization information system participation (Tdap/HZ). Conclusion Adult vaccination coverage and compliance continue to show substantial variation by state even after adjusting for individual and state-level characteristics associated with vaccination. Further research is needed to assess additional state or local factors impacting vaccination disparities. Funding GlaxoSmithKline Biologicals SA (study identifier: HO-18-19794) Disclosures Shannon Hunter, MS, GSK (Other Financial or Material Support, Ms. Hunter is an employee of RTI Health Solutions, who received consultancy fees from GSK for conduct of the study. Ms. Hunter received no direct compensation from the Sponsor.) Diana Garbinsky, MS, GSK (Other Financial or Material Support, The study was conducted by RTI Health Solutions, which received consultancy fees from GSK. I am a salaried employee at RTI Health Solutions and received no direct compensation from GSK for the conduct of this study..) Elizabeth M. La, PhD, RTI Health Solutions (Employee) Sara Poston, PharmD, The GlaxoSmithKline group of companies (Employee, Shareholder) Cosmina Hogea, PhD, GlaxoSmithKline (Employee, Shareholder)

scholarly journals Application of Multilevel Models to Morphometric Data. Part 2. Correlations

2003 ◽  
Vol 25 (4) ◽  
pp. 187-191 ◽  
Author(s):  
O. Tsybrovskyy ◽  
A. Berghold
Keyword(s):  
Multilevel Modeling ◽  
Multilevel Models ◽  
Correlation Coefficients ◽  
Morphometric Data ◽  
Cell Level ◽  
Units Of Analysis ◽  
Major Interest ◽  
Level Statistics ◽  
Indispensable Tool ◽  
Multivariate Multilevel Models

Multilevel organization of morphometric data (cells are “nested” within patients) requires special methods for studying correlations between karyometric features. The most distinct feature of these methods is that separate correlation (covariance) matrices are produced for every level in the hierarchy. In karyometric research, the cell‐level (i.e., within‐tumor) correlations seem to be of major interest. Beside their biological importance, these correlation coefficients (CC) are compulsory when dimensionality reduction is required. Using MLwiN, a dedicated program for multilevel modeling, we show how to use multivariate multilevel models (MMM) to obtain and interpret CC in each of the levels. A comparison with two usual, “single‐level” statistics shows that MMM represent the only way to obtain correct cell‐level correlation coefficients. The summary statistics method (take average values across each patient) produces patient‐level CC only, and the “pooling” method (merge all cells together and ignore patients as units of analysis) yields incorrect CC at all. We conclude that multilevel modeling is an indispensable tool for studying correlations between morphometric variables.

scholarly journals Within-cluster resampling for multilevel models under informative cluster size

Biometrika ◽  
2019 ◽  
Vol 106 (4) ◽  
pp. 965-972
Author(s):  
D Lee ◽  
J K Kim ◽  
C J Skinner
Keyword(s):  
Maximum Likelihood ◽  
Cluster Size ◽  
Multilevel Model ◽  
Multilevel Models ◽  
Fixed Number ◽  
Regression Coefficients ◽  
Likelihood Estimator ◽  
Correct Model ◽  
Resampling Method ◽  
Informative Cluster Size

Summary A within-cluster resampling method is proposed for fitting a multilevel model in the presence of informative cluster size. Our method is based on the idea of removing the information in the cluster sizes by drawing bootstrap samples which contain a fixed number of observations from each cluster. We then estimate the parameters by maximizing an average, over the bootstrap samples, of a suitable composite loglikelihood. The consistency of the proposed estimator is shown and does not require that the correct model for cluster size is specified. We give an estimator of the covariance matrix of the proposed estimator, and a test for the noninformativeness of the cluster sizes. A simulation study shows, as in Neuhaus & McCulloch (2011), that the standard maximum likelihood estimator exhibits little bias for some regression coefficients. However, for those parameters which exhibit nonnegligible bias, the proposed method is successful in correcting for this bias.

How Does Fidelity of Implementation Matter? Using Multilevel Models to Detect Relationships Between Participant Outcomes and the Delivery and Receipt of Treatment

2012 ◽  
Vol 33 (4) ◽  
pp. 547-565 ◽  
Author(s):  
Keith Zvoch
Keyword(s):  
Program Evaluation ◽  
Multilevel Modeling ◽  
Multilevel Models ◽  
Growth Models ◽  
Fidelity Of Implementation ◽  
Literacy Intervention ◽  
Multidimensional Construct ◽  
Modeling Techniques ◽  
Model Treatment ◽  
Participant Outcomes

Multilevel modeling techniques facilitated examination of relationships between fidelity indicators and outcomes associated with a summer literacy intervention. Three-level growth models were specified to capture the extent to which students experienced instruction and to demonstrate the ways in which dosage–response relationships manifest in program evaluation contexts. The observation that outcome-related deviations from program protocol occurred both at the provider and at the recipient levels suggests that evaluators will often need to conceptualize, measure, and model “treatment fidelity” as a multilevel, multidimensional construct.

Inadmissibility of the Maximum Likelihood Estimator in the Presence of Prior Information

1970 ◽  
Vol 13 (3) ◽  
pp. 391-393 ◽  
Author(s):  
B. K. Kale
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Maximum Likelihood Estimator ◽  
Loss Function ◽  
Prior Information ◽  
Mean Squared Error ◽  
Closed Interval ◽  
Likelihood Estimator ◽  
Usual Estimator ◽  
Squared Error

Lehmann [1] in his lecture notes on estimation shows that for estimating the unknown mean of a normal distribution, N(θ, 1), the usual estimator is neither minimax nor admissible if it is known that θ belongs to a finite closed interval [a, b] and the loss function is squared error. It is shown that , the maximum likelihood estimator (MLE) of θ, has uniformly smaller mean squared error (MSE) than that of . It is natural to ask the question whether the MLE of θ in N(θ, 1) is admissible or not if it is known that θ ∊ [a, b]. The answer turns out to be negative and the purpose of this note is to present this result in a slightly generalized form.

scholarly journals Application of Multilevel Models to Morphometric Data. Part 1. Linear Models and Hypothesis Testing

2003 ◽  
Vol 25 (4) ◽  
pp. 173-185 ◽  
Author(s):  
O. Tsybrovskyy ◽  
A. Berghold
Keyword(s):  
Multilevel Modeling ◽  
Multilevel Models ◽  
Linear Models ◽  
Nuclear Morphology ◽  
Hierarchical Data ◽  
Morphometric Data ◽  
Statistical Software ◽  
Level Statistics ◽  
Thyroid Adenomas ◽  
Theoretical Issues

Morphometric data usually have a hierarchical structure (i.e., cells are nested within patients), which should be taken into consideration in the analysis. In the recent years, special methods of handling hierarchical data, called multilevel models (MM), as well as corresponding software have received considerable development. However, there has been no application of these methods to morphometric data yet. In this paper we report our first experience of analyzing karyometric data by means of MLwiN – a dedicated program for multilevel modeling. Our data were obtained from 34 follicular adenomas and 44 follicular carcinomas of the thyroid. We show examples of fitting and interpreting MM of different complexity, and draw a number of interesting conclusions about the differences in nuclear morphology between follicular thyroid adenomas and carcinomas. We also demonstrate substantial advantages of multilevel models over conventional, single‐level statistics, which have been adopted previously to analyze karyometric data. In addition, some theoretical issues related to MM as well as major statistical software for MM are briefly reviewed.

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