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IEEE Transactions on Bio-medical... Dec 2014This study aims to analyze the protein aggregates spatial distribution for different cataract degrees, and correlate this information with the lens acoustical parameters...
This study aims to analyze the protein aggregates spatial distribution for different cataract degrees, and correlate this information with the lens acoustical parameters and by this way, assess the cataract regional hardness. Different cataract degrees were induced ex vivo in porcine lenses. A 25 MHz ultrasonic transducer was used to obtain the acoustical parameters (velocity, attenuation, and backscattering signals). B-scan and Nakagami images were constructed. Also, lenses with different cataract degrees were sliced in two regions (nucleus and cortex), for fibers and collagen detection. A significant increase with cataract formation was found for the velocity, attenuation, and brightness intensity of the B-scan images and Nakagami m parameter ( ). The acoustical parameters showed a good to moderate correlation with the m parameter for the different stages of cataract formation. A strong correlation was found between the protein aggregates in the cortex and the m parameter. Lenses without cataract are characterized using a classification and regression tree, by a mean brightness intensity ≤0.351, a variance of the B-scan brightness intensity ≤0.070, a velocity ≤1625 m/s, and an attenuation ≤0.415 dB/mm·MHz (sensitivity: 100% and specificity: 72.6%). To characterize different cataract degrees, the m parameter should be considered. Initial stages of cataract are characterized by a mean brightness intensity >0.351 and a variance of the m parameter >0.110. Advanced stages of cataract are characterized by a mean brightness intensity >0.351, a variance of the m parameter ≤0.110, and a mean m parameter >0.374. For initial and advanced stages of cataract, a sensitivity of 78.4% and a specificity of 86.5% are obtained.
Topics: Algorithms; Animals; Cataract; Data Interpretation, Statistical; Elasticity Imaging Techniques; Hardness; Image Interpretation, Computer-Assisted; In Vitro Techniques; Reproducibility of Results; Scattering, Radiation; Sensitivity and Specificity; Statistical Distributions; Swine
PubMed: 25014952
DOI: 10.1109/TBME.2014.2335739 -
Behavior Research Methods Dec 2021Recent replication crisis has led to a number of ad hoc suggestions to decrease the chance of making false positive findings. Among them, Johnson (Proceedings of the...
Recent replication crisis has led to a number of ad hoc suggestions to decrease the chance of making false positive findings. Among them, Johnson (Proceedings of the National Academy of Sciences, 110, 19313-19317, 2013) and Benjamin et al. (Nature Human Behaviour, 2, 6-10 2018) recommend using the significance level of α = 0.005 (0.5%) as opposed to the conventional 0.05 (5%) level. Even though their suggestion is easy to implement, it is unclear whether or not the commonly used statistical tests are robust and/or powerful at such a small significance level. Therefore, the main aim of our study is to investigate the robustness and power curve behaviors of independent (unpaired) two-sample tests for metric and ordinal data at nominal significance levels of α = 0.005 and α = 0.05. Through an extensive simulation study, it is found that the permutation versions of the Welch t-test and the Brunner-Munzel test are particularly robust and powerful while the commonly used two-sample tests which utilize t-distribution tend to be either liberal or conservative, and have peculiar power curve behaviors under skewed distributions with variance heterogeneity.
Topics: Computer Simulation; False Positive Reactions; Humans; Models, Statistical; Probability; Statistical Distributions
PubMed: 34050436
DOI: 10.3758/s13428-021-01595-5 -
Statistics in Medicine Dec 2020Recently developed accelerometer devices have been used in large epidemiological studies for continuous and objective monitoring of physical activities. Typically,...
Recently developed accelerometer devices have been used in large epidemiological studies for continuous and objective monitoring of physical activities. Typically, physical movements are summarized as minutes in light, moderate, and vigorous physical activities in each wearing day. Because of preponderance of zeros, zero-inflated distributions have been used for modeling the daily moderate or higher levels of physical activity. Yet, these models do not fully account for variations in daily physical activity and cannot be extended to model weekly physical activity explicitly, while the weekly physical activity is considered as an indicator for a subject's average level of physical activity. To overcome these limitations, we propose to use a zero-inflated Poisson mixture distribution that can model daily and weekly physical activity in same family of mixture distributions. Under this method, the likelihood of an inactive day and the amount of exercise in an active day are simultaneously modeled by a joint random effects model to incorporate heterogeneity across participants. If needed, the method has the flexibility to include an additional random effect to address extra variations in daily physical activity. Maximum likelihood estimation can be obtained through Gaussian quadrature technique, which is implemented conveniently in an R package GLMMadaptive. Method performances are examined using simulation studies. The method is applied to data from the Hispanic Community Health Study/Study of Latinos to examine the relationship between physical activity and BMI groups and within a participant the difference in physical activity between weekends and weekdays.
Topics: Computer Simulation; Exercise; Humans; Models, Statistical; Poisson Distribution; Research Design
PubMed: 32949036
DOI: 10.1002/sim.8748 -
Scientific Reports Nov 2015Meta-analysis is a very useful tool to combine information from different sources. Fixed effect and random effect models are widely used in meta-analysis. Despite their...
Meta-analysis is a very useful tool to combine information from different sources. Fixed effect and random effect models are widely used in meta-analysis. Despite their popularity, they may give us misleading results if the models don't fit the data but are blindly used. Therefore, like any statistical analysis, checking the model fitting is an important step. However, in practice, the goodness-of-fit in meta-analysis is rarely discussed. In this paper, we propose some tests to check the goodness-of-fit for the fixed and random effect models with assumption of normal distributions in meta-analysis. Through simulation study, we show that the proposed tests control type I error rate very well. To demonstrate the usefulness of the proposed tests, we also apply them to some real data sets. Our study shows that the proposed tests are useful tools in checking the goodness-of-fit of the normal models used in meta-analysis.
Topics: Humans; Meta-Analysis as Topic; Models, Statistical; Normal Distribution
PubMed: 26592212
DOI: 10.1038/srep16983 -
Biometrical Journal. Biometrische... Apr 2023Disease mapping models have been popularly used to model disease incidence with spatial correlation. In disease mapping models, zero inflation is an important issue,...
Disease mapping models have been popularly used to model disease incidence with spatial correlation. In disease mapping models, zero inflation is an important issue, which often occurs in disease incidence datasets with high proportions of zero disease count. It is originated from limited survey coverage or unadvanced testing equipment, which makes some regions have no observed patients. Then excessive zeros recorded in the disease incidence dataset would mess up the true distributions of disease incidence and lead to inaccurate estimates. To address this issue, a zero-inflated disease mapping model is developed in this work. In this model, a zero-inflated process using Bernoulli indicators is assumed to characterize whether the zero inflation occurs for each region. For regions without zero inflation, a coherent and generative disease mapping model is applied for mapping the spatially correlated disease incidence. Independent spatial random effects are incorporated in both processes to account for the spatial patterns of zero inflation and disease incidence. External covariates are also considered in both processes to better explain the disease count data. To estimate the model, a Markov chain Monte Carlo algorithm is proposed. We evaluate model performance via a variety of simulation experiments. Finally, a Lyme disease dataset of Virginia is analyzed to illustrate the application of the proposed model.
Topics: Humans; Incidence; Poisson Distribution; Computer Simulation; Monte Carlo Method; Algorithms; Models, Statistical
PubMed: 36732909
DOI: 10.1002/bimj.202200090 -
Statistics in Medicine Oct 2015Zero-inflated Poisson (ZIP) and negative binomial (ZINB) models are widely used to model zero-inflated count responses. These models extend the Poisson and negative...
Zero-inflated Poisson (ZIP) and negative binomial (ZINB) models are widely used to model zero-inflated count responses. These models extend the Poisson and negative binomial (NB) to address excessive zeros in the count response. By adding a degenerate distribution centered at 0 and interpreting it as describing a non-risk group in the population, the ZIP (ZINB) models a two-component population mixture. As in applications of Poisson and NB, the key difference between ZIP and ZINB is the allowance for overdispersion by the ZINB in its NB component in modeling the count response for the at-risk group. Overdispersion arising in practice too often does not follow the NB, and applications of ZINB to such data yield invalid inference. If sources of overdispersion are known, other parametric models may be used to directly model the overdispersion. Such models too are subject to assumed distributions. Further, this approach may not be applicable if information about the sources of overdispersion is unavailable. In this paper, we propose a distribution-free alternative and compare its performance with these popular parametric models as well as a moment-based approach proposed by Yu et al. [Statistics in Medicine 2013; 32: 2390-2405]. Like the generalized estimating equations, the proposed approach requires no elaborate distribution assumptions. Compared with the approach of Yu et al., it is more robust to overdispersed zero-inflated responses. We illustrate our approach with both simulated and real study data.
Topics: Binomial Distribution; Biometry; Computer Simulation; HIV Infections; Humans; Likelihood Functions; Male; Models, Statistical; Poisson Distribution; Randomized Controlled Trials as Topic
PubMed: 26078035
DOI: 10.1002/sim.6560 -
Journal of Theoretical Biology Mar 2020Cellular heterogeneity is known to have important effects on signal processing and cellular decision making. To understand these processes, multiple classes of...
Cellular heterogeneity is known to have important effects on signal processing and cellular decision making. To understand these processes, multiple classes of mathematical models have been introduced. The hierarchical population model builds a novel class which allows for the mechanistic description of heterogeneity and explicitly takes into account subpopulation structures. However, this model requires a parametric distribution assumption for the cell population and, so far, only the normal distribution has been employed. Here, we incorporate alternative distribution assumptions into the model, assess their robustness against outliers and evaluate their influence on the performance of model calibration in a simulation study and a real-world application example. We found that alternative distributions provide reliable parameter estimates even in the presence of outliers, and can in fact increase the convergence of model calibration.
Topics: Calibration; Computer Simulation; Models, Statistical; Models, Theoretical; Normal Distribution
PubMed: 31866394
DOI: 10.1016/j.jtbi.2019.110118 -
Behavior Research Methods Apr 2024Understanding causal mechanisms is a central goal in the behavioral, developmental, and social sciences. When estimating and probing causal effects using observational...
Understanding causal mechanisms is a central goal in the behavioral, developmental, and social sciences. When estimating and probing causal effects using observational data, covariate adjustment is a crucial element to remove dependencies between focal predictors and the error term. Covariate selection, however, constitutes a challenging task because availability alone is not an adequate criterion to decide whether a covariate should be included in the statistical model. The present study introduces a non-Gaussian method for covariate selection and provides a forward selection algorithm for linear models (i.e., non-Gaussian forward selection; nGFS) to select appropriate covariates from a set of potential control variables to avoid inconsistent and biased estimators of the causal effect of interest. Further, we demonstrate that the forward selection algorithm has properties compatible with principles of direction of dependence, i.e., probing whether the causal target model is correctly specified with respect to the causal direction of effects. Results of a Monte Carlo simulation study suggest that the selection algorithm performs well, in particular when sample sizes are large (i.e., n ≥ 250) and data strongly deviate from Gaussianity (e.g., distributions with skewness beyond 1.5). An empirical example is given for illustrative purposes.
Topics: Humans; Algorithms; Monte Carlo Method; Models, Statistical; Normal Distribution; Linear Models; Learning; Causality; Computer Simulation; Data Interpretation, Statistical
PubMed: 37704788
DOI: 10.3758/s13428-023-02217-y -
PloS One 2020A new generalized linear mixed quantile model for panel data is proposed. This proposed approach applies GEE with smoothed estimating functions, which leads to...
A new generalized linear mixed quantile model for panel data is proposed. This proposed approach applies GEE with smoothed estimating functions, which leads to asymptotically equivalent estimation of the regression coefficients. Random effects are predicted by using the best linear unbiased predictors (BLUP) based on the Tweedie exponential dispersion distributions which cover a wide range of distributions, including those widely used ones, such as the normal distribution, Poisson distribution and gamma distribution. A Taylor expansion of the quantile estimating function is used to linearize the random effects in the quantile process. The parameter estimation is based on the Newton-Raphson iteration method. Our proposed quantile mixed model gives consistent estimates that have asymptotic normal distributions. Simulation studies are carried out to investigate the small sample performance of the proposed approach. As an illustration, the proposed method is applied to analyze the epilepsy data.
Topics: Computer Simulation; Data Interpretation, Statistical; Linear Models; Normal Distribution
PubMed: 32780767
DOI: 10.1371/journal.pone.0237326 -
Computational Intelligence and... 2022A two-parameter continuous distribution, namely, power-modified Lindley (PML), is proposed. Various structural properties of the new distribution, including moments,...
A two-parameter continuous distribution, namely, power-modified Lindley (PML), is proposed. Various structural properties of the new distribution, including moments, moment-generating function, conditional moments, mean deviations, mean residual lifetime, and mean past lifetime, are provided. The reliability of a system is discussed when the strength of the system and the stress imposed on it are independent. Maximum-likelihood estimation of the parameters and their estimated asymptotic standard errors are derived. Bayesian estimation methods of the parameters with independent gamma prior are discussed based on symmetric and asymmetric loss functions. We proposed using the MCMC technique with the Metropolis-Hastings algorithm to approximate the posteriors of the stress-strength parameters for Bayesian calculations. The confidence interval for likelihood and the Bayesian estimation method is obtained for the parameter of the model and stress-strength reliability. We prove empirically the importance and flexibility of the new distribution in modeling with real data applications.
Topics: Algorithms; Bayes Theorem; Likelihood Functions; Reproducibility of Results; Statistical Distributions
PubMed: 35242174
DOI: 10.1155/2022/1154705