A Cox Model for Biostatistics of the Future

Professor Sir David R. Cox (DRC) is widely acknowledged as among the most important scientists of the second half of the twentieth century. He inherited the mantle of statistical science from Pearson and Fisher, advanced their ideas, and translated statistical theory into practice so as to forever change the application of statistics in many fields, but especially biology and medicine. The logistic and proportional hazards models he substantially developed, are arguably among the most influential biostatistical methods in current practice. This paper looks forward over the period from DRC's 80th to 90th birthdays, to speculate about the future of biostatistics, drawing lessons from DRC's contributions along the way. We consider "Cox's model" of biostatistics, an approach to statistical science that: formulates scientific questions or quantities in terms of parameters gamma in probability models f(y; gamma) that represent in a parsimonious fashion, the underlying scientific mechanisms (Cox, 1997); partition the parameters gamma = theta, eta into a subset of interest theta and other "nuisance parameters" eta necessary to complete the probability distribution (Cox and Hinkley, 1974); develops methods of inference about the scientific quantities that depend as little as possible upon the nuisance parameters (Barndorff-Nielsen and Cox, 1989); and thinks critically about the appropriate conditional distribution on which to base infrences. We briefly review exciting biomedical and public health challenges that are capable of driving statistical developments in the next decade. We discuss the statistical models and model-based inferences central to the CM approach, contrasting them with computationally-intensive strategies for prediction and inference advocated by Breiman and others (e.g. Breiman, 2001) and to more traditional design-based methods of inference (Fisher, 1935). We discuss the hierarchical (multi-level) model as an example of the future challanges and opportunities for model-based inference. We then consider the role of conditional inference, a second key element of the CM. Recent examples from genetics are used to illustrate these ideas. Finally, the paper examines causal inference and statistical computing, two other topics we believe will be central to biostatistics research and practice in the coming decade. Throughout the paper, we attempt to indicate how DRC's work and the "Cox Model" have set a standard of excellence to which all can aspire in the future.

A MULTILEVEL MODEL TO ADDRESS BATCH EFFECTS IN COPY NUMBER ESTIMATION USING SNP ARRAYS

Submicroscopic changes in chromosomal DNA copy number dosage are common and have been implicated in many heritable diseases and cancers. Recent high-throughput technologies have a resolution that permits the detection of segmental changes in DNA copy number that span thousands of basepairs across the genome. Genome-wide association studies (GWAS) may simultaneously screen for copy number-phenotype and SNP-phenotype associations as part of the analytic strategy. However, genome-wide array analyses are particularly susceptible to batch effects as the logistics of preparing DNA and processing thousands of arrays often involves multiple laboratories and technicians, or changes over calendar time to the reagents and laboratory equipment. Failure to adjust for batch effects can lead to incorrect inference and requires inefficient post-hoc quality control procedures that exclude regions that are associated with batch. Our work extends previous model-based approaches for copy number estimation by explicitly modeling batch effects and using shrinkage to improve locus-specific estimates of copy number uncertainty. Key features of this approach include the use of diallelic genotype calls from experimental data to estimate batch- and locus-specific parameters of background and signal without the requirement of training data. We illustrate these ideas using a study of bipolar disease and a study of chromosome 21 trisomy. The former has batch effects that dominate much of the observed variation in quantile-normalized intensities, while the latter illustrates the robustness of our approach to datasets where as many as 25% of the samples have altered copy number. Locus-specific estimates of copy number can be plotted on the copy-number scale to investigate mosaicism and guide the choice of appropriate downstream approaches for smoothing the copy number as a function of physical position. The software is open source and implemented in the R package CRLMM available at Bioconductor (http:www.bioconductor.org).

A Mechanistic Latent Variable Model for Estimating Drug Concentrations in the Male Genital Tract

The purpose of this study is to develop statistical methodology to facilitate indirect estimation of the concentration of antiretroviral drugs and viral loads in the prostate gland and the seminal vesicle. The differences in antiretroviral drug concentrations in these organs may lead to suboptimal concentrations in one gland compared to the other. Suboptimal levels of the antiretroviral drugs will not be able to fully suppress the virus in that gland, lead to a source of sexually transmissible virus and increase the chance of selecting for drug resistant virus. This information may be useful selecting antiretroviral drug regimen that will achieve optimal concentrations in most of male genital tract glands. Using fractionally collected semen ejaculates, Lundquist (1949) measured levels of surrogate markers in each fraction that are uniquely produced by specific male accessory glands. To determine the original glandular concentrations of the surrogate markers, Lundquist solved a simultaneous series of linear equations. This method has several limitations. In particular, it does not yield a unique solution, it does not address measurement error, and it disregards inter-subject variability in the parameters. To cope with these limitations, we developed a mechanistic latent variable model based on the physiology of the male genital tract and surrogate markers. We employ a Bayesian approach and perform a sensitivity analysis with regard to the distributional assumptions on the random effects and priors. The model and Bayesian approach is validated on experimental data where the concentration of a drug should be (biologically) differentially distributed between the two glands. In this example, the Bayesian model-based conclusions are found to be robust to model specification and this hierarchical approach leads to more scientifically valid conclusions than the original methodology. In particular, unlike existing methods, the proposed model based approach was not affected by a common form of outliers.

A coronary heart disease risk model for predicting the effect of potent antiretroviral therapy in HIV-1 infected men

BACKGROUND: Many HIV-infected patients on highly active antiretroviral therapy (HAART) experience metabolic complications including dyslipidaemia and insulin resistance, which may increase their coronary heart disease (CHD) risk. We developed a prognostic model for CHD tailored to the changes in risk factors observed in patients starting HAART. METHODS: Data from five cohort studies (British Regional Heart Study, Caerphilly and Speedwell Studies, Framingham Offspring Study, Whitehall II) on 13,100 men aged 40-70 and 114,443 years of follow up were used. CHD was defined as myocardial infarction or death from CHD. Model fit was assessed using the Akaike Information Criterion; generalizability across cohorts was examined using internal-external cross-validation. RESULTS: A parametric model based on the Gompertz distribution generalized best. Variables included in the model were systolic blood pressure, total cholesterol, high-density lipoprotein cholesterol, triglyceride, glucose, diabetes mellitus, body mass index and smoking status. Compared with patients not on HAART, the estimated CHD hazard ratio (HR) for patients on HAART was 1.46 (95% CI 1.15-1.86) for moderate and 2.48 (95% CI 1.76-3.51) for severe metabolic complications. CONCLUSIONS: The change in the risk of CHD in HIV-infected men starting HAART can be estimated based on typical changes in risk factors, assuming that HRs estimated using data from non-infected men are applicable to HIV-infected men. Based on this model the risk of CHD is likely to increase, but increases may often be modest, and could be offset by lifestyle changes.

Stochastic knock detection model for spark ignited engines

This report presents the development of a Stochastic Knock Detection (SKD) method for combustion knock detection in a spark-ignition engine using a model based design approach. Knock Signal Simulator (KSS) was developed as the plant model for the engine. The KSS as the plant model for the engine generates cycle-to-cycle accelerometer knock intensities following a stochastic approach with intensities that are generated using a Monte Carlo method from a lognormal distribution whose parameters have been predetermined from engine tests and dependent upon spark-timing, engine speed and load. The lognormal distribution has been shown to be a good approximation to the distribution of measured knock intensities over a range of engine conditions and spark-timings for multiple engines in previous studies. The SKD method is implemented in Knock Detection Module (KDM) which processes the knock intensities generated by KSS with a stochastic distribution estimation algorithm and outputs estimates of high and low knock intensity levels which characterize knock and reference level respectively. These estimates are then used to determine a knock factor which provides quantitative measure of knock level and can be used as a feedback signal to control engine knock. The knock factor is analyzed and compared with a traditional knock detection method to detect engine knock under various engine operating conditions. To verify the effectiveness of the SKD method, a knock controller was also developed and tested in a model-in-loop (MIL) system. The objective of the knock controller is to allow the engine to operate as close as possible to its border-line spark-timing without significant engine knock. The controller parameters were tuned to minimize the cycle-to-cycle variation in spark timing and the settling time of the controller in responding to step increase in spark advance resulting in the onset of engine knock. The simulation results showed that the combined system can be used adequately to model engine knock and evaluated knock control strategies for a wide range of engine operating conditions.

Model to describe the mode I fracture of steel fiber reinforced ultra-high performance concrete

Ultra-high performance fiber reinforced concrete (UHPFRC) has arisen from the implementation of a variety of concrete engineering and materials science concepts developed over the last century. This material offers superior strength, serviceability, and durability over its conventional counterparts. One of the most important differences for UHPFRC over other concrete materials is its ability to resist fracture through the use of randomly dispersed discontinuous fibers and improvements to the fiber-matrix bond. Of particular interest is the materials ability to achieve higher loads after first crack, as well as its high fracture toughness. In this research, a study of the fracture behavior of UHPFRC with steel fibers was conducted to look at the effect of several parameters related to the fracture behavior and to develop a fracture model based on a non-linear curve fit of the data. To determine this, a series of three-point bending tests were performed on various single edge notched prisms (SENPs). Compression tests were also performed for quality assurance. Testing was conducted on specimens of different cross-sections, span/depth (S/D) ratios, curing regimes, ages, and fiber contents. By comparing the results from prisms of different sizes this study examines the weakening mechanism due to the size effect. Furthermore, by employing the concept of fracture energy it was possible to obtain a comparison of the fracture toughness and ductility. The model was determined based on a fit to P-w fracture curves, which was cross referenced for comparability to the results. Once obtained the model was then compared to the models proposed by the AFGC in the 2003 and to the ACI 544 model for conventional fiber reinforced concretes.

Adenovirus-mediated transforming growth factor-beta ameliorates ischemic necrosis of epigastric skin flaps in a rat model

BACKGROUND: Gene therapy has been recently introduced as a novel approach to treat ischemic tissues by using the angiogenic potential of certain growth factors. We investigated the effect of adenovirus-mediated gene therapy with transforming growth factor-beta (TGF-beta) delivered into the subdermal space to treat ischemically challenged epigastric skin flaps in a rat model. MATERIAL AND METHODS: A pilot study was conducted in a group of 5 animals pretreated with Ad-GFP and expression of green fluorescent protein in the skin flap sections was demonstrated under fluorescence microscopy at 2, 4, and 7 days after the treatment, indicating a successful transfection of the skin flaps following subdermal gene therapy. Next, 30 male Sprague Dawley rats were divided into 3 groups of 10 rats each. An epigastric skin flap model, based solely on the right inferior epigastric vessels, was used as the model in this study. Rats received subdermal injections of adenovirus encoding TGF-beta (Ad-TGF-beta) or green fluorescent protein (Ad-GFP) as treatment control. The third group (n = 10) received saline and served as a control group. A flap measuring 8 x 8 cm was outlined on the abdominal skin extending from the xiphoid process proximally and the pubic region distally, to the anterior axillary lines bilaterally. Just prior to flap elevation, the injections were given subdermally in the left upper corner of the flap. The flap was then sutured back to its bed. Flap viability was evaluated seven days after the initial operation. Digital images of the epigastric flaps were taken and areas of necrotic zones relative to total flap surface area were measured and expressed as percentages by using a software program. RESULTS: There was a significant increase in mean percent surviving area between the Ad-TGF-beta group and the two other control groups (P < 0.05). (Ad-TGF-beta: 90.3 +/- 4.0% versus Ad-GFP: 82.2 +/- 8.7% and saline group: 82.6 +/- 4.3%.) CONCLUSIONS: In this study, the authors were able to demonstrate that adenovirus-mediated gene therapy using TGF-beta ameliorated ischemic necrosis in an epigastric skin flap model, as confirmed by significant reduction in the necrotic zones of the flap. The results of this study raise the possibility of using adenovirus-mediated TGF-beta gene therapy to promote perfusion in random portion of skin flaps, especially in high-risk patients.

A system for 3-D reconstruction of a patient-specific surface model from calibrated X-ray images

This paper presents a system for 3-D reconstruction of a patient-specific surface model from calibrated X-ray images. Our system requires two X-ray images of a patient with one acquired from the anterior-posterior direction and the other from the axial direction. A custom-designed cage is utilized in our system to calibrate both images. Starting from bone contours that are interactively identified from the X-ray images, our system constructs a patient-specific surface model of the proximal femur based on a statistical model based 2D/3D reconstruction algorithm. In this paper, we present the design and validation of the system with 25 bones. An average reconstruction error of 0.95 mm was observed.

Constructing a user experience user experience-based mobile learning environment

Mobile learning, in the past defined as learning with mobile devices, now refers to any type of learning-on-the-go or learning that takes advantage of mobile technologies. This new definition shifted its focus from the mobility of technology to the mobility of the learner (O'Malley and Stanton 2002; Sharples, Arnedillo-Sanchez et al. 2009). Placing emphasis on the mobile learner’s perspective requires studying “how the mobility of learners augmented by personal and public technology can contribute to the process of gaining new knowledge, skills, and experience” (Sharples, Arnedillo-Sanchez et al. 2009). The demands of an increasingly knowledge based society and the advances in mobile phone technology are combining to spur the growth of mobile learning. Around the world, mobile learning is predicted to be the future of online learning, and is slowly entering the mainstream education. However, for mobile learning to attain its full potential, it is essential to develop more advanced technologies that are tailored to the needs of this new learning environment. A research field that allows putting the development of such technologies onto a solid basis is user experience design, which addresses how to improve usability and therefore user acceptance of a system. Although there is no consensus definition of user experience, simply stated it focuses on how a person feels about using a product, system or service. It is generally agreed that user experience adds subjective attributes and social aspects to a space that has previously concerned itself mainly with ease-of-use. In addition, it can include users’ perceptions of usability and system efficiency. Recent advances in mobile and ubiquitous computing technologies further underline the importance of human-computer interaction and user experience (feelings, motivations, and values) with a system. Today, there are plenty of reports on the limitations of mobile technologies for learning (e.g., small screen size, slow connection), but there is a lack of research on user experience with mobile technologies. This dissertation will fill in this gap by a new approach in building a user experience-based mobile learning environment. The optimized user experience we suggest integrates three priorities, namely a) content, by improving the quality of delivered learning materials, b) the teaching and learning process, by enabling live and synchronous learning, and c) the learners themselves, by enabling a timely detection of their emotional state during mobile learning. In detail, the contributions of this thesis are as follows: • A video codec optimized for screencast videos which achieves an unprecedented compression rate while maintaining a very high video quality, and a novel UI layout for video lectures, which together enable truly mobile access to live lectures. • A new approach in HTTP-based multimedia delivery that exploits the characteristics of live lectures in a mobile context and enables a significantly improved user experience for mobile live lectures. • A non-invasive affective learning model based on multi-modal emotion detection with very high recognition rates, which enables real-time emotion detection and subsequent adaption of the learning environment on mobile devices. The technology resulting from the research presented in this thesis is in daily use at the School of Continuing Education of Shanghai Jiaotong University (SOCE), a blended-learning institution with 35.000 students.

Volcanic forcing for climate modeling: a new microphysics-based data set covering years 1600–present

As the understanding and representation of the impacts of volcanic eruptions on climate have improved in the last decades, uncertainties in the stratospheric aerosol forcing from large eruptions are now linked not only to visible optical depth estimates on a global scale but also to details on the size, latitude and altitude distributions of the stratospheric aerosols. Based on our understanding of these uncertainties, we propose a new model-based approach to generating a volcanic forcing for general circulation model (GCM) and chemistry–climate model (CCM) simulations. This new volcanic forcing, covering the 1600–present period, uses an aerosol microphysical model to provide a realistic, physically consistent treatment of the stratospheric sulfate aerosols. Twenty-six eruptions were modeled individually using the latest available ice cores aerosol mass estimates and historical data on the latitude and date of eruptions. The evolution of aerosol spatial and size distribution after the sulfur dioxide discharge are hence characterized for each volcanic eruption. Large variations are seen in hemispheric partitioning and size distributions in relation to location/date of eruptions and injected SO2 masses. Results for recent eruptions show reasonable agreement with observations. By providing these new estimates of spatial distributions of shortwave and long-wave radiative perturbations, this volcanic forcing may help to better constrain the climate model responses to volcanic eruptions in the 1600–present period. The final data set consists of 3-D values (with constant longitude) of spectrally resolved extinction coefficients, single scattering albedos and asymmetry factors calculated for different wavelength bands upon request. Surface area densities for heterogeneous chemistry are also provided.

Application of a computational model for complex fluvial ecosystems: The population dynamics of zebra mussel Dreissena polymorpha as a case study

The potential and adaptive flexibility of population dynamic P-systems (PDP) to study population dynamics suggests that they may be suitable for modelling complex fluvial ecosystems, characterized by a composition of dynamic habitats with many variables that interact simultaneously. Using as a model a reservoir occupied by the zebra mussel Dreissena polymorpha, we designed a computational model based on P systems to study the population dynamics of larvae, in order to evaluate management actions to control or eradicate this invasive species. The population dynamics of this species was simulated under different scenarios ranging from the absence of water flow change to a weekly variation with different flow rates, to the actual hydrodynamic situation of an intermediate flow rate. Our results show that PDP models can be very useful tools to model complex, partially desynchronized, processes that work in parallel. This allows the study of complex hydroecological processes such as the one presented, where reproductive cycles, temperature and water dynamics are involved in the desynchronization of the population dynamics both, within areas and among them. The results obtained may be useful in the management of other reservoirs with similar hydrodynamic situations in which the presence of this invasive species has been documented.

2D-3D Reconstruction-Based Planning of Total Hip Arthroplasty

This chapter proposed a personalized X-ray reconstruction-based planning and post-operative treatment evaluation framework called iJoint for advancing modern Total Hip Arthroplasty (THA). Based on a mobile X-ray image calibration phantom and a unique 2D-3D reconstruction technique, iJoint can generate patient-specific models of hip joint by non-rigidly matching statistical shape models to the X-ray radiographs. Such a reconstruction enables a true 3D planning and treatment evaluation of hip arthroplasty from just 2D X-ray radiographs whose acquisition is part of the standard diagnostic and treatment loop. As part of the system, a 3D model-based planning environment provides surgeons with hip arthroplasty related parameters such as implant type, size, position, offset and leg length equalization. With this newly developed system, we are able to provide true 3D solutions for computer assisted planning of THA using only 2D X-ray radiographs, which is not only innovative but also cost-effective.

Biomechanical validation of computer assisted planning of periacetabular osteotomy: A preliminary study based on finite element analysis

Periacetabular Osteotomy (PAO) is a joint preserving surgical intervention intended to increase femoral head coverage and thereby to improve stability in young patients with hip dysplasia. Previously, we developed a CT-based, computer-assisted program for PAO diagnosis and planning, which allows for quantifying the 3D acetabular morphology with parameters such as acetabular version, inclination, lateral center edge (LCE) angle and femoral head coverage ratio (CO). In order to verify the hypothesis that our morphology-based planning strategy can improve biomechanical characteristics of dysplastic hips, we developed a 3D finite element model based on patient-specific geometry to predict cartilage contact stress change before and after morphology-based planning. Our experimental results demonstrated that the morphology-based planning strategy could reduce cartilage contact pressures and at the same time increase contact areas. In conclusion, our computer-assisted system is an efficient tool for PAO planning.

A model for use by local public health departments to evaluate pandemic influenza plans

The events of the 1990's and early 2000's demonstrated the need for effective planning and response to natural and man-made disasters. One of those potential natural disasters is pandemic flu. Once defined, the CDC stated that program, or plan, effectiveness is improved through the process of program evaluation. (Centers for Disease Control and Prevention, 1999) Program evaluation should be accomplished not only periodically, but in the course of routine administration of the program. (Centers for Disease Control and Prevention, 1999) Accomplishing this task for a "rare, but significant event" is challenging. (Herbold, John R., PhD., 2008) To address this challenge, the RAND Corporation (under contract to the CDC) developed the "Facilitated Look-Backs" approach that was tested and validated at the state level. (Aledort et al., 2006).^ Nevertheless, no comprehensive and generally applicable pandemic influenza program evaluation tool or model is readily found for use at the local public health department level. This project developed such a model based on the "Facilitated Look-Backs" approach developed by RAND Corporation. (Aledort et al., 2006) Modifications to the RAND model included stakeholder additions, inclusion of all six CDC program evaluation steps, and suggestions for incorporating pandemic flu response plans in seasonal flu management implementation. Feedback on the model was then obtained from three LPHD's—one rural, one suburban, and one urban. These recommendations were incorporated into the final model. Feedback from the sites also supported the assumption that this model promotes the effective and efficient evaluation of both pandemic flu and seasonal flu response by reducing redundant evaluations of pandemic flu plans, seasonal flu plans, and funding requirement accountability. Site feedback also demonstrated that the model is comprehensive and flexible, so it can be adapted and applied to different LPHD needs and settings. It also stimulates evaluation of the major issues associated with pandemic flu planning. ^ The next phase in evaluating this model should be to apply it in a program evaluation of one or more LPHD's seasonal flu response that incorporates pandemic flu response plans.^