Evaluation of bone strength: microtomographic tecniques

This thesis is a part of a larger study about the characterization of mechanical and histomorphometrical properties of bone. The main objects of this study were the bone tissue properties and its resistance to mechanical loads. Moreover, the knowledge about the equipment selected to carry out the analyses, the micro-computed tomography (micro-CT), was improved. Particular attention was given to the reliability over time of the measuring instrument. In order to understand the main characteristics of bone mechanical properties a study of the skeletal, the bones of which it is composed and biological principles that drive their formation and remodelling, was necessary. This study has led to the definition of two macro-classes describing the main components responsible for the resistance to fracture of bone: quantity and quality of bone. The study of bone quantity is the current clinical standard measure for so-called bone densitometry, and research studies have amply demonstrated that the amount of tissue is correlated with its mechanical properties of elasticity and fracture. However, the models presented in the literature, including information on the mere quantity of tissue, have often been limited in describing the mechanical behaviour. Recent investigations have underlined that also the bone-structure and the tissue-mineralization play an important role in the mechanical characterization of bone tissue. For this reason in this thesis the class defined as bone quality was mainly studied, splitting it into two sub-classes of bone structure and tissue quality. A study on bone structure was designed to identify which structural parameters, among the several presented in the literature, could be integrated with the information about quantity, in order to better describe the mechanical properties of bone. In this way, it was also possible to analyse the iteration between structure and function. It has been known for long that bone tissue is capable of remodeling and changing its internal structure according to loads, but the dynamics of these changes are still being analysed. This part of the study was aimed to identify the parameters that could quantify the structural changes of bone tissue during the development of a given disease: osteoarthritis. A study on tissue quality would have to be divided into different classes, which would require a scale of analysis not suitable for the micro-CT. For this reason the study was focused only on the mineralization of the tissue, highlighting the difference between bone density and tissue density, working in a context where there is still an ongoing scientific debate.

Development of Clinical Decision Support Systems based on Mathematical Models of Physiological Systems

In the last years of research, I focused my studies on different physiological problems. Together with my supervisors, I developed/improved different mathematical models in order to create valid tools useful for a better understanding of important clinical issues. The aim of all this work is to develop tools for learning and understanding cardiac and cerebrovascular physiology as well as pathology, generating research questions and developing clinical decision support systems useful for intensive care unit patients. I. ICP-model Designed for Medical Education We developed a comprehensive cerebral blood flow and intracranial pressure model to simulate and study the complex interactions in cerebrovascular dynamics caused by multiple simultaneous alterations, including normal and abnormal functional states of auto-regulation of the brain. Individual published equations (derived from prior animal and human studies) were implemented into a comprehensive simulation program. Included in the normal physiological modelling was: intracranial pressure, cerebral blood flow, blood pressure, and carbon dioxide (CO2) partial pressure. We also added external and pathological perturbations, such as head up position and intracranial haemorrhage. The model performed clinically realistically given inputs of published traumatized patients, and cases encountered by clinicians. The pulsatile nature of the output graphics was easy for clinicians to interpret. The manoeuvres simulated include changes of basic physiological inputs (e.g. blood pressure, central venous pressure, CO2 tension, head up position, and respiratory effects on vascular pressures) as well as pathological inputs (e.g. acute intracranial bleeding, and obstruction of cerebrospinal outflow). Based on the results, we believe the model would be useful to teach complex relationships of brain haemodynamics and study clinical research questions such as the optimal head-up position, the effects of intracranial haemorrhage on cerebral haemodynamics, as well as the best CO2 concentration to reach the optimal compromise between intracranial pressure and perfusion. We believe this model would be useful for both beginners and advanced learners. It could be used by practicing clinicians to model individual patients (entering the effects of needed clinical manipulations, and then running the model to test for optimal combinations of therapeutic manoeuvres). II. A Heterogeneous Cerebrovascular Mathematical Model Cerebrovascular pathologies are extremely complex, due to the multitude of factors acting simultaneously on cerebral haemodynamics. In this work, the mathematical model of cerebral haemodynamics and intracranial pressure dynamics, described in the point I, is extended to account for heterogeneity in cerebral blood flow. The model includes the Circle of Willis, six regional districts independently regulated by autoregulation and CO2 reactivity, distal cortical anastomoses, venous circulation, the cerebrospinal fluid circulation, and the intracranial pressure-volume relationship. Results agree with data in the literature and highlight the existence of a monotonic relationship between transient hyperemic response and the autoregulation gain. During unilateral internal carotid artery stenosis, local blood flow regulation is progressively lost in the ipsilateral territory with the presence of a steal phenomenon, while the anterior communicating artery plays the major role to redistribute the available blood flow. Conversely, distal collateral circulation plays a major role during unilateral occlusion of the middle cerebral artery. In conclusion, the model is able to reproduce several different pathological conditions characterized by heterogeneity in cerebrovascular haemodynamics and can not only explain generalized results in terms of physiological mechanisms involved, but also, by individualizing parameters, may represent a valuable tool to help with difficult clinical decisions. III. Effect of Cushing Response on Systemic Arterial Pressure. During cerebral hypoxic conditions, the sympathetic system causes an increase in arterial pressure (Cushing response), creating a link between the cerebral and the systemic circulation. This work investigates the complex relationships among cerebrovascular dynamics, intracranial pressure, Cushing response, and short-term systemic regulation, during plateau waves, by means of an original mathematical model. The model incorporates the pulsating heart, the pulmonary circulation and the systemic circulation, with an accurate description of the cerebral circulation and the intracranial pressure dynamics (same model as in the first paragraph). Various regulatory mechanisms are included: cerebral autoregulation, local blood flow control by oxygen (O2) and/or CO2 changes, sympathetic and vagal regulation of cardiovascular parameters by several reflex mechanisms (chemoreceptors, lung-stretch receptors, baroreceptors). The Cushing response has been described assuming a dramatic increase in sympathetic activity to vessels during a fall in brain O2 delivery. With this assumption, the model is able to simulate the cardiovascular effects experimentally observed when intracranial pressure is artificially elevated and maintained at constant level (arterial pressure increase and bradicardia). According to the model, these effects arise from the interaction between the Cushing response and the baroreflex response (secondary to arterial pressure increase). Then, patients with severe head injury have been simulated by reducing intracranial compliance and cerebrospinal fluid reabsorption. With these changes, oscillations with plateau waves developed. In these conditions, model results indicate that the Cushing response may have both positive effects, reducing the duration of the plateau phase via an increase in cerebral perfusion pressure, and negative effects, increasing the intracranial pressure plateau level, with a risk of greater compression of the cerebral vessels. This model may be of value to assist clinicians in finding the balance between clinical benefits of the Cushing response and its shortcomings. IV. Comprehensive Cardiopulmonary Simulation Model for the Analysis of Hypercapnic Respiratory Failure We developed a new comprehensive cardiopulmonary model that takes into account the mutual interactions between the cardiovascular and the respiratory systems along with their short-term regulatory mechanisms. The model includes the heart, systemic and pulmonary circulations, lung mechanics, gas exchange and transport equations, and cardio-ventilatory control. Results show good agreement with published patient data in case of normoxic and hyperoxic hypercapnia simulations. In particular, simulations predict a moderate increase in mean systemic arterial pressure and heart rate, with almost no change in cardiac output, paralleled by a relevant increase in minute ventilation, tidal volume and respiratory rate. The model can represent a valid tool for clinical practice and medical research, providing an alternative way to experience-based clinical decisions. In conclusion, models are not only capable of summarizing current knowledge, but also identifying missing knowledge. In the former case they can serve as training aids for teaching the operation of complex systems, especially if the model can be used to demonstrate the outcome of experiments. In the latter case they generate experiments to be performed to gather the missing data.

Multi-level models and infrastructures for simulating biological system development

The hierarchical organisation of biological systems plays a crucial role in the pattern formation of gene expression resulting from the morphogenetic processes, where autonomous internal dynamics of cells, as well as cell-to-cell interactions through membranes, are responsible for the emergent peculiar structures of the individual phenotype. Being able to reproduce the systems dynamics at different levels of such a hierarchy might be very useful for studying such a complex phenomenon of self-organisation. The idea is to model the phenomenon in terms of a large and dynamic network of compartments, where the interplay between inter-compartment and intra-compartment events determines the emergent behaviour resulting in the formation of spatial patterns. According to these premises the thesis proposes a review of the different approaches already developed in modelling developmental biology problems, as well as the main models and infrastructures available in literature for modelling biological systems, analysing their capabilities in tackling multi-compartment / multi-level models. The thesis then introduces a practical framework, MS-BioNET, for modelling and simulating these scenarios exploiting the potential of multi-level dynamics. This is based on (i) a computational model featuring networks of compartments and an enhanced model of chemical reaction addressing molecule transfer, (ii) a logic-oriented language to flexibly specify complex simulation scenarios, and (iii) a simulation engine based on the many-species/many-channels optimised version of Gillespie’s direct method. The thesis finally proposes the adoption of the agent-based model as an approach capable of capture multi-level dynamics. To overcome the problem of parameter tuning in the model, the simulators are supplied with a module for parameter optimisation. The task is defined as an optimisation problem over the parameter space in which the objective function to be minimised is the distance between the output of the simulator and a target one. The problem is tackled with a metaheuristic algorithm. As an example of application of the MS-BioNET framework and of the agent-based model, a model of the first stages of Drosophila Melanogaster development is realised. The model goal is to generate the early spatial pattern of gap gene expression. The correctness of the models is shown comparing the simulation results with real data of gene expression with spatial and temporal resolution, acquired in free on-line sources.

Fiber beam-columns models with flexure-shear interaction for nonlinear analysis of reinforced concrete structures

The aim of this study was to develop a model capable to capture the different contributions which characterize the nonlinear behaviour of reinforced concrete structures. In particular, especially for non slender structures, the contribution to the nonlinear deformation due to bending may be not sufficient to determine the structural response. Two different models characterized by a fibre beam-column element are here proposed. These models can reproduce the flexure-shear interaction in the nonlinear range, with the purpose to improve the analysis in shear-critical structures. The first element discussed is based on flexibility formulation which is associated with the Modified Compression Field Theory as material constitutive law. The other model described in this thesis is based on a three-field variational formulation which is associated with a 3D generalized plastic-damage model as constitutive relationship. The first model proposed in this thesis was developed trying to combine a fibre beamcolumn element based on the flexibility formulation with the MCFT theory as constitutive relationship. The flexibility formulation, in fact, seems to be particularly effective for analysis in the nonlinear field. Just the coupling between the fibre element to model the structure and the shear panel to model the individual fibres allows to describe the nonlinear response associated to flexure and shear, and especially their interaction in the nonlinear field. The model was implemented in an original matlab® computer code, for describing the response of generic structures. The simulations carried out allowed to verify the field of working of the model. Comparisons with available experimental results related to reinforced concrete shears wall were performed in order to validate the model. These results are characterized by the peculiarity of distinguishing the different contributions due to flexure and shear separately. The presented simulations were carried out, in particular, for monotonic loading. The model was tested also through numerical comparisons with other computer programs. Finally it was applied for performing a numerical study on the influence of the nonlinear shear response for non slender reinforced concrete (RC) members. Another approach to the problem has been studied during a period of research at the University of California Berkeley. The beam formulation follows the assumptions of the Timoshenko shear beam theory for the displacement field, and uses a three-field variational formulation in the derivation of the element response. A generalized plasticity model is implemented for structural steel and a 3D plastic-damage model is used for the simulation of concrete. The transverse normal stress is used to satisfy the transverse equilibrium equations of at each control section, this criterion is also used for the condensation of degrees of freedom from the 3D constitutive material to a beam element. In this thesis is presented the beam formulation and the constitutive relationships, different analysis and comparisons are still carrying out between the two model presented.

Development of control-oriented models of Dual Clutch Transmission systems

A control-oriented model of a Dual Clutch Transmission was developed for real-time Hardware In the Loop (HIL) applications, to support model-based development of the DCT controller. The model is an innovative attempt to reproduce the fast dynamics of the actuation system while maintaining a step size large enough for real-time applications. The model comprehends a detailed physical description of hydraulic circuit, clutches, synchronizers and gears, and simplified vehicle and internal combustion engine sub-models. As the oil circulating in the system has a large bulk modulus, the pressure dynamics are very fast, possibly causing instability in a real-time simulation; the same challenge involves the servo valves dynamics, due to the very small masses of the moving elements. Therefore, the hydraulic circuit model has been modified and simplified without losing physical validity, in order to adapt it to the real-time simulation requirements. The results of offline simulations have been compared to on-board measurements to verify the validity of the developed model, that was then implemented in a HIL system and connected to the TCU (Transmission Control Unit). Several tests have been performed: electrical failure tests on sensors and actuators, hydraulic and mechanical failure tests on hydraulic valves, clutches and synchronizers, and application tests comprehending all the main features of the control performed by the TCU. Being based on physical laws, in every condition the model simulates a plausible reaction of the system. The first intensive use of the HIL application led to the validation of the new safety strategies implemented inside the TCU software. A test automation procedure has been developed to permit the execution of a pattern of tests without the interaction of the user; fully repeatable tests can be performed for non-regression verification, allowing the testing of new software releases in fully automatic mode.

Understanding the Combined Role of Internal and External Factors in New Service Development Process within the Professional Knowledge Intensive Business Service Firms

Our research asked the following main questions: how the characteristics of professionals service firms allow them to successfully innovate in exploiting through exploring by combining internal and external factors of innovation and how these ambidextrous organisations perceive these factors; and how do successful innovators in professional service firms use corporate entrepreneurship models in their new service development processes? With a goal to shed light on innovation in professional knowledge intensive business service firms’ (PKIBS), we concluded a qualitative analysis of ten globally acting law firms, providing business legal services. We analyse the internal and factors of innovation that are critical for PKIBS’ innovation. We suggest how these firms become ambidextrous in changing environment. Our findings show that this kind of firms has particular type of ambidexterity due to their specific characteristics. As PKIBS are very dependant on its human capital, governance structure, and the high expectations of their clients, their ambidexterity is structural, but also contextual at the same time. In addition, we suggest 3 types of corporate entrepreneurship models that international PKIBS use to enhance innovation in turbulent environments. We looked at how law firms going through turbulent environments were using corporate entrepreneurship activities as a part of their strategies to be more innovative. Using visual mapping methodology, we developed three types of innovation patterns in the law firms. We suggest that corporate entrepreneurship models depend on successful application of mainly three elements: who participates in corporate entrepreneurship initiatives; what are the formal processes that enhances these initiatives; and what are the policies applied to this type of behaviour.

Comparative study of the different models for the calculation of BLEVEs overpressure effects

The BLEVE, acronym for Boiling Liquid Expanding Vapour Explosion, is one of the most dangerous accidents that can occur in pressure vessels. It can be defined as an explosion resulting from the failure of a vessel containing a pressure liquefied gas stored at a temperature significantly above its boiling point at atmospheric pressure. This phenomenon frequently appears when a vessel is engulfed by a fire: the heat causes the internal pressure to raise and the mechanical proprieties of the wall to decrease, with the consequent rupture of the tank and the instantaneous release of its whole content. After the breakage, the vapour outflows and expands and the liquid phase starts boiling due to the pressure drop. The formation and propagation of a distructive schock wave may occur, together with the ejection of fragments, the generation of a fireball if the stored fluid is flammable and immediately ignited or the atmospheric dispersion of a toxic cloud if the fluid contained inside the vessel is toxic. Despite the presence of many studies on the BLEVE mechanism, the exact causes and conditions of its occurrence are still elusive. In order to better understand this phenomenon, in the present study first of all the concept and definition of BLEVE are investigated. A historical analysis of the major events that have occurred over the past 60 years is described. A research of the principal causes of this event, including the analysis of the substances most frequently involved, is presented too. Afterwards a description of the main effects of BLEVEs is reported, focusing especially on the overpressure. Though the major aim of the present thesis is to contribute, with a comparative analysis, to the validation of the main models present in the literature for the calculation and prediction of the overpressure caused by BLEVEs. In line with this purpose, after a short overview of the available approaches, their ability to reproduce the trend of the overpressure is investigated. The overpressure calculated with the different models is compared with values deriving from events happened in the past and ad-hoc experiments, focusing the attention especially on medium and large scale phenomena. The ability of the models to consider different filling levels of the reservoir and different substances is analyzed too. The results of these calculations are extensively discussed. Finally some conclusive remarks are reported.

Predictive ability of a modified Örebro Musculoskeletal Pain Questionnaire in an acute/subacute low back pain working population

The original 'Örebro Musculoskeletal Pain Questionnaire' (original-ÖMPQ) has been shown to have limitations in practicality, factor structure, face and content validity. This study addressed these concerns by modifying its content producing the 'Örebro Musculoskeletal Screening Questionnaire' (ÖMSQ). The ÖMSQ and original-ÖMPQ were tested concurrently in acute/subacute low back pain working populations (pilot n = 44, main n = 106). The ÖMSQ showed improved face and content validity, which broadened potential application, and improved practicality with two-thirds less missing responses. High reliability (0.975, p < 0.05, ICC: 2.1), criterion validity (Spearman's r = 0.97) and internal consistency (α = 0.84) were achieved, as were predictive ability cut-off scores from ROC curves (112-120 ÖMSQ-points), statistically different ÖMSQ scores (p < 0.001) for each outcome trait, and a strong correlation with recovery time (Spearman's, r = 0.71). The six-component factor structure reflected the constructs originally proposed. The ÖMSQ can be substituted for the original-ÖMPQ in this population. Further research will assess its applicability in broader populations.

The Effects of Privatization of State-Owned Enterprises in Poland and East Germany

The main goal of this project was to propose appropriate methods of analysing the effects of the privatisation of state-owned enterprises, methods which were then tested on a limited sample of 16 Polish and 8 German enterprises privatised in 1992. A considerable amount of information was collected relating to the six-year period 1989-1994 relating to most aspects of the companies' activities. The effects of privatisation were taken to be those changes within the enterprises which were the result of privatisation, in such areas as production, the productivity of labour and fixed assets, investments and innovations, employment and wages, economic incentives (especially for top managers), financing (internal and external sources), bad debts and economic effects (financial analysis). A second important goal was to identify the main factors which represent methodological obstacles in surveys of the effects of privatisation during a period of fundamental transformation of the entire economic system. The list of enterprises for the research was compiled in such a way as to allow for the differentiation of ownership structures of privatised firms and to permit (at least to a certain extent) the empirical verification of some hypotheses regarding the privatisation process. The enterprises selected were divided into the following three groups representing (as far as possible) various types of ownership structures or types of control: (1) enterprises control by strategic investors (domestic or foreign), (2) enterprises controlled by employees (employee-owned companies), (3) enterprises controlled by managers. Formal methods such as econometric models with varying parameters were used to separate pure privatisation effects from other factors which influence various aspects of an enterprise's working, including policies on the productivity of labour and capital, average wages, the remuneration of top managers, etc. While the group admits that their findings and conclusions cannot be treated as representative of all privatised enterprises in Poland and Germany, they found considerable convergence with their findings and those of other surveys conducted on a wider scale. The main hypotheses that were confirmed included that privatisation (especially in companies controlled by large investors and managers) leads to a significant increase in the effectiveness of these production process, growing pay differentials between different employee groups (e.g. between executives and rank-and-file employees) and between different jobs and positions within particular professional groups. They also confirmed the growing importance in incentives to top executives of incentives linked with the company's economic effects (particularly profit-related incentives), long-term incentives and the capital market.

Towards a Variety of Family Models: Economic Contributions of Spouses and Family Power

In Western societies the increase in female employment (especially among married women) is seen as having brought about the crisis of the traditional model of the family, reinforcing the position of the "modern" model - the egalitarian family with two working spouses and a "dual-career" family. In contrast, the transitional situation in the post-communist countries during the 1990s is producing a crisis of the family with two working spouses (the basic type of the communist period) and leading to new power relations within the family. While the growth of dual-earner households in this century has implied modification of family models towards greater symmetry of responsibility for breadwinning and homemaking, there is considerable evidence that women's increased employment does not necessarily lead to a more egalitarian approach to gender roles within the family. The group set out to investigate the economic situation of families and economic power within the fame as a crucial factor in the transformation of families with two working spouses in order to reveal the specific patterns of gender contracts and power relations within the family that are emerging in response to the current political and economic transformation. They opted for a comparative approach, selecting the Czech Republic as a country where the very similar tendencies of a few years ago (almost 100% of women employed and the family as a realm of considerable private freedom where both women's and men's gender identities and the traditional distribution of family responsibilities were largely preserved) are combined with a very different experience in terms of economic inequalities during the 1990s to that of Russia. In the first stage of the study they surveyed 300 married couples (150 in each country) on the question of breadwinning. They then carried out in-depth interviews with 10 couples from each country (selected from among the educated layers of the population), focusing on the process of the social construction of gender, using breadwinning and homemaking as gender boundaries which distinguish men from women. By analysing changes in social position and the type of interpersonal interaction of spouses they distinguished two main types of family contracts: the neo-traditional "communal sharing" (with male breadwinner, traditional distribution of family chores and negotiated family power) and the modern one based on negotiated agreement. The most important pre-conditions of husband-wife agreement about breadwinning seemed to imply their overall gender ideology rather than the economic and/or family circumstances. In general, wives were more likely to express egalitarian views, supporting the blurring or even elimination of many gender boundaries. Husbands, on the other hand, more often gave responses calling for the continued maintenance of gender boundaries. The analysis showed that breadwinning is still an important gender boundary in these cultures, one that is assumed unless it is explicitly questioned and that is seen as part of what makes a man a "real man". The majority of respondents seemed to be committed to egalitarian ideology on gender roles and the distribution of family tasks, including decision making, but this is contradicted by the persistent idea of the husband as the breadwinner. This contradiction is more characteristic of the Russian situation than of the Czech. The quantitative study showed a difference in prevailing family models between the two countries, with a clearer shift towards the traditional family contract in the Russian case. The Czechs were more likely to consider their partnerships as based on negotiated agreement, while the Russians saw theirs as based on egalitarian contract, in both cases seeing this as the norm. The majority of couples said they felt satisfied with their marriage, although in both countries wives seemed to be less satisfied. There was however a difference in the issues that aroused dissatisfaction, with Czech women being more sensitive to issues such as self-realisation, personal independence, understanding and recognition in the family, and Russians to issues of love, understanding and recognition. The most disputed area for the majority of families was chores in the home, presumably because in many families both husband and wife were working hard outside the home and because a number of partners had differing views as to the ideal distribution of chores within the family. The distribution of power in the family seems to be linked to the level of well being. The analysis showed that in the dominant democratic model there is still an inverse connection between family leadership and well being: the more prominent the wife's position as head of the family is, the lower the level of family income. This may reflect both the husband's refusal to play the leading role in the family and even his rejection of any involvement in family issues in such a family. The qualitative research revealed that both men and women see the breadwinning role to be an essential part of masculine identity, a role which the female partner would take on temporarily to assist the male but not permanently since this would threaten the gender boundaries and the man's identity. At the same time, few breadwinners expressed a sense of job satisfaction and all considered their choice as imposed on them by the circumstances (i.e. having a family in difficult times). The group feel that family orientation and some loss of personal involvement in their profession is partly reflected in the fact that many of the men felt more comfortable and self-confident at home than at work. Women's work, on the other hand, was largely seen as a source of personal and self-realisation and social life. Eight out of ten of the Russian women interviewed were employed, although only two on a full-time basis, but none saw their jobs as adding substantially to the family budget. Both partners see the most important factor as the wife's wish to work or stay at home, and do not think it wise for the wife to work at the expense of her part of the "family contract", although husbands from the "egalitarian" relationships expressed more willingness to compromise. The analysis showed clearly that wives and husbands did not construct gender boundaries in isolation, with the interviews providing clear evidence of negotiation. At the same time, husbands' interpretations of their wives' employment were less susceptible to the influence of negotiation than were their gender attitudes and norms about breadwinning. One of the most interesting aspects of the spouses' negotiations was the extent to which they disagreed about what they seemed to have agreed upon. Most disagreements about the breadwinning boundaries, however, were over norms and were settled by changes in norms rather than in behavioural interpretation. Changes in norms were often a form of peace offering or were in response in changes in circumstances. The study did show, however, that many of the efforts at cooperation and compensation were more symbolic than real and the group found the plasticity of expressed gender ideology to be one of the most striking findings of their work. They conclude that the shift towards more traditional gednder distributions of incomes and domestic chores does not automatically mean the reestablishment of a patriarchal model of family power. On the contrary, it seems to be a compromise formation, relatively unstable, temporary and containing self-defeating forces as the split between the personal and professional value of work and its social value expressed in a money equivalent cannot be maintained for generations.

USE OF HIDDEN MARKOV MODELS FOR QTL MAPPING

An important aspect of the QTL mapping problem is the treatment of missing genotype data. If complete genotype data were available, QTL mapping would reduce to the problem of model selection in linear regression. However, in the consideration of loci in the intervals between the available genetic markers, genotype data is inherently missing. Even at the typed genetic markers, genotype data is seldom complete, as a result of failures in the genotyping assays or for the sake of economy (for example, in the case of selective genotyping, where only individuals with extreme phenotypes are genotyped). We discuss the use of algorithms developed for hidden Markov models (HMMs) to deal with the missing genotype data problem.

Large Sample Theory for Semiparametric Regression Models with Two-Phase, Outcome Dependent Sampling

Outcome-dependent, two-phase sampling designs can dramatically reduce the costs of observational studies by judicious selection of the most informative subjects for purposes of detailed covariate measurement. Here we derive asymptotic information bounds and the form of the efficient score and influence functions for the semiparametric regression models studied by Lawless, Kalbfleisch, and Wild (1999) under two-phase sampling designs. We show that the maximum likelihood estimators for both the parametric and nonparametric parts of the model are asymptotically normal and efficient. The efficient influence function for the parametric part aggress with the more general information bound calculations of Robins, Hsieh, and Newey (1995). By verifying the conditions of Murphy and Van der Vaart (2000) for a least favorable parametric submodel, we provide asymptotic justification for statistical inference based on profile likelihood.

Asymptotics for Marginal Generalized Linear Models With Sparse Correlations

Marginal generalized linear models can be used for clustered and longitudinal data by fitting a model as if the data were independent and using an empirical estimator of parameter standard errors. We extend this approach to data where the number of observations correlated with a given one grows with sample size and show that parameter estimates are consistent and asymptotically Normal with a slower convergence rate than for independent data, and that an information sandwich variance estimator is consistent. We present two problems that motivated this work, the modelling of patterns of HIV genetic variation and the behavior of clustered data estimators when clusters are large.

Markers Models in Survival Analysis and Applications to Issues Associated with AIDS

Jewell and Kalbfleisch (1992) consider the use of marker processes for applications related to estimation of the survival distribution of time to failure. Marker processes were assumed to be stochastic processes that, at a given point in time, provide information about the current hazard and consequently on the remaining time to failure. Particular attention was paid to calculations based on a simple additive model for the relationship between the hazard function at time t and the history of the marker process up until time t. Specific applications to the analysis of AIDS data included the use of markers as surrogate responses for onset of AIDS with censored data and as predictors of the time elapsed since infection in prevalent individuals. Here we review recent work on the use of marker data to tackle these kinds of problems with AIDS data. The Poisson marker process with an additive model, introduced in Jewell and Kalbfleisch (1992) may be a useful "test" example for comparison of various procedures.

Locally Efficient Estimation in Censored Data Models: Theory and Examples

In many applications the observed data can be viewed as a censored high dimensional full data random variable X. By the curve of dimensionality it is typically not possible to construct estimators that are asymptotically efficient at every probability distribution in a semiparametric censored data model of such a high dimensional censored data structure. We provide a general method for construction of one-step estimators that are efficient at a chosen submodel of the full-data model, are still well behaved off this submodel and can be chosen to always improve on a given initial estimator. These one-step estimators rely on good estimators of the censoring mechanism and thus will require a parametric or semiparametric model for the censoring mechanism. We present a general theorem that provides a template for proving the desired asymptotic results. We illustrate the general one-step estimation methods by constructing locally efficient one-step estimators of marginal distributions and regression parameters with right-censored data, current status data and bivariate right-censored data, in all models allowing the presence of time-dependent covariates. The conditions of the asymptotics theorem are rigorously verified in one of the examples and the key condition of the general theorem is verified for all examples.