A joint estimation approach for monotonic regression functions in general dimensions

Regression analysis under the assumption of monotonicity is a well-studied statistical problem and has been used in a wide range of applications. However, there remains a lack of a broadly applicable methodology that permits information borrowing, for efficiency gains, when jointly estimating multiple monotonic regression functions. We introduce such a methodology by extending the isotonic regression problem presented in the article "The isotonic regression problem and its dual" (Barlow and Brunk, 1972). The presented approach can be applied to both fixed and random designs and any number of explanatory variables (regressors). Our framework penalizes pairwise differences in the values (levels) of the monotonic function estimates, with the weight of penalty being determined based on a statistical test, which results in information being shared across data sets if similarities in the regression functions exist. Function estimates are subsequently derived using an iterative optimization routine that uses existing solution algorithms for the isotonic regression problem. Simulation studies for normally and binomially distributed response data illustrate that function estimates are consistently improved if similarities between functions exist, and are not oversmoothed otherwise. We further apply our methodology to analyse two public health data sets: neonatal mortality data for Porto Alegre, Brazil, and stroke patient data for North West England

Idiopathic Focal Eosinophilic Enteritis (IFEE), an emerging cause of abdominal pain in horses:the effect of age, time and geographical location on risk

Background: Idiopathic focal eosinophilic enteritis (IFEE) is an emerging cause of abdominal pain (colic) in horses that frequently requires surgical intervention to prevent death. IFEE lesions were first identified in the late 1990’s and the incidence of this form of colic has continued to increase in certain equine hospital populations. The epidemiology of IFEE is poorly understood and it is difficult to diagnose pre-operatively. In addition, the aetiology of this condition and methods of possible prevention are also currently unknown. Based upon a UK equine hospital population the aims of this study were to investigate temporal and spatial heterogeneity in IFEE risk and to ascertain the effect of horse age on the risk process. Methodology/Principal Findings: A retrospective, nested case-control study was undertaken. Data were extracted and pertained to 85 observed IFEE cases and 848 randomly selected controls (non-cases) admitted to a UK equine hospital for exploratory laparotomy to investigate the cause of colic over a 10-year period. Spatial clustering was investigated via K-function analysis, and generalised additive models (GAM's) were used to quantify temporal and age effects on the odds of IFEE and to provide mapped estimates of ‘residual’ risk over the study region. The relative risk of IFEE increased over the study period (p=0.001) and a seasonal pattern was evident (p<0.01) with greatest risk of IFEE being identified between the months of July-November. Age was found to be a contributory factor (p<0.001) with IFEE risk decreasing with increasing age and younger (0 - 5 years old) horses being at greatest risk. Spatial clustering of cases was significantly different to that of controls (p<0.001) over a wide range of spatial scales (from 4km to at least 50km). The mapped surface estimate exhibited significantly atypical sub-regions (p<0.001) with increased IFEE risk in horses residing in the north-west of the study region. Conclusions/Significance: IFEE exhibits both spatial and temporal clustering and is more likely to occur in younger horses. This evidence-based information can be used by clinicians to identify horses at increased risk of IFEE; to provide clues as to the aetiology of the disease and to justify further research into environmental factors that may account for the observed spatial and temporal clustering

Metacomprehension Accuracy of Health-Related Information

As part of the production of written information, patient reader panels provide judgments of their understanding to evaluate the comprehensibility of draft documents. Previous research has suggested i) that there is a limited association, on average, between judgments of understanding and the comprehension demonstrated in tests of understanding and ii) that there is considerable variability between individuals in the direction and magnitude of this association. Unfortunately, while previous research implies, critically, that reader judgments of comprehensibility have limited utility, this research itself is characterized by important limitations that prevent firm conclusions. This thesis comprises three experimental studies. The study design, method of measurement, and the approach to analysis were motivated by a critical review of previous research. The specification of participant, text and question sample sizes was determined by a novel method of prospective study design analysis, evaluating the accuracy and precision in effect estimation. The robustness of effect estimates are established through the series of empirical replications and in analytical sensitivity checks. Across the studies, a weakly positive association between perceived and assessed comprehension was found across individuals, on average. Differences in reading ability and background knowledge did not reliably influence metacomprehension accuracy. Further, metacomprehension judgements were similarly predictive of performance on comprehension questions that targeted more versus less semantically central information. In contrast, metacomprehension judgements targeting specific ideas within texts were more predictive of understanding. The findings of this thesis indicate that metacomprehension judgements are not a gold-standard method of evaluation: judgements show some predictive validity of comprehension outcomes, yet provide little insight into whether critical elements of the documents are sufficiently understood. Overall, whilst situated within an applied context, the present research contributes more widely to the metacomprehension literature, making clear the need for a shift from traditional analytical approaches, in addition to greater theoretical precision

Bayesian spatial monotonic multiple regression

We consider monotonic, multiple regression for contiguous regions. The regression functions vary regionally and may exhibit spatial structure. We develop Bayesian nonparametric methodology that permits estimation of both continuous and discontinuous functional shapes using marked point process and reversible jump Markov chain Monte Carlo techniques. Spatial dependence is incorporated by a flexible prior distribution which is tuned using cross-validation and Bayesian optimization. We derive the mean and variance of the prior induced by the marked point process approach. Asymptotic results show consistency of the estimated functions. Posterior realizations enable variable selection, the detection of discontinuities and prediction. In simulations and in an application to a Norwegian insurance data set, our methodology shows better performance than existing approaches

A study into drug-trying behaviour among young people in England : categorical analysis models in the Presence of missing data

This research reviewed the "Smoking, Drinking and Drug Use among Young People in England" 2010 survey (the Year 2010 Survey) study in terms of its data collection, processing and analysis. The research aim was to gain increased understanding of young people’s drug-trying behaviour in England through appropriate handling of missing data, as well as, to build upon the previous work done, developing and applying statistical methodologies for analysis of multivariate categorical data collected by the Year 2010 Survey study. The main work done in this research included: (1) modifying the original data set to arrive the useful working data set; (2) conducting exploratory data analysis with the working data set to identify direction for further empirical investigation; (3) properly handling the missing data problem in the working data set and (4) developing and applying advanced statistical methodologies to further analyse the working data set. Apart from supporting the main findings of the Year 2010 Survey study that smoking, drinking and some drug-related socio-demographic covariates were positively associated with the students’ drug-trying behaviour, additional significant results found by the univariate logistic regression models, log-linear analysis models, two-parameter item response theory models and latent class analysis models reported that (1) the 15 drugs were highly and positively associated with each other and each drug exerted different extent of influences on the students’ drug-trying behaviour and (2) generally, students’ drug-trying behaviour could be further explained by numerous smoking, drinking and drug related socio-demographic factors at different extent. These additional findings contributed to a deeper understanding of the drug use problem, added evidence to the drug related research literature and provided helpful guidance on formulating policies to combat against drug use problem in England. Another contribution of this research was the development of a new methodology for backward elimination of latent class analysis models which provided a more thorough evaluation of the optimal number of latent class and covariate elimination from saturated model

Chromosomal microarray testing in adults with intellectual disability presenting with comorbid psychiatric disorders.

Chromosomal copy-number variations (CNVs) are a class of genetic variants highly implicated in the aetiology of neurodevelopmental disorders, including intellectual disabilities (ID), schizophrenia and autism spectrum disorders (ASD). Yet the majority of adults with idiopathic ID presenting to psychiatric services have not been tested for CNVs. We undertook genome-wide chromosomal microarray analysis (CMA) of 202 adults with idiopathic ID recruited from community and in-patient ID psychiatry services across England. CNV pathogenicity was assessed using standard clinical diagnostic methods and participants underwent comprehensive medical and psychiatric phenotyping. We found an 11% yield of likely pathogenic CNVs (22/202). CNVs at recurrent loci, including the 15q11-q13 and 16p11.2-p13.11 regions were most frequently observed. We observed an increased frequency of 16p11.2 duplications compared with those reported in single-disorder cohorts. CNVs were also identified in genes known to effect neurodevelopment, namely NRXN1 and GRIN2B. Furthermore deletions at 2q13, 12q21.2-21.31 and 19q13.32, and duplications at 4p16.3, 13q32.3-33.3 and Xq24-25 were observed. Routine CMA in ID psychiatry could uncover ~11% new genetic diagnoses with potential implications for patient management. We advocate greater consideration of CMA in the assessment of adults with idiopathic ID presenting to psychiatry services

Bayesian Partitioning for Modeling and Mapping Spatial Case-Control Data

Methods for modeling and mapping spatial variation in disease risk continue to motivate much research. In particular, spatial analyses provide a useful tool for exploring geographical heterogeneity in health outcomes, and consequently can yield clues as to disease aetiology, direct public health management and generate research hypotheses. This article presents a Bayesian partitioning approach for the analysis of individual level geo-referenced health data. The model makes few assumptions about the underlying form of the risk surface, is data adaptive and allows for the inclusion of known determinants of disease. The methodology is used to model spatial variation in neonatal mortality in Porto Alegre, Brazil