Joint Regression and Association Models for Repeated Categorical Responses

The focus of this study is on statistical analysis of categorical responses, where the response values are dependent of each other. The most typical example of this kind of dependence is when repeated responses have been obtained from the same study unit. For example, in Paper I, the response of interest is the pneumococcal nasopharengyal carriage (yes/no) on 329 children. For each child, the carriage is measured nine times during the first 18 months of life, and thus repeated respones on each child cannot be assumed independent of each other. In the case of the above example, the interest typically lies in the carriage prevalence, and whether different risk factors affect the prevalence. Regression analysis is the established method for studying the effects of risk factors. In order to make correct inferences from the regression model, the associations between repeated responses need to be taken into account. The analysis of repeated categorical responses typically focus on regression modelling. However, further insights can also be gained by investigating the structure of the association. The central theme in this study is on the development of joint regression and association models. The analysis of repeated, or otherwise clustered, categorical responses is computationally difficult. Likelihood-based inference is often feasible only when the number of repeated responses for each study unit is small. In Paper IV, an algorithm is presented, which substantially facilitates maximum likelihood fitting, especially when the number of repeated responses increase. In addition, a notable result arising from this work is the freely available software for likelihood-based estimation of clustered categorical responses.

Short and long term mortality rates after a lower limb amputation

Objective To determine mortality rates after a first lower limb amputation and explore the rates for different subpopulations. Methods Retrospective cohort study of all people who underwent a first amputation at or proximal to transtibial level, in an area of 1.7 million people. Analysis with Kaplan-Meier curves and Log Rank tests for univariate associations of psycho-social and health variables. Logistic regression for odds of death at 30-days, 1-year and 5-years. Results 299 people were included. Median time to death was 20.3 months (95%CI: 13.1; 27.5). 30-day mortality = 22%; odds of death 2.3 times higher in people with history of cerebrovascular disease (95%CI: 1.2; 4.7, P = 0.016). 1 year mortality = 44%; odds of death 3.5 times higher for people with renal disease (95%CI: 1.8; 7.0, P < 0.001). 5-years mortality = 77%; odds of death 5.4 times higher for people with renal disease (95%CI: 1.8; 16.0,P = 0.003). Variation in mortality rates was most apparent in different age groups; people 75–84 years having better short term outcomes than those younger and older. Conclusions Mortality rates demonstrated the frailty of this population, with almost one quarter of people dying within 30-days, and almost half at 1 year. People with cerebrovascular had higher odds of death at 30 days, and those with renal disease and 1 and 5 years, respectively.

Rank-Augmented LU-Algorithm for Computing Generalized Matrix Inverses

A rank-augmnented LU-algorithm is suggested for computing a generalized inverse of a matrix. Initially suitable diagonal corrections are introduced in (the symmetrized form of) the given matrix to facilitate decomposition; a backward-correction scheme then yields a desired generalized inverse.

Deformation and stability regression models for soil nail walls

Lateral displacement and global stability are the two main stability criteria for soil nail walls. Conventional design methods do not adequately address the deformation behaviour of soil nail walls, owing to the complexity involved in handling a large number of influencing factors. Consequently, limited methods of deformation estimates based on empirical relationships and in situ performance monitoring are available in the literature. It is therefore desirable that numerical techniques and statistical methods are used in order to gain a better insight into the deformation behaviour of soil nail walls. In the present study numerical experiments are conducted using a 2 4 factorial design method. Based on analysis of the maximum lateral deformation and factor-of-safety observations from the numerical experiments, regression models for maximum lateral deformation and factor-of-safety prediction are developed and checked for adequacy. Selection of suitable design factors for the 2 4 factorial design of numerical experiments enabled the use of the proposed regression models over a practical range of soil nail wall heights and in situ soil variability. It is evident from the model adequacy analyses and illustrative example that the proposed regression models provided a reasonably good estimate of the lateral deformation and global factor of safety of the soil nail walls.

Land use regression model (LUR) for ultrafine particles in Brisbane

Traffic-related air pollution has been associated with a wide range of adverse health effects. One component of traffic emissions that has been receiving increasing attention is ultrafine particles(UFP, < 100 nm), which are of concern to human health due to their small diameters. Vehicles are the dominant source of UFP in urban environments. Small-scale variation in ultrafine particle number concentration (PNC) can be attributed to local changes in land use and road abundance. UFPs are also formed as a result of particle formation events. Modelling the spatial patterns in PNC is integral to understanding human UFP exposure and also provides insight into particle formation mechanisms that contribute to air pollution in urban environments. Land-use regression (LUR) is a technique that can use to improve the prediction of air pollution.

Prognostic tumour markers in pancreatic cancer

Background. Pancreatic cancer is one of the major causes of cancer death in the industrialised world. The overall survival of patients with ductal pancreatic adenocarcinoma is poor: 5-year survival is only 0.2 to 4%. Tumour stage and histological grade are used as prognostic markers in pancreatic cancer. However, there are differences in survival within stages and histological grades. New, additional and more accurate prognostic tools are needed. Aims. The purpose of this study was to investigate whether the tissue expression of potential and promising tumour markers p27, tenascin C, syndecan-1, COX-2 and MMP-2 are associated with clinicopathological parameters in pancreatic cancer. The expression of p27, tenascin C and syndecan-1 was also evaluated in acute and chronic pancreatitis. The main purpose in the study was to find new prognostic markers for pancreatic adenocarcinoma. Patients. The study included 147 patients with histologically verified pancreatic adenocarcinoma treated at Helsinki University Central Hospital from 1974 to1998. Methods. The expression of tumour marker antigens was demonstrated by immunohistochemistry using monoclonal antibodies against p27, syndecan-1, tenascin C, COX-2 and MMP-2. The results were compared with clinicopathological variables, i.e. age, sex, TNM stage and histological grade. Survival analyses were performed with univariate Kaplan-Meier life-tables and the log-rank test, while multivariate analyses were performed using Cox regression. Results. Pancreatic adenocarcinomas expressed p27, syndecan-1, tenascin C, COX-2 and MMP-2 in 30, 94, 92, 36 and 50% of the samples, respectively. Loss of p27 expression was associated with poor prognosis in stage I and II pancreatic cancer. Stromal syndecan-1 expression was an independent prognostic marker in pancreatic cancer, whereas epithelial syndecan-1 expression predicted better prognosis only in stage I and II disease. Tenascin C expression did not correlate with survival but was associated with differentiation. COX-2 expression was associated with poor outcome and was an independent prognostic factor. Epithelial MMP-2 correlated with poor prognosis in pancreatic cancer. Conclusion: p27 and epithelial syndecan-1 are prognostic markers in early (stage I and II) pancreatic cancer. Stromal syndecan-1, COX-2 and epithelial MMP-2 are prognostic factors in ductal pancreatic adenocarcinoma.

A fast dual algorithm for kernel logistic regression

This paper gives a new iterative algorithm for kernel logistic regression. It is based on the solution of a dual problem using ideas similar to those of the Sequential Minimal Optimization algorithm for Support Vector Machines. Asymptotic convergence of the algorithm is proved. Computational experiments show that the algorithm is robust and fast. The algorithmic ideas can also be used to give a fast dual algorithm for solving the optimization problem arising in the inner loop of Gaussian Process classifiers.

Generalised regression estimation for domain class frequencies

This study examines the properties of Generalised Regression (GREG) estimators for domain class frequencies and proportions. The family of GREG estimators forms the class of design-based model-assisted estimators. All GREG estimators utilise auxiliary information via modelling. The classic GREG estimator with a linear fixed effects assisting model (GREG-lin) is one example. But when estimating class frequencies, the study variable is binary or polytomous. Therefore logistic-type assisting models (e.g. logistic or probit model) should be preferred over the linear one. However, other GREG estimators than GREG-lin are rarely used, and knowledge about their properties is limited. This study examines the properties of L-GREG estimators, which are GREG estimators with fixed-effects logistic-type models. Three research questions are addressed. First, I study whether and when L-GREG estimators are more accurate than GREG-lin. Theoretical results and Monte Carlo experiments which cover both equal and unequal probability sampling designs and a wide variety of model formulations show that in standard situations, the difference between L-GREG and GREG-lin is small. But in the case of a strong assisting model, two interesting situations arise: if the domain sample size is reasonably large, L-GREG is more accurate than GREG-lin, and if the domain sample size is very small, estimation of assisting model parameters may be inaccurate, resulting in bias for L-GREG. Second, I study variance estimation for the L-GREG estimators. The standard variance estimator (S) for all GREG estimators resembles the Sen-Yates-Grundy variance estimator, but it is a double sum of prediction errors, not of the observed values of the study variable. Monte Carlo experiments show that S underestimates the variance of L-GREG especially if the domain sample size is minor, or if the assisting model is strong. Third, since the standard variance estimator S often fails for the L-GREG estimators, I propose a new augmented variance estimator (A). The difference between S and the new estimator A is that the latter takes into account the difference between the sample fit model and the census fit model. In Monte Carlo experiments, the new estimator A outperformed the standard estimator S in terms of bias, root mean square error and coverage rate. Thus the new estimator provides a good alternative to the standard estimator.

Bootstrap and Fast Double Bootstrap Tests of Cointegration Rank with Financial Time Series

The likelihood ratio test of cointegration rank is the most widely used test for cointegration. Many studies have shown that its finite sample distribution is not well approximated by the limiting distribution. The article introduces and evaluates by Monte Carlo simulation experiments bootstrap and fast double bootstrap (FDB) algorithms for the likelihood ratio test. It finds that the performance of the bootstrap test is very good. The more sophisticated FDB produces a further improvement in cases where the performance of the asymptotic test is very unsatisfactory and the ordinary bootstrap does not work as well as it might. Furthermore, the Monte Carlo simulations provide a number of guidelines on when the bootstrap and FDB tests can be expected to work well. Finally, the tests are applied to US interest rates and international stock prices series. It is found that the asymptotic test tends to overestimate the cointegration rank, while the bootstrap and FDB tests choose the correct cointegration rank.

Minimum enclosing spheres formulations for support vector ordinal regression

We present two new support vector approaches for ordinal regression. These approaches find the concentric spheres with minimum volume that contain most of the training samples. Both approaches guarantee that the radii of the spheres are properly ordered at the optimal solution. The size of the optimization problem is linear in the number of training samples. The popular SMO algorithm is adapted to solve the resulting optimization problem. Numerical experiments on some real-world data sets verify the usefulness of our approaches for data mining.

The Power of Bootstrap Tests of Cointegration Rank with Financial Time Series

Bootstrap likelihood ratio tests of cointegration rank are commonly used because they tend to have rejection probabilities that are closer to the nominal level than the rejection probabilities of the correspond- ing asymptotic tests. The e¤ect of bootstrapping the test on its power is largely unknown. We show that a new computationally inexpensive procedure can be applied to the estimation of the power function of the bootstrap test of cointegration rank. The bootstrap test is found to have a power function close to that of the level-adjusted asymp- totic test. The bootstrap test estimates the level-adjusted power of the asymptotic test highly accurately. The bootstrap test may have low power to reject the null hypothesis of cointegration rank zero, or underestimate the cointegration rank. An empirical application to Euribor interest rates is provided as an illustration of the findings.

Construction and use of linear regression models for processor performance analysis

Processor architects have a challenging task of evaluating a large design space consisting of several interacting parameters and optimizations. In order to assist architects in making crucial design decisions, we build linear regression models that relate Processor performance to micro-architecture parameters, using simulation based experiments. We obtain good approximate models using an iterative process in which Akaike's information criteria is used to extract a good linear model from a small set of simulations, and limited further simulation is guided by the model using D-optimal experimental designs. The iterative process is repeated until desired error bounds are achieved. We used this procedure to establish the relationship of the CPI performance response to 26 key micro-architectural parameters using a detailed cycle-by-cycle superscalar processor simulator The resulting models provide a significance ordering on all micro-architectural parameters and their interactions, and explain the performance variations of micro-architectural techniques.

Tests for Cointegration Rank and the Initial Condition

Many economic events involve initial observations that substantially deviate from long-run steady state. Initial conditions of this type have been found to impact diversely on the power of univariate unit root tests, whereas the impact on multivariate tests is largely unknown. This paper investigates the impact of the initial condition on tests for cointegration rank. We compare the local power of the widely used likelihood ratio (LR) test with the local power of a test based on the eigenvalues of the companion matrix. We find that the power of the LR test is increasing in the magnitude of the initial condition, whereas the power of the other test is decreasing. The behaviour of the tests is investigated in an application to price convergence.