Yields Parameter Estimates Research Articles

Determining ellipses from low-resolution images with a comprehensive image formation model.

When determining the parameters of a parametric planar shape based on a single low-resolution image, common estimation paradigms lead to inaccurate parameter estimates. The reason behind poor estimation results is that standard estimation frameworks fail to model the image formation process at a sufficiently detailed level of analysis. We propose a new method for estimating the parameters of a planar elliptic shape based on a single photon-limited, low-resolution image. Our technique incorporates the effects of several elements-point-spread function, discretization step, quantization step, and photon noise-into a single cohesive and manageable statistical model. While we concentrate on the particular task of estimating the parameters of elliptic shapes, our ideas and methods have a much broader scope and can be used to address the problem of estimating the parameters of an arbitrary parametrically representable planar shape. Comprehensive experimental results on simulated and real imagery demonstrate that our approach yields parameter estimates with unprecedented accuracy. Furthermore, our method supplies a parameter covariance matrix as a measure of uncertainty for the estimated parameters, as well as a planar confidence region as a means for visualizing parameter uncertainty. The mathematical model developed in this paper may prove useful in a variety of disciplines that operate with imagery at the limits of resolution.

Modeling outbreak data: Analysis of a 2012 Ebola virus disease epidemic in DRC.

We describe two approaches to modeling data from a small to moderate-sized epidemic outbreak. The first approach is based on a branching process approximation and direct analysis of the transmission network, whereas the second one is based on a survival model derived from the classical SIR equations with no explicit transmission information. We compare these approaches using data from a 2012 outbreak of Ebola virus disease caused by Bundibugyo ebolavirus in city of Isiro, Democratic Republic of the Congo. The branching process model allows for a direct comparison of disease transmission across different environments, such as the general community or the Ebola treatment unit. However, the survival model appears to yield parameter estimates with more accuracy and better precision in some circumstances.

Bayesian selective response‐adaptive design using the historical control

High quality historical control data, if incorporated, may reduce sample size, trial cost, and duration. A too optimistic use of the data, however, may result in bias under prior‐data conflict. Motivated by well‐publicized two‐arm comparative trials in stroke, we propose a Bayesian design that both adaptively incorporates historical control data and selectively adapt the treatment allocation ratios within an ongoing trial responsively to the relative treatment effects. The proposed design differs from existing designs that borrow from historical controls. As opposed to reducing the number of subjects assigned to the control arm blindly, this design does so adaptively to the relative treatment effects only if evaluation of cumulated current trial data combined with the historical control suggests the superiority of the intervention arm. We used the effective historical sample size approach to quantify borrowed information on the control arm and modified the treatment allocation rules of the doubly adaptive biased coin design to incorporate the quantity. The modified allocation rules were then implemented under the Bayesian framework with commensurate priors addressing prior‐data conflict. Trials were also more frequently concluded earlier in line with the underlying truth, reducing trial cost, and duration and yielded parameter estimates with smaller standard errors.

Monitoring spatial and temporal variation of dissolved oxygen and water temperature in the Savannah River using a sensor network.

Dissolved oxygen is a critical component of river water quality. This study investigated average weekly dissolved oxygen (AWDO) and average weekly water temperature (AWT) in the Savannah River during 2015 and 2016 using data from the Intelligent River® sensor network. Weekly data and seasonal summary statistics revealed distinct seasonal patterns that impact both AWDO and AWT regardless of location along the river. Within seasons, spatial patterns of AWDO and AWT along the river are also evident. Linear mixed effects models indicate that AWT and low and high river flow conditions had a significant impact on AWDO, but added little predictive information to the models. Low and high river flow conditions had a significant impact on AWT, but also added little predictive information to the models. Spatial linear mixed effects models yielded parameter estimates that were effectively the same as non-spatial linear mixed effects models. However, components of variance from spatial linear mixed effects models indicate that 23-32% of the total variance in AWDO and that 12-18% of total variance in AWT can be apportioned to the effect of spatial covariance. These results indicate that location, week, and flow-directional spatial relationships are critically important considerations for investigating relationships between space- and time-varying water quality metrics.

Optimization of selective inversion recovery magnetization transfer imaging for macromolecular content mapping in the human brain.

To optimize a selective inversion recovery (SIR) sequence for macromolecular content mapping in the human brain at 3.0T. SIR is a quantitative method for measuring magnetization transfer (qMT) that uses a low-power, on-resonance inversion pulse. This results in a biexponential recovery of free water signal that can be sampled at various inversion/predelay times (tI/ tD ) to estimate a subset of qMT parameters, including the macromolecular-to-free pool-size-ratio (PSR), the R1 of free water (R1f ), and the rate of MT exchange (kmf ). The adoption of SIR has been limited by long acquisition times (≈4 min/slice). Here, we use Cramér-Rao lower bound theory and data reduction strategies to select optimal tI /tD combinations to reduce imaging times. The schemes were experimentally validated in phantoms, and tested in healthy volunteers (N = 4) and a multiple sclerosis patient. Two optimal sampling schemes were determined: (i) a 5-point scheme (kmf estimated) and (ii) a 4-point scheme (kmf assumed). In phantoms, the 5/4-point schemes yielded parameter estimates with similar SNRs as our previous 16-point scheme, but with 4.1/6.1-fold shorter scan times. Pair-wise comparisons between schemes did not detect significant differences for any scheme/parameter. In humans, parameter values were consistent with published values, and similar levels of precision were obtained from all schemes. Furthermore, fixing kmf reduced the sensitivity of PSR to partial-volume averaging, yielding more consistent estimates throughout the brain. qMT parameters can be robustly estimated in ≤1 min/slice (without independent measures of ΔB0 , B1+, and T1 ) when optimized tI -tD combinations are selected.

Information Criteria for Comparing Partition Schemes.

When inferring phylogenies, one important decision is whether and how nucleotide substitution parameters should be shared across different subsets or partitions of the data. One sort of partitioning error occurs when heterogeneous subsets are mistakenly lumped together and treated as if they share parameter values. The opposite kind of error is mistakenly treating homogeneous subsets as if they result from distinct sets of parameters. Lumping and splitting errors are not equally bad. Lumping errors can yield parameter estimates that do not accurately reflect any of the subsets that were combined whereas splitting errors yield estimates that did not benefit from sharing information across partitions. Phylogenetic partitioning decisions are often made by applying information criteria such as the Akaike information criterion (AIC). As with other information criteria, the AIC evaluates a model or partition scheme by combining the maximum log-likelihood value with a penalty that depends on the number of parameters being estimated. For the purpose of selecting an optimal partitioning scheme, we derive an adjustment to the AIC that we refer to as the AIC$^{(p)}$ and that is motivated by the idea that splitting errors are less serious than lumping errors. We also introduce a similar adjustment to the Bayesian information criterion (BIC) that we refer to as the BIC$^{(p)}$. Via simulation and empirical data analysis, we contrast AIC and BIC behavior to our suggested adjustments. We discuss these results and also emphasize why we expect the probability of lumping errors with the AIC$^{(p)}$ and the BIC$^{(p)}$ to be relatively robust to model parameterization.

C-YES: An Efficient Parametric Yield Estimation Approach for Analog and Mixed-Signal Circuits Based on Multicorner-Multiperformance Correlations

Parametric yield estimation is a critical task for design and validation of analog and mixed-signal (AMS) circuits. However, the computational cost for yield estimation based on Monte Carlo (MC) analysis is often prohibitively high, especially when multiple circuit performances and/or environmental corners (e.g., voltage and temperature corners) are considered. In this paper, a novel statistical method named correlation-aided yield estimation (C-YES) is proposed to reduce the computational cost for parametric yield estimation. Our proposed approach exploits the fact that multiple circuit performances over different environmental corners are often correlated. Hence, we can accurately predict the performance value at one corner from the simulation results for other performances and/or corners. Based upon this observation, instead of running a large number of MC simulations to cover all performances and corners, an efficient algorithm is developed to select a small set of the most “informative” simulations that should be performed for yield estimation. Our numerical experiments show that for parametric yield estimation with multiple circuit performances and environmental corners, C-YES achieves 6.5– $9.3{ \boldsymbol {\times } }$ runtime speedups over other conventional methods.

A bivariate contaminated binormal model for robust fitting of proper ROC curves to a pair of correlated, possibly degenerate, ROC datasets

The objective was to design and implement a bivariate extension to the contaminated binormal model (CBM) to fit paired receiver operating characteristic (ROC) datasets-possibly degenerate-with proper ROC curves. Paired datasets yield two correlated ratings per case. Degenerate datasets have no interior operating points and proper ROC curves do not inappropriately cross the chance diagonal. The existing method, developed more than three decades ago utilizes a bivariate extension to the binormal model, implemented in CORROC2 software, which yields improper ROC curves and cannot fit degenerate datasets. CBM can fit proper ROC curves to unpaired (i.e., yielding one rating per case) and degenerate datasets, and there is a clear scientific need to extend it to handle paired datasets. In CBM, nondiseased cases are modeled by a probability density function (pdf) consisting of a unit variance peak centered at zero. Diseased cases are modeled with a mixture distribution whose pdf consists of two unit variance peaks, one centered at positive μ with integrated probability α, the mixing fraction parameter, corresponding to the fraction of diseased cases where the disease was visible to the radiologist, and one centered at zero, with integrated probability (1-α), corresponding to disease that was not visible. It is shown that: (a) for nondiseased cases the bivariate extension is a unit variances bivariate normal distribution centered at (0,0) with a specified correlation ρ1 ; (b) for diseased cases the bivariate extension is a mixture distribution with four peaks, corresponding to disease not visible in either condition, disease visible in only one condition, contributing two peaks, and disease visible in both conditions. An expression for the likelihood function is derived. A maximum likelihood estimation (MLE) algorithm, CORCBM, was implemented in the R programming language that yields parameter estimates and the covariance matrix of the parameters, and other statistics. A limited simulation validation of the method was performed. CORCBM and CORROC2 were applied to two datasets containing nine readers each contributing paired interpretations. CORCBM successfully fitted the data for all readers, whereas CORROC2 failed to fit a degenerate dataset. All fits were visually reasonable. All CORCBM fits were proper, whereas all CORROC2 fits were improper. CORCBM and CORROC2 were in agreement (a) in declaring only one of the nine readers as having significantly different performances in the two modalities; (b) in estimating higher correlations for diseased cases than for nondiseased ones; and (c) in finding that the intermodality correlation estimates for nondiseased cases were consistent between the two methods. All CORCBM fits yielded higher area under curve (AUC) than the CORROC2 fits, consistent with the fact that a proper ROC model like CORCBM is based on a likelihood-ratio-equivalent decision variable, and consequently yields higher performance than the binormal model-based CORROC2. The method gave satisfactory fits to four simulated datasets. CORCBM is a robust method for fitting paired ROC datasets, always yielding proper ROC curves, and able to fit degenerate datasets.

Cross-Laboratory Comparative Study of the Impact of Experimental and Regression Methodologies on Salmonella Thermal Inactivation Parameters in Ground Beef

Isothermal inactivation studies are commonly used to quantify thermal inactivation kinetics of bacteria. Meta-analyses and comparisons utilizing results from multiple sources have revealed large variations in reported thermal resistance parameters for Salmonella, even when in similar food materials. Different laboratory or regression methodologies likely are the source of methodology-specific artifacts influencing the estimated parameters; however, such effects have not been quantified. The objective of this study was to evaluate the effects of laboratory and regression methodologies on thermal inactivation data generation, interpretation, modeling, and inherent error, based on data generated in two independent laboratories. The overall experimental design consisted of a cross-laboratory comparison using two independent laboratories (Michigan State University and U.S. Department of Agriculture, Agricultural Research Service, Eastern Regional Research Center [ERRC] laboratories), both conducting isothermal Salmonella inactivation studies (55, 60, 62°C) in ground beef, and each using two methodologies reported in prior studies. Two primary models (log-linear and Weibull) with one secondary model (Bigelow) were fitted to the resultant data using three regression methodologies (two two-step regressions and a one-step regression). Results indicated that laboratory methodology impacted the estimated D60°C- and z-values (α = 0.05), with the ERRC methodology yielding parameter estimates ∼25% larger than the Michigan State University methodology, regardless of the laboratory. Regression methodology also impacted the model and parameter error estimates. Two-step regressions yielded root mean square error values on average 40% larger than the one-step regressions. The Akaike Information Criterion indicated the Weibull as the more correct model in most cases; however, caution should be used to confirm model robustness in application to real-world data. Overall, the results suggested that laboratory and regression methodologies have a large influence on resultant data and the subsequent estimation of thermal resistance parameters.

How to model temporal changes in comorbidity for cancer patients using prospective cohort data.

BackgroundThe presence of comorbid conditions is strongly related to survival and also affects treatment choices in cancer patients. This comorbidity is often quantified by the Charlson Comorbidity Index (CCI) using specific weights (1, 2, 3, or 6) for different comorbidities. It has been shown that the CCI increases at different times and with different sizes, so that traditional time to event analysis is not adequate to assess these temporal changes. Here, we present a method to model temporal changes in CCI in cancer patients using data from PCBaSe Sweden, a nation-wide population-based prospective cohort of men diagnosed with prostate cancer. Our proposed model is based on the assumption that a change in comorbidity, as quantified by the CCI, is an irreversible one-way process, i.e., CCI accumulates over time and cannot decrease.MethodsCCI was calculated based on 17 disease categories, which were defined using ICD-codes for discharge diagnoses in the National Patient Register. A state transition model in discrete time steps (i.e., four weeks) was applied to capture all changes in CCI. The transition probabilities were estimated from three modelling steps: 1) Logistic regression model for vital status, 2) Logistic regression model to define any changes in CCI, and 3) Poisson regression model to determine the size of CCI change, with an additional logistic regression model for CCI changes ≥ 6. The four models combined yielded parameter estimates to calculate changes in CCI with their confidence intervals.ResultsThese methods were applied to men with low-risk prostate cancer who received active surveillance (AS), radical prostatectomy (RP), or curative radiotherapy (RT) as primary treatment. There were large differences in CCI changes according to treatment.ConclusionsOur method to model temporal changes in CCI efficiently captures changes in comorbidity over time with a small number of regression analyses to perform – which would be impossible with tradition time to event analyses. However, our approach involves a simulation step that is not yet included in standard statistical software packages. In our prostate cancer example we showed that there are large differences in development of comorbidities among men receiving different treatments for prostate cancer.Electronic supplementary materialThe online version of this article (doi:10.1186/s12911-015-0217-8) contains supplementary material, which is available to authorized users.

Ideal, nonideal, and no-marker variables: The confirmatory factor analysis (CFA) marker technique works when it matters.

A persistent concern in the management and applied psychology literature is the effect of common method variance on observed relations among variables. Recent work (i.e., Richardson, Simmering, & Sturman, 2009) evaluated 3 analytical approaches to controlling for common method variance, including the confirmatory factor analysis (CFA) marker technique. Their findings indicated significant problems with this technique, especially with nonideal marker variables (those with theoretical relations with substantive variables). Based on their simulation results, Richardson et al. concluded that not correcting for method variance provides more accurate estimates than using the CFA marker technique. We reexamined the effects of using marker variables in a simulation study and found the degree of error in estimates of a substantive factor correlation was relatively small in most cases, and much smaller than error associated with making no correction. Further, in instances in which the error was large, the correlations between the marker and substantive scales were higher than that found in organizational research with marker variables. We conclude that in most practical settings, the CFA marker technique yields parameter estimates close to their true values, and the criticisms made by Richardson et al. are overstated.

Analysis of mcDESPOT‐ and CPMG‐derived parameter estimates for two‐component nonexchanging systems

To compare the reliability and stability of the multicomponent-driven equilibrium single pulse observation of T1 and T2 (mcDESPOT) and Carl-Purcell-Meiboom-Gill (CPMG) approaches to parameter estimation. The stability and reliability of mcDESPOT and CPMG-derived parameter estimates were compared through examination of energy surfaces, evaluation of model sloppiness, and Monte Carlo simulations. Comparisons were performed on an equal time basis and assuming a two-component system. Parameter estimation bias, reflecting accuracy, and dispersion, reflecting precision, were derived for a range of signal-to-noise ratios (SNRs) and relaxation parameters. The energy surfaces for parameters incorporated into the mcDESPOT signal model exhibit flatness, a complex structure of local minima, and instability to noise to a much greater extent than the corresponding surfaces for CPMG. Although both mcDESPOT and CPMG performed well at high SNR, the CPMG approach yielded parameter estimates of considerably greater accuracy and precision at lower SNR. mcDESPOT and CPMG both permit high-quality parameter estimates under SNR that are clinically achievable under many circumstances, depending upon available hardware and resolution and acquisition time constraints. At moderate to high SNR, the mcDESPOT approach incorporating two-step phase increments can yield accurate parameter estimates while providing values for longitudinal relaxation times that are not available through CPMG. However, at low SNR, the CPMG approach is more stable and provides superior parameter estimates. Magn Reson Med 75:2406-2420, 2016. © 2015 Wiley Periodicals, Inc.

Addendum to: ‘Reproductive effort accelerates actuarial senescence in wild birds: an experimental study’

We recently showed that manipulation of reproductive effort over the entire lifespan modulated the rate of actuarial senescence in free-living jackdaws Corvus monedula (Boonekamp et al. 2014). We manipulated reproductive effort by giving birds either enlarged or reduced broods to rear (there were no unmanipulated birds), and quantified manipulation effects on parameters of the Gompertz equation fitted to our data using BaSTA (Colchero et al. 2012). We showed that the ageing rate was higher in birds rearing enlarged broods, while the baseline mortality rate was not affected. However, there was individual variation in the age at which birds entered the experiment, and colleagues noted that the way we incorporated the age of first manipulation in our statistical model could bias our Gompertz parameters estimates. We agree with this notion, and present an alternative model that addresses this point in the Supporting Information (S-AD). This model can generally be applied in settings where one aims to quantify differences between groups in mortality parameters, while there is variation in the age at which individuals are entered in the group. However, in our experiment, the variation in age at which birds were entered into the experiment was small, and as a consequence the alternative model yielded parameter estimates that are indistinguishable from our previous estimates (S-AD). Thus, applying the improved model did not change our results, but we recommend the new model when analysing mortality parameters in experiments where there is variation in the age at which individuals are entered into the experiment.

Bayesian analysis of transverse signal decay with application to human brain.

Transverse relaxation analysis with several signal models has been used extensively to determine tissue and material properties. However, the derivation of corresponding parameter values is notoriously unreliable. We evaluate improvements in the quality of parameter estimation using Bayesian analysis and incorporating the Rician noise model, as appropriate for magnitude MR images. Monoexponential, stretched exponential, and biexponential signal models were analyzed using nonlinear least squares (NLLS) and Bayesian approaches. Simulations and phantom and human brain data were analyzed using three different approaches to account for noise. Parameter estimation bias (reflecting accuracy) and dispersion (reflecting precision) were derived for a range of signal-to-noise ratios (SNR) and relaxation parameters. All methods performed well at high SNR. At lower SNR, the Bayesian approach yielded parameter estimates of considerably greater precision, as well as greater accuracy, than did NLLS. Incorporation of the Rician noise model greatly improved accuracy and, to a somewhat lesser extent, precision, in derived transverse relaxation parameters. Analyses of data obtained from solution phantoms and from brain were consistent with simulations. Overall, estimation of parameters characterizing several different transverse relaxation models was markedly improved through use of Bayesian analysis and through incorporation of the Rician noise model.

Lithography parametric yield estimation model to predict layout pattern distortions with a reduced set of lithography simulations

A lithography parametric yield estimation model is presented to evaluate the lithography distortion in a printed layout due to lithography hotspots. The aim of the proposed yield model is to provide a new metric that enables the possibility to objectively compare the lithography quality of different layout design implementations. Moreover, we propose a pattern construct classifier to reduce the set of lithography simulations necessary to estimate the litho degradation. The application of the yield model is demonstrated for different layout configurations showing that a certain degree of layout regularity improves the parametric yield and increases the number of good dies per wafer.

Variability-Aware Parametric Yield Estimation for Analog/Mixed-Signal Circuits: Concepts, Algorithms, and Challenges

Accurate yield estimation is always an important director of design. For analog/mixed signal circuits, the dominant yield loss mechanisms are parametric in nature. This paper provides an informative discussion of varied approaches to parametric yield estimation, including recently developed methods that provide a highly accurate and fast alternative to Monte Carlo methods for some types of analysis.

Reprint of: Fitting population growth models in the presence of measurement and detection error

Population time series data from field studies are complex and statistical analysis requires models that describe nonlinear population dynamics and observational errors. State-space formulations of stochastic population growth models have been used to account for measurement error caused by the data collection process. Parameter estimation, inference, and prediction are all sensitive to measurement error. The observational process may also result in detection errors and if unaccounted for will result in biased parameter estimates. We developed an N-mixture state-space modeling framework to estimate and correct for errors in detection while estimating population model parameters. We tested our methods using simulated data sets and compared the results to those obtained with state-space models when detection is perfect and when detection is ignored. Our N-mixture state-space model yielded parameter estimates of similar quality to a state-space model when detection is perfect. Our results show that ignoring detection errors can lead to biased parameter estimates including an overestimated growth rate, underestimated equilibrium population size and estimated population state that is misleading. We recommend that researchers consider the possibility of detection errors when collecting and analyzing population time series data.

HIV-1 Transmission Networks in a Small World

HIV-1 Transmission Networks in a Small World

Fitting population growth models in the presence of measurement and detection error

Population time series data from field studies are complex and statistical analysis requires models that describe nonlinear population dynamics and observational errors. State-space formulations of stochastic population growth models have been used to account for measurement error caused by the data collection process. Parameter estimation, inference, and prediction are all sensitive to measurement error. The observational process may also result in detection errors and if unaccounted for will result in biased parameter estimates. We developed an N-mixture state-space modeling framework to estimate and correct for errors in detection while estimating population model parameters. We tested our methods using simulated data sets and compared the results to those obtained with state-space models when detection is perfect and when detection is ignored. Our N-mixture state-space model yielded parameter estimates of similar quality to a state-space model when detection is perfect. Our results show that ignoring detection errors can lead to biased parameter estimates including an overestimated growth rate, underestimated equilibrium population size and estimated population state that is misleading. We recommend that researchers consider the possibility of detection errors when collecting and analyzing population time series data.

Application of a mechanism-based disease systems model for osteoporosis to clinical data

A recently proposed mechanism-based disease systems model for osteoporosis (Schmidt et al., J Pharmacokinet Pharmacodyn 38:873-900, 2011) was applied to clinical data from post-menopausal women (n = 767) receiving various doses of the selective estrogen receptor modulator tibolone. Plasma bone-specific alkaline phosphatase activity and urinary N-telopeptide were used as biomarkers reflecting the activity of osteoblasts (bone forming cells) and osteoclasts (bone removing cells), respectively. These data were analyzed in conjunction with data on osteocalcin and on bone mineral density (BMD) (both lumbar spine and total hip), which reflect the activity of both cell types. While the dynamics of bone turnover markers changes rapidly, closely following changes in the activity of bone cells, changes in BMD are slower and have their own dynamics. Application of the mechanism-based disease systems model to the clinical data allowed for an adequate description of the data and yielded parameter estimates that are consistent with physiological values reported in the literature (Lemaire et al., J Theor Biol 229:293-309, 2004). The fitted model enabled characterization of (i) the critical time scales involved in disease progression, (ii) the dynamics of the system during onset and offset of the therapeutic intervention, and (iii) the distinction between responders and low-responders to tibolone treatment.