Statistical finite element model for bone shape and biomechanical properties

We present a framework for statistical finite element analysis combining shape and material properties, and allowing performing statistical statements of biomechanical performance across a given population. In this paper, we focus on the design of orthopaedic implants that fit a maximum percentage of the target population, both in terms of geometry and biomechanical stability. CT scans of the bone under consideration are registered non-rigidly to obtain correspondences in position and intensity between them. A statistical model of shape and intensity (bone density) is computed by means of principal component analysis. Afterwards, finite element analysis (FEA) is performed to analyse the biomechanical performance of the bones. Realistic forces are applied on the bones and the resulting displacement and bone stress distribution are calculated. The mechanical behaviour of different PCA bone instances is compared.

Semiparametric Normal Transformation Models for Spatially Correlated Survival Data

There is an emerging interest in modeling spatially correlated survival data in biomedical and epidemiological studies. In this paper, we propose a new class of semiparametric normal transformation models for right censored spatially correlated survival data. This class of models assumes that survival outcomes marginally follow a Cox proportional hazard model with unspecified baseline hazard, and their joint distribution is obtained by transforming survival outcomes to normal random variables, whose joint distribution is assumed to be multivariate normal with a spatial correlation structure. A key feature of the class of semiparametric normal transformation models is that it provides a rich class of spatial survival models where regression coefficients have population average interpretation and the spatial dependence of survival times is conveniently modeled using the transformed variables by flexible normal random fields. We study the relationship of the spatial correlation structure of the transformed normal variables and the dependence measures of the original survival times. Direct nonparametric maximum likelihood estimation in such models is practically prohibited due to the high dimensional intractable integration of the likelihood function and the infinite dimensional nuisance baseline hazard parameter. We hence develop a class of spatial semiparametric estimating equations, which conveniently estimate the population-level regression coefficients and the dependence parameters simultaneously. We study the asymptotic properties of the proposed estimators, and show that they are consistent and asymptotically normal. The proposed method is illustrated with an analysis of data from the East Boston Ashma Study and its performance is evaluated using simulations.

Measuring Consumers' Willingness to Pay. Which Method fits best?

Gauging the maximum willingness to pay (WTP) of a product accurately is a critical success factor that determines not only market performance but also financial results. A number of approaches have therefore been developed to accurately estimate consumers’ willingness to pay. Here, four commonly used measurement approaches are compared using real purchase data as a benchmark. The relative strengths of each method are analyzed on the basis of statistical criteria and, more importantly, on their potential to predict managerially relevant criteria such as optimal price, quantity and profit. The results show a slight advantage of incentive-aligned approaches though the market settings need to be considered to choose the best-fitting procedure.

Good just isn't Good enough. Best System Probabilities and the Foundations of Statistical Mechanics

Statistical physicists assume a probability distribution over micro-states to explain thermodynamic behavior. The question of this paper is whether these probabilities are part of a best system and can thus be interpreted as Humean chances. I consider two strategies, viz. a globalist as suggested by Loewer, and a localist as advocated by Frigg and Hoefer. Both strategies fail because the system they are part of have rivals that are roughly equally good, while ontic probabilities should be part of a clearly winning system. I conclude with the diagnosis that well-defined micro-probabilities under-estimate the robust character of explanations in statistical physics.

Population genetics of VNTR loci and their applications in evolutionary studies

Variable number of tandem repeats (VNTR) are genetic loci at which short sequence motifs are found repeated different numbers of times among chromosomes. To explore the potential utility of VNTR loci in evolutionary studies, I have conducted a series of studies to address the following questions: (1) What are the population genetic properties of these loci? (2) What are the mutational mechanisms of repeat number change at these loci? (3) Can DNA profiles be used to measure the relatedness between a pair of individuals? (4) Can DNA fingerprint be used to measure the relatedness between populations in evolutionary studies? (5) Can microsatellite and short tandem repeat (STR) loci which mutate stepwisely be used in evolutionary analyses?^ A large number of VNTR loci typed in many populations were studied by means of statistical methods developed recently. The results of this work indicate that there is no significant departure from Hardy-Weinberg expectation (HWE) at VNTR loci in most of the human populations examined, and the departure from HWE in some VNTR loci are not solely caused by the presence of population sub-structure.^ A statistical procedure is developed to investigate the mutational mechanisms of VNTR loci by studying the allele frequency distributions of these loci. Comparisons of frequency distribution data on several hundreds VNTR loci with the predictions of two mutation models demonstrated that there are differences among VNTR loci grouped by repeat unit sizes.^ By extending the ITO method, I derived the distribution of the number of shared bands between individuals with any kinship relationship. A maximum likelihood estimation procedure is proposed to estimate the relatedness between individuals from the observed number of shared bands between them.^ It was believed that classical measures of genetic distance are not applicable to analysis of DNA fingerprints which reveal many minisatellite loci simultaneously in the genome, because the information regarding underlying alleles and loci is not available. I proposed a new measure of genetic distance based on band sharing between individuals that is applicable to DNA fingerprint data.^ To address the concern that microsatellite and STR loci may not be useful for evolutionary studies because of the convergent nature of their mutation mechanisms, by a theoretical study as well as by computer simulation, I conclude that the possible bias caused by the convergent mutations can be corrected, and a novel measure of genetic distance that makes the correction is suggested. In summary, I conclude that hypervariable VNTR loci are useful in evolutionary studies of closely related populations or species, especially in the study of human evolution and the history of geographic dispersal of Homo sapiens. (Abstract shortened by UMI.) ^

Models of DNA sequence evolution

Models of DNA sequence evolution and methods for estimating evolutionary distances are needed for studying the rate and pattern of molecular evolution and for inferring the evolutionary relationships of organisms or genes. In this dissertation, several new models and methods are developed.^ The rate variation among nucleotide sites: To obtain unbiased estimates of evolutionary distances, the rate heterogeneity among nucleotide sites of a gene should be considered. Commonly, it is assumed that the substitution rate varies among sites according to a gamma distribution (gamma model) or, more generally, an invariant+gamma model which includes some invariable sites. A maximum likelihood (ML) approach was developed for estimating the shape parameter of the gamma distribution $(\alpha)$ and/or the proportion of invariable sites $(\theta).$ Computer simulation showed that (1) under the gamma model, $\alpha$ can be well estimated from 3 or 4 sequences if the sequence length is long; and (2) the distance estimate is unbiased and robust against violations of the assumptions of the invariant+gamma model.^ However, this ML method requires a huge amount of computational time and is useful only for less than 6 sequences. Therefore, I developed a fast method for estimating $\alpha,$ which is easy to implement and requires no knowledge of tree. A computer program was developed for estimating $\alpha$ and evolutionary distances, which can handle the number of sequences as large as 30.^ Evolutionary distances under the stationary, time-reversible (SR) model: The SR model is a general model of nucleotide substitution, which assumes (i) stationary nucleotide frequencies and (ii) time-reversibility. It can be extended to SRV model which allows rate variation among sites. I developed a method for estimating the distance under the SR or SRV model, as well as the variance-covariance matrix of distances. Computer simulation showed that the SR method is better than a simpler method when the sequence length $L>1,000$ bp and is robust against deviations from time-reversibility. As expected, when the rate varies among sites, the SRV method is much better than the SR method.^ The evolutionary distances under nonstationary nucleotide frequencies: The statistical properties of the paralinear and LogDet distances under nonstationary nucleotide frequencies were studied. First, I developed formulas for correcting the estimation biases of the paralinear and LogDet distances. The performances of these formulas and the formulas for sampling variances were examined by computer simulation. Second, I developed a method for estimating the variance-covariance matrix of the paralinear distance, so that statistical tests of phylogenies can be conducted when the nucleotide frequencies are nonstationary. Third, a new method for testing the molecular clock hypothesis was developed in the nonstationary case. ^

Self-Reported Psychotic-Like Experiences Are a Poor Estimate of Clinician-Rated Attenuated and Frank Delusions and Hallucinations

Background: One reason for the decision to delay the introduction of an Attenuated Psychosis Syndrome in the main text of the fifth edition of the American Psychiatric Association's Diagnostic and Statistical Manual of Mental Disorders was the concern that attenuated psychotic symptoms (APS) might in fact be common features in adolescents and young adults from the general population of no psychopathological significance in themselves. This concern was based on reports of high prevalence rates of psychotic-like experiences (PLEs) in the general population and the assumption that PLEs are a good estimate of APS. Although the criterion validity of self-reported PLEs had already been studied with respect to clinician-rated psychotic symptoms and found insufficient, it had been argued that PLEs might in fact be more comparable with mild, subclinical expressions of psychotic symptoms and, therefore, with APS. The present paper is the first to specifically study this assumption. Sampling and Methods: The sample consisted of 123 persons seeking help at a service for the early detection of psychosis, of whom 54 had an at-risk mental state or psychosis, 55 had a nonpsychotic mental disorder and 14 had no full-blown mental disorder. PLEs were assessed with the Peters Delusion Inventory and the revised Launay-Slade Hallucination Scale, and psychotic symptoms and APS were assessed with the Structured Interview for Prodromal Syndromes. Results: At a level of agreement between the presence of any PLE (in 98.4% of patients) and any APS (in 40.7%) just exceeding chance (κ = 0.022), the criterion validity of PLEs for APS was insufficient. Even if additional qualifiers (high agreement or distress, preoccupation and conviction) were considered, PLEs (in 52.8%) still tended to significantly overestimate APS, and agreement was only fair (κ = 0.340). Furthermore, the group effect on PLE prevalence was, at most, moderate (Cramer's V ≤ 0.382). Conclusions: The prevalence of APS cannot be deduced from studies of PLEs. Thus, the high population prevalence rate of PLEs does not allow the conclusion that APS are common features of no pathological significance and would lack clinical validity as an Attenuated Psychosis Syndrome in the Diagnostic and Statistical Manual of Mental Disorders, 5th edition. Rather, the population prevalence rate of APS has to be assumed to be largely unknown at present but is likely lower than indicated by epidemiological studies of PLEs. Therefore, dedicated studies are warranted, in which APS are assessed in a way that equates to their clinical evaluation.

Good just isn't Good Enough: Humean Chances and Boltzmannian Statistical Physics

Statistical physicists assume a probability distribution over micro-states to explain thermodynamic behavior. The question of this paper is whether these probabilities are part of a best system and can thus be interpreted as Humean chances. I consider two Boltzmannian accounts of the Second Law, viz.\ a globalist and a localist one. In both cases, the probabilities fail to be chances because they have rivals that are roughly equally good. I conclude with the diagnosis that well-defined micro-probabilities under-estimate the robust character of explanations in statistical physics.

Automatic estimation of noise parameters in Fourier-domain optical coherence tomography cross sectional images using statistical information

We present an application and sample independent method for the automatic discrimination of noise and signal in optical coherence tomography Bscans. The proposed algorithm models the observed noise probabilistically and allows for a dynamic determination of image noise parameters and the choice of appropriate image rendering parameters. This overcomes the observer variability and the need for a priori information about the content of sample images, both of which are challenging to estimate systematically with current systems. As such, our approach has the advantage of automatically determining crucial parameters for evaluating rendered image quality in a systematic and task independent way. We tested our algorithm on data from four different biological and nonbiological samples (index finger, lemon slices, sticky tape, and detector cards) acquired with three different experimental spectral domain optical coherence tomography (OCT) measurement systems including a swept source OCT. The results are compared to parameters determined manually by four experienced OCT users. Overall, our algorithm works reliably regardless of which system and sample are used and estimates noise parameters in all cases within the confidence interval of those found by observers.

Statistical Learning, Syllable Processing, and Speech Production in Healthy Hearing and Hearing-Impaired Preschool Children: A Mismatch Negativity Study

OBJECTIVES The objectives of the present study were to investigate temporal/spectral sound-feature processing in preschool children (4 to 7 years old) with peripheral hearing loss compared with age-matched controls. The results verified the presence of statistical learning, which was diminished in children with hearing impairments (HIs), and elucidated possible perceptual mediators of speech production. DESIGN Perception and production of the syllables /ba/, /da/, /ta/, and /na/ were recorded in 13 children with normal hearing and 13 children with HI. Perception was assessed physiologically through event-related potentials (ERPs) recorded by EEG in a multifeature mismatch negativity paradigm and behaviorally through a discrimination task. Temporal and spectral features of the ERPs during speech perception were analyzed, and speech production was quantitatively evaluated using speech motor maximum performance tasks. RESULTS Proximal to stimulus onset, children with HI displayed a difference in map topography, indicating diminished statistical learning. In later ERP components, children with HI exhibited reduced amplitudes in the N2 and early parts of the late disciminative negativity components specifically, which are associated with temporal and spectral control mechanisms. Abnormalities of speech perception were only subtly reflected in speech production, as the lone difference found in speech production studies was a mild delay in regulating speech intensity. CONCLUSIONS In addition to previously reported deficits of sound-feature discriminations, the present study results reflect diminished statistical learning in children with HI, which plays an early and important, but so far neglected, role in phonological processing. Furthermore, the lack of corresponding behavioral abnormalities in speech production implies that impaired perceptual capacities do not necessarily translate into productive deficits.

MATHEMATICAL STUDIES ON THE EVOLUTIONARY CHANGE OF DNA SEQUENCES

With the aim of understanding the mechanism of molecular evolution, mathematical problems on the evolutionary change of DNA sequences are studied. The problems studied and the results obtained are as follows: (1) Estimation of evolutionary distance between nucleotide sequences. Studying the pattern of nucleotide substitution for the case of unequal substitution rates, a new mathematical formula for estimating the average number of nucleotide substitutions per site between two homologous DNA sequences is developed. It is shown that this formula has a wider applicability than currently available formulae. A statistical method for estimating the number of nucleotide changes due to deletion and insertion is also developed. (2) Biases of the estimates of nucleotide substitutions obtained by the restriction enzyme method. The deviation of the estimate of nucleotide substitutions obtained by the restriction enzyme method from the true value is investigated theoretically. It is shown that the amount of the deviation depends on the nucleotides in the recognition sequence of the restriction enzyme used, unequal rates of substitution among different nucleotides, and nucleotide frequences, but the primary factor is the unequal rates of nucleotide substitution. When many different kinds of enzymes are used, however, the amount of average deviation is generally small. (3) Distribution of restriction fragment lengths. To see the effect of undetectable restriction fragments and fragment differences on the estimate of nucleotide differences, the theoretical distribution of fragment lengths is studied. This distribution depends on the type of restriction enzymes used as well as on the relative frequencies of four nucleotides. It is shown that undetectability of small fragments or fragment differences gives a serious underestimate of nucleotide substitutions when the length-difference method of estimation is used, but the extent of underestimation is small when the site-difference method is used. (4) Evolutionary relationships of DNA sequences in finite populations. A mathematical theory on the expected evolutionary relationships among DNA sequences (nucleons) randomly chosen from the same or different populations is developed under the assumption that the evolutionary change of nucleons is determined solely by mutation and random genetic drift. . . . (Author's abstract exceeds stipulated maximum length. Discontinued here with permission of author). UMI ^

Logistic regression with Markov chains as covariates

The tobacco-specific nitrosamine 4-(methylnitrosamino)-1-(3-pyridyl)-1-butanone (NNK) is an obvious carcinogen for lung cancer. Since CBMN (Cytokinesis-blocked micronucleus) has been found to be extremely sensitive to NNK-induced genetic damage, it is a potential important factor to predict the lung cancer risk. However, the association between lung cancer and NNK-induced genetic damage measured by CBMN assay has not been rigorously examined. ^ This research develops a methodology to model the chromosomal changes under NNK-induced genetic damage in a logistic regression framework in order to predict the occurrence of lung cancer. Since these chromosomal changes were usually not observed very long due to laboratory cost and time, a resampling technique was applied to generate the Markov chain of the normal and the damaged cell for each individual. A joint likelihood between the resampled Markov chains and the logistic regression model including transition probabilities of this chain as covariates was established. The Maximum likelihood estimation was applied to carry on the statistical test for comparison. The ability of this approach to increase discriminating power to predict lung cancer was compared to a baseline "non-genetic" model. ^ Our method offered an option to understand the association between the dynamic cell information and lung cancer. Our study indicated the extent of DNA damage/non-damage using the CBMN assay provides critical information that impacts public health studies of lung cancer risk. This novel statistical method could simultaneously estimate the process of DNA damage/non-damage and its relationship with lung cancer for each individual.^