Checking Assumptions in Latent Class Regression Models via a Markov Chain Monte Carlo Estimation Approach: An Application to Depression and Socio-Economic Status

Latent class regression models are useful tools for assessing associations between covariates and latent variables. However, evaluation of key model assumptions cannot be performed using methods from standard regression models due to the unobserved nature of latent outcome variables. This paper presents graphical diagnostic tools to evaluate whether or not latent class regression models adhere to standard assumptions of the model: conditional independence and non-differential measurement. An integral part of these methods is the use of a Markov Chain Monte Carlo estimation procedure. Unlike standard maximum likelihood implementations for latent class regression model estimation, the MCMC approach allows us to calculate posterior distributions and point estimates of any functions of parameters. It is this convenience that allows us to provide the diagnostic methods that we introduce. As a motivating example we present an analysis focusing on the association between depression and socioeconomic status, using data from the Epidemiologic Catchment Area study. We consider a latent class regression analysis investigating the association between depression and socioeconomic status measures, where the latent variable depression is regressed on education and income indicators, in addition to age, gender, and marital status variables. While the fitted latent class regression model yields interesting results, the model parameters are found to be invalid due to the violation of model assumptions. The violation of these assumptions is clearly identified by the presented diagnostic plots. These methods can be applied to standard latent class and latent class regression models, and the general principle can be extended to evaluate model assumptions in other types of models.

Nonparametric Estimation of the Bivariate Recurrence Time Distribution

This paper considers statistical models in which two different types of events, such as the diagnosis of a disease and the remission of the disease, occur alternately over time and are observed subject to right censoring. We propose nonparametric estimators for the joint distribution of bivariate recurrence times and the marginal distribution of the first recurrence time. In general, the marginal distribution of the second recurrence time cannot be estimated due to an identifiability problem, but a conditional distribution of the second recurrence time can be estimated non-parametrically. In literature, statistical methods have been developed to estimate the joint distribution of bivariate recurrence times based on data of the first pair of censored bivariate recurrence times. These methods are efficient in the current model because recurrence times of higher orders are not used. Asymptotic properties of the estimators are established. Numerical studies demonstrate the estimator performs well with practical sample sizes. We apply the proposed method to a Denmark psychiatric case register data set for illustration of the methods and theory.

Kernel Estimation of Rate Function for Recurrent Event Data

Recurrent event data are largely characterized by the rate function but smoothing techniques for estimating the rate function have never been rigorously developed or studied in statistical literature. This paper considers the moment and least squares methods for estimating the rate function from recurrent event data. With an independent censoring assumption on the recurrent event process, we study statistical properties of the proposed estimators and propose bootstrap procedures for the bandwidth selection and for the approximation of confidence intervals in the estimation of the occurrence rate function. It is identified that the moment method without resmoothing via a smaller bandwidth will produce curve with nicks occurring at the censoring times, whereas there is no such problem with the least squares method. Furthermore, the asymptotic variance of the least squares estimator is shown to be smaller under regularity conditions. However, in the implementation of the bootstrap procedures, the moment method is computationally more efficient than the least squares method because the former approach uses condensed bootstrap data. The performance of the proposed procedures is studied through Monte Carlo simulations and an epidemiological example on intravenous drug users.

Statistical evaluation of time-dependent metabolite concentrations: estimation of post-mortem intervals based on in situ 1H-MRS of the brain

Knowledge of the time interval from death (post-mortem interval, PMI) has an enormous legal, criminological and psychological impact. Aiming to find an objective method for the determination of PMIs in forensic medicine, 1H-MR spectroscopy (1H-MRS) was used in a sheep head model to follow changes in brain metabolite concentrations after death. Following the characterization of newly observed metabolites (Ith et al., Magn. Reson. Med. 2002; 5: 915-920), the full set of acquired spectra was analyzed statistically to provide a quantitative estimation of PMIs with their respective confidence limits. In a first step, analytical mathematical functions are proposed to describe the time courses of 10 metabolites in the decomposing brain up to 3 weeks post-mortem. Subsequently, the inverted functions are used to predict PMIs based on the measured metabolite concentrations. Individual PMIs calculated from five different metabolites are then pooled, being weighted by their inverse variances. The predicted PMIs from all individual examinations in the sheep model are compared with known true times. In addition, four human cases with forensically estimated PMIs are compared with predictions based on single in situ MRS measurements. Interpretation of the individual sheep examinations gave a good correlation up to 250 h post-mortem, demonstrating that the predicted PMIs are consistent with the data used to generate the model. Comparison of the estimated PMIs with the forensically determined PMIs in the four human cases shows an adequate correlation. Current PMI estimations based on forensic methods typically suffer from uncertainties in the order of days to weeks without mathematically defined confidence information. In turn, a single 1H-MRS measurement of brain tissue in situ results in PMIs with defined and favorable confidence intervals in the range of hours, thus offering a quantitative and objective method for the determination of PMIs.

Accurate and robust reconstruction of proximal femur from sparse intraoperative data and dense point distribution model for surgical navigation

Constructing a 3D surface model from sparse-point data is a nontrivial task. Here, we report an accurate and robust approach for reconstructing a surface model of the proximal femur from sparse-point data and a dense-point distribution model (DPDM). The problem is formulated as a three-stage optimal estimation process. The first stage, affine registration, is to iteratively estimate a scale and a rigid transformation between the mean surface model of the DPDM and the sparse input points. The estimation results of the first stage are used to establish point correspondences for the second stage, statistical instantiation, which stably instantiates a surface model from the DPDM using a statistical approach. This surface model is then fed to the third stage, kernel-based deformation, which further refines the surface model. Handling outliers is achieved by consistently employing the least trimmed squares (LTS) approach with a roughly estimated outlier rate in all three stages. If an optimal value of the outlier rate is preferred, we propose a hypothesis testing procedure to automatically estimate it. We present here our validations using four experiments, which include 1 leave-one-out experiment, 2 experiment on evaluating the present approach for handling pathology, 3 experiment on evaluating the present approach for handling outliers, and 4 experiment on reconstructing surface models of seven dry cadaver femurs using clinically relevant data without noise and with noise added. Our validation results demonstrate the robust performance of the present approach in handling outliers, pathology, and noise. An average 95-percentile error of 1.7-2.3 mm was found when the present approach was used to reconstruct surface models of the cadaver femurs from sparse-point data with noise added.

Estimation of sex and age of "virtual skeletons"--a feasibility study

This article presents a feasibility study with the objective of investigating the potential of multi-detector computed tomography (MDCT) to estimate the bone age and sex of deceased persons. To obtain virtual skeletons, the bodies of 22 deceased persons with known age at death were scanned by MDCT using a special protocol that consisted of high-resolution imaging of the skull, shoulder girdle (including the upper half of the humeri), the symphysis pubis and the upper halves of the femora. Bone and soft-tissue reconstructions were performed in two and three dimensions. The resulting data were investigated by three anthropologists with different professional experience. Sex was determined by investigating three-dimensional models of the skull and pelvis. As a basic orientation for the age estimation, the complex method according to Nemeskéri and co-workers was applied. The final estimation was effected using additional parameters like the state of dentition, degeneration of the spine, etc., which where chosen individually by the three observers according to their experience. The results of the study show that the estimation of sex and age is possible by the use of MDCT. Virtual skeletons present an ideal collection for anthropological studies, because they are obtained in a non-invasive way and can be investigated ad infinitum.

Estimation of the flammability zone boundaries with thermodynamic and empirical equations

The flammability zone boundaries are very important properties to prevent explosions in the process industries. Within the boundaries, a flame or explosion can occur so it is important to understand these boundaries to prevent fires and explosions. Very little work has been reported in the literature to model the flammability zone boundaries. Two boundaries are defined and studied: the upper flammability zone boundary and the lower flammability zone boundary. Three methods are presented to predict the upper and lower flammability zone boundaries: The linear model The extended linear model, and An empirical model The linear model is a thermodynamic model that uses the upper flammability limit (UFL) and lower flammability limit (LFL) to calculate two adiabatic flame temperatures. When the proper assumptions are applied, the linear model can be reduced to the well-known equation yLOC = zyLFL for estimation of the limiting oxygen concentration. The extended linear model attempts to account for the changes in the reactions along the UFL boundary. Finally, the empirical method fits the boundaries with linear equations between the UFL or LFL and the intercept with the oxygen axis. xx Comparison of the models to experimental data of the flammability zone shows that the best model for estimating the flammability zone boundaries is the empirical method. It is shown that is fits the limiting oxygen concentration (LOC), upper oxygen limit (UOL), and the lower oxygen limit (LOL) quite well. The regression coefficient values for the fits to the LOC, UOL, and LOL are 0.672, 0.968, and 0.959, respectively. This is better than the fit of the "zyLFL" method for the LOC in which the regression coefficient’s value is 0.416.

Estimation of scots pine defoliation by the common pine sawfly (Diprion pini L.) using multi-temporal radar data

In 1998-2001 Finland suffered the most severe insect outbreak ever recorded, over 500,000 hectares. The outbreak was caused by the common pine sawfly (Diprion pini L.). The outbreak has continued in the study area, Palokangas, ever since. To find a good method to monitor this type of outbreaks, the purpose of this study was to examine the efficacy of multi-temporal ERS-2 and ENVISAT SAR imagery for estimating Scots pine (Pinus sylvestris L.) defoliation. Three methods were tested: unsupervised k-means clustering, supervised linear discriminant analysis (LDA) and logistic regression. In addition, I assessed if harvested areas could be differentiated from the defoliated forest using the same methods. Two different speckle filters were used to determine the effect of filtering on the SAR imagery and subsequent results. The logistic regression performed best, producing a classification accuracy of 81.6% (kappa 0.62) with two classes (no defoliation, >20% defoliation). LDA accuracy was with two classes at best 77.7% (kappa 0.54) and k-means 72.8 (0.46). In general, the largest speckle filter, 5 x 5 image window, performed best. When additional classes were added the accuracy was usually degraded on a step-by-step basis. The results were good, but because of the restrictions in the study they should be confirmed with independent data, before full conclusions can be made that results are reliable. The restrictions include the small size field data and, thus, the problems with accuracy assessment (no separate testing data) as well as the lack of meteorological data from the imaging dates.

Assessing drinking water quality at source and point-of-use : a case study of Koila Bamana, Mali, West Africa

Ensuring water is safe at source and point-of-use is important in areas of the world where drinking water is collected from communal supplies. This report describes a study in rural Mali to determine the appropriateness of assumptions common among development organizations that drinking water will remain safe at point-of-use if collected from a safe (improved) source. Water was collected from ten sources (borehole wells with hand pumps, and hand-dug wells) and forty-five households using water from each source type. Water quality was evaluated seasonally (quarterly) for levels of total coliform, E.coli, and turbidity. Microbial testing was done using the 3M Petrifilm™ method. Turbidity testing was done using a turbidity tube. Microbial testing results were analyzed using statistical tests including Kruskal-Wallis, Mann Whitney, and analysis of variance. Results show that water from hand pumps did not contain total coliform or E.coli and had turbidity under 5 NTUs, whereas water from dug wells had high levels of bacteria and turbidity. However water at point-of-use (household) from hand pumps showed microbial contamination - at times being indistinguishable from households using dug wells - indicating a decline in water quality from source to point-of-use. Chemical treatment at point-of-use is suggested as an appropriate solution to eliminating any post-source contamination. Additionally, it is recommended that future work be done to modify existing water development strategies to consider water quality at point-of-use.

SPATIAL UNDERSTANDING OF MATRIX INVERSION FOR INVERSE FORCE ESTIMATION

A basic approach to study a NVH problem is to break down the system in three basic elements – source, path and receiver. While the receiver (response) and the transfer path can be measured, it is difficult to measure the source (forces) acting on the system. It becomes necessary to predict these forces to know how they influence the responses. This requires inverting the transfer path. Singular Value Decomposition (SVD) method is used to decompose the transfer path matrix into its principle components which is required for the inversion. The usual approach to force prediction requires rejecting the small singular values obtained during SVD by setting a threshold, as these small values dominate the inverse matrix. This assumption of the threshold may be subjected to rejecting important singular values severely affecting force prediction. The new approach discussed in this report looks at the column space of the transfer path matrix which is the basis for the predicted response. The response participation is an indication of how the small singular values influence the force participation. The ability to accurately reconstruct the response vector is important to establish a confidence in force vector prediction. The goal of this report is to suggest a solution that is mathematically feasible, physically meaningful, and numerically more efficient through examples. This understanding adds new insight to the effects of current code and how to apply algorithms and understanding to new codes.

High precision range estimation techniques for multi-path wireless environments

Range estimation is the core of many positioning systems such as radar, and Wireless Local Positioning Systems (WLPS). The estimation of range is achieved by estimating Time-of-Arrival (TOA). TOA represents the signal propagation delay between a transmitter and a receiver. Thus, error in TOA estimation causes degradation in range estimation performance. In wireless environments, noise, multipath, and limited bandwidth reduce TOA estimation performance. TOA estimation algorithms that are designed for wireless environments aim to improve the TOA estimation performance by mitigating the effect of closely spaced paths in practical (positive) signal-to-noise ratio (SNR) regions. Limited bandwidth avoids the discrimination of closely spaced paths. This reduces TOA estimation performance. TOA estimation methods are evaluated as a function of SNR, bandwidth, and the number of reflections in multipath wireless environments, as well as their complexity. In this research, a TOA estimation technique based on Blind signal Separation (BSS) is proposed. This frequency domain method estimates TOA in wireless multipath environments for a given signal bandwidth. The structure of the proposed technique is presented and its complexity and performance are theoretically evaluated. It is depicted that the proposed method is not sensitive to SNR, number of reflections, and bandwidth. In general, as bandwidth increases, TOA estimation performance improves. However, spectrum is the most valuable resource in wireless systems and usually a large portion of spectrum to support high performance TOA estimation is not available. In addition, the radio frequency (RF) components of wideband systems suffer from high cost and complexity. Thus, a novel, multiband positioning structure is proposed. The proposed technique uses the available (non-contiguous) bands to support high performance TOA estimation. This system incorporates the capabilities of cognitive radio (CR) systems to sense the available spectrum (also called white spaces) and to incorporate white spaces for high-performance localization. First, contiguous bands that are divided into several non-equal, narrow sub-bands that possess the same SNR are concatenated to attain an accuracy corresponding to the equivalent full band. Two radio architectures are proposed and investigated: the signal is transmitted over available spectrum either simultaneously (parallel concatenation) or sequentially (serial concatenation). Low complexity radio designs that handle the concatenation process sequentially and in parallel are introduced. Different TOA estimation algorithms that are applicable to multiband scenarios are studied and their performance is theoretically evaluated and compared to simulations. Next, the results are extended to non-contiguous, non-equal sub-bands with the same SNR. These are more realistic assumptions in practical systems. The performance and complexity of the proposed technique is investigated as well. This study’s results show that selecting bandwidth, center frequency, and SNR levels for each sub-band can adapt positioning accuracy.

A new method to monitor visual field defects caused by photoreceptor degeneration by quantitative optical coherence tomography

PURPOSE: To correlate the dimension of the visual field (VF) tested by Goldman kinetic perimetry with the extent of visibility of the highly reflective layer between inner and outer segments of photoreceptors (IOS) seen in optical coherence tomography (OCT) images in patients with retinitis pigmentosa (RP). METHODS: In a retrospectively designed cross-sectional study, 18 eyes of 18 patients with RP were examined with OCT and Goldmann perimetry using test target I4e and compared with 18 eyes of 18 control subjects. A-scans of raw scan data of Stratus OCT images (Carl Zeiss Meditec, AG, Oberkochen, Germany) were quantitatively analyzed for the presence of the signal generated by the highly reflective layer between the IOS in OCT images. Starting in the fovea, the distance to which this signal was detectable was measured. Visual fields were analyzed by measuring the distance from the center point to isopter I4e. OCT and visual field data were analyzed in a clockwise fashion every 30 degrees , and corresponding measures were correlated. RESULTS: In corresponding alignments, the distance from the center point to isopter I4e and the distance to which the highly reflective signal from the IOS can be detected correlate significantly (r = 0.75, P < 0.0001). The greater the distance in VF, the greater the distance measured in OCT. CONCLUSIONS: The authors hypothesize that the retinal structure from which the highly reflective layer between the IOS emanates is of critical importance for visual and photoreceptor function. Further research is warranted to determine whether this may be useful as an objective marker of progression of retinal degeneration in patients with RP.

Parametric estimation of pulse arrival time: a robust approach to pulse wave velocity

Pulse wave velocity (PWV) is a surrogate of arterial stiffness and represents a non-invasive marker of cardiovascular risk. The non-invasive measurement of PWV requires tracking the arrival time of pressure pulses recorded in vivo, commonly referred to as pulse arrival time (PAT). In the state of the art, PAT is estimated by identifying a characteristic point of the pressure pulse waveform. This paper demonstrates that for ambulatory scenarios, where signal-to-noise ratios are below 10 dB, the performance in terms of repeatability of PAT measurements through characteristic points identification degrades drastically. Hence, we introduce a novel family of PAT estimators based on the parametric modeling of the anacrotic phase of a pressure pulse. In particular, we propose a parametric PAT estimator (TANH) that depicts high correlation with the Complior(R) characteristic point D1 (CC = 0.99), increases noise robustness and reduces by a five-fold factor the number of heartbeats required to obtain reliable PAT measurements.

Is perioperative point-of-care prothrombin time testing accurate compared to the standard laboratory test?

There is no accepted way of measuring prothrombin time without time loss for patients undergoing major surgery who are at risk of intraoperative dilution and consumption coagulopathy due to bleeding and volume replacement with crystalloids or colloids. Decisions to transfuse fresh frozen plasma and procoagulatory drugs have to rely on clinical judgment in these situations. Point-of-care devices are considerably faster than the standard laboratory methods. In this study we assessed the accuracy of a Point-of-care (PoC) device measuring prothrombin time compared to the standard laboratory method. Patients undergoing major surgery and intensive care unit patients were included. PoC prothrombin time was measured by CoaguChek XS Plus (Roche Diagnostics, Switzerland). PoC and reference tests were performed independently and interpreted under blinded conditions. Using a cut-off prothrombin time of 50%, we calculated diagnostic accuracy measures, plotted a receiver operating characteristic (ROC) curve and tested for equivalence between the two methods. PoC sensitivity and specificity were 95% (95% CI 77%, 100%) and 95% (95% CI 91%, 98%) respectively. The negative likelihood ratio was 0.05 (95% CI 0.01, 0.32). The positive likelihood ratio was 19.57 (95% CI 10.62, 36.06). The area under the ROC curve was 0.988. Equivalence between the two methods was confirmed. CoaguChek XS Plus is a rapid and highly accurate test compared with the reference test. These findings suggest that PoC testing will be useful for monitoring intraoperative prothrombin time when coagulopathy is suspected. It could lead to a more rational use of expensive and limited blood bank resources.