A Bayesian Joinpoint regression model with an unknown number of break-points

Joinpoint regression is used to determine the number of segments needed to adequately explain the relationship between two variables. This methodology can be widely applied to real problems, but we focus on epidemiological data, the main goal being to uncover changes in the mortality time trend of a specific disease under study. Traditionally, Joinpoint regression problems have paid little or no attention to the quantification of uncertainty in the estimation of the number of change-points. In this context, we found a satisfactory way to handle the problem in the Bayesian methodology. Nevertheless, this novel approach involves significant difficulties (both theoretical and practical) since it implicitly entails a model selection (or testing) problem. In this study we face these challenges through (i) a novel reparameterization of the model, (ii) a conscientious definition of the prior distributions used and (iii) an encompassing approach which allows the use of MCMC simulation-based techniques to derive the results. The resulting methodology is flexible enough to make it possible to consider mortality counts (for epidemiological applications) as Poisson variables. The methodology is applied to the study of annual breast cancer mortality during the period 1980--2007 in Castell\'{o}n, a province in Spain.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS471 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

A Study of Joinpoint Models for Longitudinal Data

In many medical studies, data are collected simultaneously on multiple biomarkers from each individual. Levels of these biomarkers are measured periodically over certain time duration, giving rise to longitudinal trajectories. The subjects under study may also be subject to dropout due to several competing causes, the likelihood of which may be affected by the levels of these biomarkers. In this dissertation, we investigate flexible Bayesian modeling of such data, taking into account any available covariate information as well as possible censoring of the drop-out times. We propose joint models for multiple biomarkers with multiple causes of dropout. Our proposed models allow the trajectories to have multiple joinpoints, the locations of which are estimated from the data. We explore two ways of modeling longitudinal data incorporating the dropout information. Dirichlet process priors are used to make the models robust to misspecication. The Dirichlet process also leads to a natural clustering of subjects with similar trajectories, which can be of importance in efficiently estimating the joinpoints. Efficient Markov chain Monte Carlo algorithms are developed for fitting the proposed models. The performance of all the methods is investigated through simulation studies. One of the proposed models is seen to give rise to improved estimates of individual trajectories. Data from ACTG 398 study is used to illustrate the applicability of that model

The Epidemiology of Out of Hospital Cardiac Arrest in Western Australia: A Population-based linked Data Study

This thesis investigates the epidemiology of out-of-hospital cardiac arrest (OHCA), in Perth, Western Australia. The thesis examines long-term trends in OHCA incidence and survival, with subsequent detailed analyses of the equivalence of different survival metrics, the long-term survival of OHCA patients relative to the general population, and the role of initial cardiac arrest rhythm in long-term survival. In addition, the thesis includes a systematic review of the association between patient comorbidity and OHCA survival

Random Number Generators

The quasi-negative-binomial distribution was applied to queuing theory for determining the distribution of total number of customers served before the queue vanishes under certain assumptions. Some structural properties (probability generating function, convolution, mode and recurrence relation) for the moments of quasi-negative-binomial distribution are discussed. The distribution’s characterization and its relation with other distributions were investigated. A computer program was developed using R to obtain ML estimates and the distribution was fitted to some observed sets of data to test its goodness of fit

A comparison of spatio-temporal prediction methods of cancer incidence in the U.S

Cancer is the cause of one out of four deaths in the United States, and in 2009, researchers expected over 1.5 million new patients to be diagnosed with some form of cancer. People diagnosed with cancer, whether a common or rare type, need to undergo treatments, the amount and kind of which will depend on the severity of the cancer. So how do healthcare providers know how much funding is needed for treatment? What would better enable a pharmaceutical company to determine how much to allocate for research and development of drugs, the amount of each drug to manufacture, or the time spent to improve or reformulate those drugs? How do government planners determine which cancers need more attention than others? To answer these questions, it becomes extremely important to get accurate predictions of new cancer cases (also known as cancer incidences) that will occur in the future based on past data. Past data on cancer incidences in the U.S. is available only at certain cancer registries. These registries did not all come online at the same time, resulting in varying lengths of incidence data. Prediction into the future would require one to account for these varying lengths. Additionally, since these registries do not cover the entire United States, one needs to incorporate some spatial projection methods. In this thesis, we develop a Bayesian spatio-temporal method of predicting future cancer incidences based on past data. A conditional autoregressive prior is used for the spatial component and an autoregressive model is used for the temporal part. We use standard Bayesian Markov chain Monte Carlo techniques to develop predictions four years into the future for individual states. The method is illustrated using incidence data for some rare and common cancers

Change-point Problem and Regression: An Annotated Bibliography

The problems of identifying changes at unknown times and of estimating the location of changes in stochastic processes are referred to as the change-point problem or, in the Eastern literature, as disorder . The change-point problem, first introduced in the quality control context, has since developed into a fundamental problem in the areas of statistical control theory, stationarity of a stochastic process, estimation of the current position of a time series, testing and estimation of change in the patterns of a regression model, and most recently in the comparison and matching of DNA sequences in microarray data analysis. Numerous methodological approaches have been implemented in examining change-point models. Maximum-likelihood estimation, Bayesian estimation, isotonic regression, piecewise regression, quasi-likelihood and non-parametric regression are among the methods which have been applied to resolving challenges in change-point problems. Grid-searching approaches have also been used to examine the change-point problem. Statistical analysis of change-point problems depends on the method of data collection. If the data collection is ongoing until some random time, then the appropriate statistical procedure is called sequential. If, however, a large finite set of data is collected with the purpose of determining if at least one change-point occurred, then this may be referred to as non-sequential. Not surprisingly, both the former and the latter have a rich literature with much of the earlier work focusing on sequential methods inspired by applications in quality control for industrial processes. In the regression literature, the change-point model is also referred to as two- or multiple-phase regression, switching regression, segmented regression, two-stage least squares (Shaban, 1980), or broken-line regression. The area of the change-point problem has been the subject of intensive research in the past half-century. The subject has evolved considerably and found applications in many different areas. It seems rather impossible to summarize all of the research carried out over the past 50 years on the change-point problem. We have therefore confined ourselves to those articles on change-point problems which pertain to regression. The important branch of sequential procedures in change-point problems has been left out entirely. We refer the readers to the seminal review papers by Lai (1995, 2001). The so called structural change models, which occupy a considerable portion of the research in the area of change-point, particularly among econometricians, have not been fully considered. We refer the reader to Perron (2005) for an updated review in this area. Articles on change-point in time series are considered only if the methodologies presented in the paper pertain to regression analysis

Geographical and Temporal Distribution of Prostate Specific Antigen Testing Across Australia

Prostate cancer is the second most diagnosed cancer worldwide among men and the most diagnosed in Australia. Despite controversies surrounding its low specificity, the Prostate-specific antigen (PSA) test remains the most commonly used test for prostate cancer. In Australia, PSA “screening” test rates have consistently been high among men living in socio-economically advantaged and urban areas compared to disadvantaged and rural areas. Long term national level data on these trends has not been available. Additionally, there is limited information about the prevalence of PSA testing at the small geographical area level, limiting the ability to appropriately understand the role of PSA testing in the observed geographical patterns of prostate cancer incidence. The aim of this thesis was to investigate spatial and temporal patterns of PSA testing in Australia. We utilized the population-based Medicare Benefit Schedule dataset on PSA testing, developed complex methods to transform postcodes into smaller areas and used Bayesian models to identify key underlying patterns. We first computed a general PSA testing trend across Australia, as well as by area-specific regions, including socio-economic status, remoteness, and states and territories. Then, we investigated whether the national patterns were evident in smaller areas across Australia over time. Finally, to understand the impact of PSA testing on prostate cancer incidence, we examined the association between PSA testing and prostate cancer incidence by small areas. This population-based study identified substantial variation in the participation rate of PSA testing by small geographical areas across Australia and over time. However, there was a low association between PSA testing and prostate cancer incidence at the smaller area level. This information can help in reviewing and developing evidence-based strategies to reduce any identified disparities in prostate cancer indicators across Australia

Diminishing benefits of urban living for children and adolescents’ growth and development

Optimal growth and development in childhood and adolescence is crucial for lifelong health and well-being1–6. Here we used data from 2,325 population-based studies, with measurements of height and weight from 71 million participants, to report the height and body-mass index (BMI) of children and adolescents aged 5–19 years on the basis of rural and urban place of residence in 200 countries and territories from 1990 to 2020. In 1990, children and adolescents residing in cities were taller than their rural counterparts in all but a few high-income countries. By 2020, the urban height advantage became smaller in most countries, and in many high-income western countries it reversed into a small urban-based disadvantage. The exception was for boys in most countries in sub-Saharan Africa and in some countries in Oceania, south Asia and the region of central Asia, Middle East and north Africa. In these countries, successive cohorts of boys from rural places either did not gain height or possibly became shorter, and hence fell further behind their urban peers. The difference between the age-standardized mean BMI of children in urban and rural areas was &lt;1.1 kg m–2 in the vast majority of countries. Within this small range, BMI increased slightly more in cities than in rural areas, except in south Asia, sub-Saharan Africa and some countries in central and eastern Europe. Our results show that in much of the world, the growth and developmental advantages of living in cities have diminished in the twenty-first century, whereas in much of sub-Saharan Africa they have amplified.</p

Diminishing benefits of urban living for children and adolescents’ growth and development

Optimal growth and development in childhood and adolescence is crucial for lifelong health and well-being1–6. Here we used data from 2,325 population-based studies, with measurements of height and weight from 71 million participants, to report the height and body-mass index (BMI) of children and adolescents aged 5–19 years on the basis of rural and urban place of residence in 200 countries and territories from 1990 to 2020. In 1990, children and adolescents residing in cities were taller than their rural counterparts in all but a few high-income countries. By 2020, the urban height advantage became smaller in most countries, and in many high-income western countries it reversed into a small urban-based disadvantage. The exception was for boys in most countries in sub-Saharan Africa and in some countries in Oceania, south Asia and the region of central Asia, Middle East and north Africa. In these countries, successive cohorts of boys from rural places either did not gain height or possibly became shorter, and hence fell further behind their urban peers. The difference between the age-standardized mean BMI of children in urban and rural areas was &lt;1.1 kg m–2 in the vast majority of countries. Within this small range, BMI increased slightly more in cities than in rural areas, except in south Asia, sub-Saharan Africa and some countries in central and eastern Europe. Our results show that in much of the world, the growth and developmental advantages of living in cities have diminished in the twenty-first century, whereas in much of sub-Saharan Africa they have amplified