Regression models for bivariate survival data

Multivariate lifetime data arise in various forms including recurrent event data when individuals are followed to observe the sequence of occurrences of a certain type of event; correlated lifetime when an individual is followed for the occurrence of two or more types of events, or when distinct individuals have dependent event times. In most studies there are covariates such as treatments, group indicators, individual characteristics, or environmental conditions, whose relationship to lifetime is of interest. This leads to a consideration of regression models.The well known Cox proportional hazards model and its variations, using the marginal hazard functions employed for the analysis of multivariate survival data in literature are not sufficient to explain the complete dependence structure of pair of lifetimes on the covariate vector. Motivated by this, in Chapter 2, we introduced a bivariate proportional hazards model using vector hazard function of Johnson and Kotz (1975), in which the covariates under study have different effect on two components of the vector hazard function. The proposed model is useful in real life situations to study the dependence structure of pair of lifetimes on the covariate vector . The well known partial likelihood approach is used for the estimation of parameter vectors. We then introduced a bivariate proportional hazards model for gap times of recurrent events in Chapter 3. The model incorporates both marginal and joint dependence of the distribution of gap times on the covariate vector . In many fields of application, mean residual life function is considered superior concept than the hazard function. Motivated by this, in Chapter 4, we considered a new semi-parametric model, bivariate proportional mean residual life time model, to assess the relationship between mean residual life and covariates for gap time of recurrent events. The counting process approach is used for the inference procedures of the gap time of recurrent events. In many survival studies, the distribution of lifetime may depend on the distribution of censoring time. In Chapter 5, we introduced a proportional hazards model for duration times and developed inference procedures under dependent (informative) censoring. In Chapter 6, we introduced a bivariate proportional hazards model for competing risks data under right censoring. The asymptotic properties of the estimators of the parameters of different models developed in previous chapters, were studied. The proposed models were applied to various real life situations.

Polarisation von Licht im Physikunterricht : ein Elementarisierungsansatz zur Einführung in quantenphysikalische Begriffe und Prinzipien

In der vorliegenden Arbeit wird ein Unterrichtskonzept für die gymnasiale Oberstufe beschrieben, das anhand der Polarisationseigenschaft des Lichts von der Beobachtung ausgehend einen Zugang zur Quantenphysik ermöglicht. Die Unterrichtsinhalte bauen so aufeinander auf, dass ein "harter Bruch" zwischen der klassischen und der quantenphysikalischen Beschreibung von Licht vermieden wird. Das methodische Vorgehen des Unterrichtskonzeptes führt vom Phänomen ausgehend zu quantitativen Experimenten hin zu einer Einführung in quantenphysikalische Begriffe und Prinzipien. Dabei bildet der elektrische Feldvektor die Verknüpfung zwischen der klassischen und der quantenphysi-kalischen Beschreibung der Polarisationsexperimente, in dem er zunächst die Polarisationsexperimente beschreibt und im weiteren Verlauf des Unterrichtsganges als Wahrscheinlichkeitsamplitude gedeutet wird. Die Polarisation von Licht wird zu Beginn des Unterrichtsganges im Rahmen eines fächerübergreifenden Kontextes eingeführt, wobei die Navigation der Insekten nach dem polarisierten Himmelslicht als Einstieg dient. Die Erzeugung und die Eigen-schaften von polarisiertem Licht werden anhand von einfachen qualitativen Schüler- und Demonstrationsexperimenten mit Polarisationsfolien erarbeitet. Das Polarisationsphänomen der Haidinger-Büschel, das bei der Beobachtung von polarisiertem Licht wahrgenommen werden kann, ermöglicht eine Anbindung an das eigene Erleben der Schülerinnen und Schüler. Zur Erklärung dieser Experimente auf der Modellebene wird der elektrische Feldvektor und dessen Komponentenzerlegung benutzt. Im weiteren Verlauf des Unterrichtsganges wird die Komponentenzerlegung des elektrischen Feldvektors für eine quantitative Beschreibung der Polarisationsexperimente wieder aufgegriffen. In Experimenten mit Polarisationsfiltern wird durch Intensitätsmessungen das Malussche Gesetz und der quadratische Zusammenhang zwischen Intensität und elektrischem Feldvektor erarbeitet. Als Abschluss der klassischen Polarisationsexperimente wird das Verhalten von polarisiertem Licht bei Überlagerung in einem Michelson-Interferometer untersucht. Das in Abhängigkeit der Polarisationsrichtungen entstehende Interferenzmuster wird wiederum mit Hilfe der Komponentenzerlegung des elektrischen Feldvektors beschrieben und führt zum Superpositionsprinzip der elektrischen Feldvektoren. Beim Übergang zur Quantenphysik werden die bereits durchgeführten Polarisationsexperimente als Gedankenexperimente in der Photonenvorstellung gedeutet. Zur Beschreibung der Polarisation von Photonen wird der Begriff des Zustandes eingeführt, der durch die Wechselwirkung der Photonen mit dem Polarisationsfilter erzeugt wird. Das Malussche Gesetz wird in der Teilchenvorstellung wieder aufgegriffen und führt mit Hilfe der statistischen Deutung zum Begriff der Wahrscheinlichkeit. Bei der Beschreibung von Interferenzexperimenten mit einzelnen Photonen wird die Notwendigkeit eines Analogons zum elektrischen Feldvektor deutlich. Diese Betrachtungen führen zum Begriff der Wahrscheinlichkeitsamplitude und zum Superpositionsprinzip der Wahrscheinlichkeitsamplituden. Zum Abschluss des Unterrichtsganges wird anhand des Lokalisationsproblems einzelner Photonen das Fundamentalprinzip der Quantenphysik erarbeitet.

Fronts from integrodifference equations and persistence effects on the Neolithic transition

We extend a previous model of the Neolithic transition in Europe [J. Fort and V. Méndez, Phys. Rev. Lett. 82, 867 (1999)] by taking two effects into account: (i) we do not use the diffusion approximation (which corresponds to second-order Taylor expansions), and (ii) we take proper care of the fact that parents do not migrate away from their children (we refer to this as a time-order effect, in the sense that it implies that children grow up with their parents, before they become adults and can survive and migrate). We also derive a time-ordered, second-order equation, which we call the sequential reaction-diffusion equation, and use it to show that effect (ii) is the most important one, and that both of them should in general be taken into account to derive accurate results. As an example, we consider the Neolithic transition: the model predictions agree with the observed front speed, and the corrections relative to previous models are important (up to 70%)

Business cycle asymmentries: An investment cost approach

In this paper, investment cost asymmetry is introduced in order to test wheter this kind of asymmetry can account for asymmetries in business cycles. By using a smooth transition function, asymmetric investment cost is modeled and introduced in a canonical RBC model. Simulations of the model with Perturbations Method (PM) are very close to simulations through Parameterized Expectations Algorithm (PEA), which allows the use of the former for the sake of time reduction and computational costs. Both symmetric and asymmetric models were simulated and compared. Deterministic and stochastic impulse-response excersices revealed that it is possible to adequately reproduce asymmetric business cycles by modeling asymmetric investment costs. Simulations also showed that higher order moments are insu_cient to detect asymmetries. Instead, methods such as Generalized Impulse Response Analysis (GIRA) and Nonlinear Econometrics prove to be more e_cient diagnostic tools.

Stock return comovements and integration within the Latin American integrated market

Financial integration has been pursued aggressively across the globe in the last fifty years; however, there is no conclusive evidence on the diversification gains (or losses) of such efforts. These gains (or losses) are related to the degree of comovements and synchronization among increasingly integrated global markets. We quantify the degree of comovements within the integrated Latin American market (MILA). We use dynamic correlation models to quantify comovements across securities as well as a direct integration measure. Our results show an increase in comovements when we look at the country indexes, however, the increase in the trend of correlation is previous to the institutional efforts to establish an integrated market in the region. On the other hand, when we look at sector indexes and an integration measure, we find a decreased in comovements among a representative sample of securities form the integrated market.

A parametric model for the interval censored survival times of Acacia mangium plantation in a spacing trial

Survival times for the Acacia mangium plantation in the Segaliud Lokan Project, Sabah, East Malaysia were analysed based on 20 permanent sample plots (PSPs) established in 1988 as a spacing experiment. The PSPs were established following a complete randomized block design with five levels of spacing randomly assigned to units within four blocks at different sites. The survival times of trees in years are of interest. Since the inventories were only conducted annually, the actual survival time for each tree was not observed. Hence, the data set comprises censored survival times. Initial analysis of the survival of the Acacia mangium plantation suggested there is block by spacing interaction; a Weibull model gives a reasonable fit to the replicate survival times within each PSP; but a standard Weibull regression model is inappropriate because the shape parameter differs between PSPs. In this paper we investigate the form of the non-constant Weibull shape parameter. Parsimonious models for the Weibull survival times have been derived using maximum likelihood methods. The factor selection for the parameters is based on a backward elimination procedure. The models are compared using likelihood ratio statistics. The results suggest that both Weibull parameters depend on spacing and block.

Power properties if invariant tests for spatial autocorrelation in linear regression

This paper derives some exact power properties of tests for spatial autocorrelation in the context of a linear regression model. In particular, we characterize the circumstances in which the power vanishes as the autocorrelation increases, thus extending the work of Krämer (2005). More generally, the analysis in the paper sheds new light on how the power of tests for spatial autocorrelation is affected by the matrix of regressors and by the spatial structure. We mainly focus on the problem of residual spatial autocorrelation, in which case it is appropriate to restrict attention to the class of invariant tests, but we also consider the case when the autocorrelation is due to the presence of a spatially lagged dependent variable among the regressors. A numerical study aimed at assessing the practical relevance of the theoretical results is included

Investigation of the factors influencing the survival of Bifidobacterium longum in model acidic solutions and fruit juices

The survival of Bifidobacterium longum NCIMB 8809 was studied during refrigerated storage for 6 weeks in model solutions, based on which a mathematical model was constructed describing cell survival as a function of pH, citric acid, protein and dietary fibre. A Central Composite Design (CCD) was developed studying the influence of four factors at three levels, i.e., pH (3.2–4), citric acid (2–15 g/l), protein (0–10 g/l), and dietary fibre (0–8 g/l). In total, 31 experimental runs were carried out. Analysis of variance (ANOVA) of the regression model demonstrated that the model fitted well the data. From the regression coefficients it was deduced that all four factors had a statistically significant (P < 0.05) negative effect on the log decrease [log10N0 week−log10N6 week], with the pH and citric acid being the most influential ones. Cell survival during storage was also investigated in various types of juices, including orange, grapefruit, blackcurrant, pineapple, pomegranate and strawberry. The highest cell survival (less than 0.4 log decrease) after 6 weeks of storage was observed in orange and pineapple, both of which had a pH of about 3.8. Although the pH of grapefruit and blackcurrant was similar (pH ∼3.2), the log decrease of the former was ∼0.5 log, whereas of the latter was ∼0.7 log. One reason for this could be the fact that grapefruit contained a high amount of citric acid (15.3 g/l). The log decrease in pomegranate and strawberry juices was extremely high (∼8 logs). The mathematical model was able to predict adequately the cell survival in orange, grapefruit, blackcurrant, and pineapple juices. However, the model failed to predict the cell survival in pomegranate and strawberry, most likely due to the very high levels of phenolic compounds in these two juices.

Dietary, lifestyle and clinico-pathological factors associated with APC mutations and promoter methylation in colorectal cancers from the EPIC-Norfolk Study

The tumour suppressor APC is the most commonly altered gene in colorectal cancer (CRC). Genetic and epigenetic alterations of APC may therefore be associated with dietary and lifestyle risk factors for CRC. Analysis of APC mutations in the extended mutation cluster region (codons 1276-1556) and APC promoter 1A methylation was performed on 185 archival CRC samples collected from participants of the European Prospective Investigation into Cancer (EPIC)-Norfolk Study, with the aim of relating these to high quality seven-day dietary and lifestyle data collected prospectively. Truncating APC mutations (APC+) and promoter 1A methylation (PM+) were identified in 43% and 23% of CRCs analysed, respectively. Distal CRCs were more likely than proximal CRCs to be APC+ or PM+ (P = 0.04). APC+ CRCs were more likely to be moderately/well differentiated and microsatellite stable than APC- CRCs (P = 0.05 and 0.03). APC+ CRC cases consumed more alcohol than their counterparts (P = 0.01) and PM+ CRC cases consumed lower levels of folate and fibre (P = 0.01 and 0.004). APC+ or PM+ CRC cases consumedhigher levels of processed meat and iron from red meat and red meat products (P=0.007 and 0.006). Specifically, CRC cases harbouring GC to AT transition mutations consumed higher levels of processed meat (35 versus 24 g/day, P = 0.04) and iron from red meat and red meat products (0.8 versus 0.6 mg/day, P = 0.05). In a logistic regression model adjusted for age, sex and cigarette smoking status, each 19g/day (1SD) increment increase in processed meat consumption was associated with cases with GC to AT mutations (OR 1.68, 95% CI 1.03-2.75). In conclusion, APC+ and PM+ CRCs may be influenced by diet and GC to AT mutations in APC are associated with processed meat consumption, suggesting a mechanistic link with dietary alkylating agents, such as N-nitroso compounds.

Axonal velocity distributions in neural feld equations

By modelling the average activity of large neuronal populations, continuum mean field models (MFMs) have become an increasingly important theoretical tool for understanding the emergent activity of cortical tissue. In order to be computationally tractable, long-range propagation of activity in MFMs is often approximated with partial differential equations (PDEs). However, PDE approximations in current use correspond to underlying axonal velocity distributions incompatible with experimental measurements. In order to rectify this deficiency, we here introduce novel propagation PDEs that give rise to smooth unimodal distributions of axonal conduction velocities. We also argue that velocities estimated from fibre diameters in slice and from latency measurements, respectively, relate quite differently to such distributions, a significant point for any phenomenological description. Our PDEs are then successfully fit to fibre diameter data from human corpus callosum and rat subcortical white matter. This allows for the first time to simulate long-range conduction in the mammalian brain with realistic, convenient PDEs. Furthermore, the obtained results suggest that the propagation of activity in rat and human differs significantly beyond mere scaling. The dynamical consequences of our new formulation are investigated in the context of a well known neural field model. On the basis of Turing instability analyses, we conclude that pattern formation is more easily initiated using our more realistic propagator. By increasing characteristic conduction velocities, a smooth transition can occur from self-sustaining bulk oscillations to travelling waves of various wavelengths, which may influence axonal growth during development. Our analytic results are also corroborated numerically using simulations on a large spatial grid. Thus we provide here a comprehensive analysis of empirically constrained activity propagation in the context of MFMs, which will allow more realistic studies of mammalian brain activity in the future.

A unified neurofuzzy model for classification

This work proposes a unified neurofuzzy modelling scheme. To begin with, the initial fuzzy base construction method is based on fuzzy clustering utilising a Gaussian mixture model (GMM) combined with the analysis of covariance (ANOVA) decomposition in order to obtain more compact univariate and bivariate membership functions over the subspaces of the input features. The mean and covariance of the Gaussian membership functions are found by the expectation maximisation (EM) algorithm with the merit of revealing the underlying density distribution of system inputs. The resultant set of membership functions forms the basis of the generalised fuzzy model (GFM) inference engine. The model structure and parameters of this neurofuzzy model are identified via the supervised subspace orthogonal least square (OLS) learning. Finally, instead of providing deterministic class label as model output by convention, a logistic regression model is applied to present the classifier’s output, in which the sigmoid type of logistic transfer function scales the outputs of the neurofuzzy model to the class probability. Experimental validation results are presented to demonstrate the effectiveness of the proposed neurofuzzy modelling scheme.

Tensor regression based on linked multiway parameter analysis

Classical regression methods take vectors as covariates and estimate the corresponding vectors of regression parameters. When addressing regression problems on covariates of more complex form such as multi-dimensional arrays (i.e. tensors), traditional computational models can be severely compromised by ultrahigh dimensionality as well as complex structure. By exploiting the special structure of tensor covariates, the tensor regression model provides a promising solution to reduce the model’s dimensionality to a manageable level, thus leading to efficient estimation. Most of the existing tensor-based methods independently estimate each individual regression problem based on tensor decomposition which allows the simultaneous projections of an input tensor to more than one direction along each mode. As a matter of fact, multi-dimensional data are collected under the same or very similar conditions, so that data share some common latent components but can also have their own independent parameters for each regression task. Therefore, it is beneficial to analyse regression parameters among all the regressions in a linked way. In this paper, we propose a tensor regression model based on Tucker Decomposition, which identifies not only the common components of parameters across all the regression tasks, but also independent factors contributing to each particular regression task simultaneously. Under this paradigm, the number of independent parameters along each mode is constrained by a sparsity-preserving regulariser. Linked multiway parameter analysis and sparsity modeling further reduce the total number of parameters, with lower memory cost than their tensor-based counterparts. The effectiveness of the new method is demonstrated on real data sets.

The influence of chronic conditions and the environment on pubertal development. An example from medieval England

Adolescence is a unique period in human development encompassing sexual maturation (puberty) and the physical and psychological transition into adulthood. It is a crucial time for healthy development and any adverse environmental conditions, poor nutrition, or chronic infection can alter the timing of these physical changes; delaying menarche in girls or the age of peak height velocity in boys. This study explores the impact of chronic illness on the tempo of puberty in 607 adolescent skeletons from medieval England (AD 900-1550). A total of 135 (22.2%) adolescents showed some delay in their pubertal development, and this lag increased with age. Of those with a chronic condition, 40.0% (n=24/60) showed delay compared to only 20.3% (n=111/547) of the non-pathology group. This difference was statistically significant. A binary logistic regression model demonstrated a significant association between increasing delay in pubertal stage attainment with age in the pathology group. This is the first time that chronic conditions have been directly associated with a delay in maturation in the osteological record, using a new method to assess stages of puberty in skeletal remains.

Methods of Estimation in Multiple Linear Regression: Application to Clinical Data

Nesse artigo, tem-se o interesse em avaliar diferentes estratégias de estimação de parâmetros para um modelo de regressão linear múltipla. Para a estimação dos parâmetros do modelo foram utilizados dados de um ensaio clínico em que o interesse foi verificar se o ensaio mecânico da propriedade de força máxima (EM-FM) está associada com a massa femoral, com o diâmetro femoral e com o grupo experimental de ratas ovariectomizadas da raça Rattus norvegicus albinus, variedade Wistar. Para a estimação dos parâmetros do modelo serão comparadas três metodologias: a metodologia clássica, baseada no método dos mínimos quadrados; a metodologia Bayesiana, baseada no teorema de Bayes; e o método Bootstrap, baseado em processos de reamostragem.

Generalized log-gamma regression models with cure fraction

In this paper, the generalized log-gamma regression model is modified to allow the possibility that long-term survivors may be present in the data. This modification leads to a generalized log-gamma regression model with a cure rate, encompassing, as special cases, the log-exponential, log-Weibull and log-normal regression models with a cure rate typically used to model such data. The models attempt to simultaneously estimate the effects of explanatory variables on the timing acceleration/deceleration of a given event and the surviving fraction, that is, the proportion of the population for which the event never occurs. The normal curvatures of local influence are derived under some usual perturbation schemes and two martingale-type residuals are proposed to assess departures from the generalized log-gamma error assumption as well as to detect outlying observations. Finally, a data set from the medical area is analyzed.