Nigeria is one of the countries most affected by the HIV/AIDS pandemic, third only to India and South Africa. With about 10% of the global HIV/AIDS cases estimated to be in the country, the public health and socio-economic implications are enormous. This thesis has two broad aims: the first is to develop statistical models which adequately describe the spatial distribution of the Nigerian HIV/AIDS epidemic and its associated ecological risk factors; the second, to develop models that could reconstruct the HIV incidence curve, obtain an estimate of the hidden HIV/AIDS population and a short term projection for AIDS incidence and a measure of precision of the estimates. To achieve these objectives, we first examined data from various sources and selected three sets of data based on national coverage and minimal reporting delay. The data sets are the outcome of the National HIV/AIDS Sentinel Surveillance Survey conducted in 1999, 2001, 2003 and 2005 by the Federal Ministry of Health; the outcome of the survey of 1057 health and laboratory facilities conducted by the Nigerian Institute of Medical Research in 2000; and case by case HIV screening data collected from an HIV/AIDS centre of excellence. A thorough review of methods used by WHO/UNAIDS to produce estimates of the Nigerian HIV/AIDS scenario was carried out. The Estimation and Projection Package (EPP) currently being used for modelling the epidemic partitions the population into at-risk, not-at-risk and infected sub-populations. It also requires some parameter input representing the force of infection and behaviour or high risk adjustment parameter. It may be difficult to precisely ascertain the size of these population groups and parameters in countries as large and diverse as Nigeria. Also, the accuracy of vital rates used in the EPP and Spectrum program is doubtful. Literature on ordinary back-calculation, nonparametric back-calculation, and modified back-calculation methods was reviewed in detail. Also, an indepth review of disease mapping techniques including multilevel models and geostatistical methods was conducted. The existence of spatial clusters was investigated using cluster analysis and some measure of spatial autocorrelation (Moran I and Geary c coefficients, semivariogram and kriging) applied to the National HIV/AIDS Surveillance data. Results revealed the existence of spatial clusters with significant positive spatial autocorrelation coefficients that tended to get stronger as the epidemic developed through time. GAM and local regression fit on the data revealed spatial trends on the north-south and east - west axis. Analysis of hierarchical, spatial and ecological factor effects on the geographical variation of HIV prevalence using variance component and spatial multilevel models was performed using restricted maximum likelihood implemented in R and empirical and full Bayesian methods in WinBUGS. Results confirmed significant spatial effects and some ecological factors were significant in explaining the variation. Also, variation due to various levels of aggregation was prominent. Estimates of cumulative HIV infection in Nigeria were obtained from both parametric and nonparametric back-calculation methods. Step and spline functions were assumed for the HIV infection curve in the parametric case. Parameter estimates obtained using 3-step and 4-step models were similar but the standard errors of these parameters were higher in the 4-step model. Estimates obtained using linear, quadratic, cubic and natural splines differed and also depended on the number and positions of the knots. Cumulative HIV infection estimates obtained using the step function models were comparable with those obtained using nonparametric back-calculation methods. Estimates from nonparametric back-calculation were obtained using the EMS algorithm. The modified nonparametric back-calculation method makes use of HIV data instead of the AIDS incidence data that are used in parametric and ordinary nonparametric back-calculation methods. In this approach, the hazard of undergoing HIV test is different for routine and symptom-related tests. The constant hazard of routine testing and the proportionality coefficient of symptom-related tests were estimated from the data and incorporated into the HIV induction distribution function. Estimates of HIV prevalence differ widely (about three times higher) from those obtained using parametric and ordinary nonparametric back-calculation methods. Nonparametric bootstrap procedure was used to obtain point-wise confidence interval and the uncertainty in estimating or predicting precisely the most recent incidence of AIDS or HIV infection was noticeable in the models but greater when AIDS data was used in the back-projection model. Analysis of case by case HIV screening data indicate that of 33349 patients who attended the HIV laboratory of a centre of excellence for the treatment of HIV/AIDS between October 2000 and August 2006, 7646 (23%) were HIV positive with females constituting about 61% of the positive cases. The bulk of infection was found in patients aged 15-49 years, about 86 percent of infected females and 78 percent of males were in this age group. Attendance at the laboratory and the proportion of HIV positive tests witnessed a remarkable increase when screening became free of charge. Logistic regression analysis indicated a 3-way interaction between time period, age and sex. Removing the effect of time by stratifying by time period left 2-way interactions between age and sex. A Correction factor for underreporting was ascertained by studying attendance at the laboratory facility over two time periods defined by the cost of HIV screening. Estimates of HIV prevalence obtained from corrected data using the modified nonparametric back-calculation are comparable with UN estimates obtained by a different method. The Nigerian HIV/AIDS pandemic is made up of multiple epidemics spatially located in different parts of the country with most of them having the potential of being sustained into the future given information on some risk factors. It is hoped that the findings of this research will be a ready tool in the hands of policy makers in the formulation of policy and design of programs to combat the epidemic in the country. Access to data on HIV/AIDS are highly restricted in the country and this hampers more in-depth modelling of the epidemic. Subject to data availability, we recommend that further work be done on the construction of stratification models based on sex, age and the geopolitical zones in order to estimate the infection intensity in each of the population groups. Uncertainties surrounding assumptions of infection intensity and incubation distribution can be minimized using Bayesian methods in back-projection.

In this study, the most prominent goodness-of-fit tests for censored samples are reviewed. Power properties of goodness-of-fit statistics of the null hypothesis that a sample which is censored from right, left and both right and left which comes from uniform, normal and exponential distributions are investigated. Then, by a similar argument extreme value, student t with 6 degrees of freedom and generalized logistic distributions are discussed in detail through a comprehensive simulation study. A variety of real life applications are given. Suitable test statistics for testing the above distributions for censored samples are also suggested in the conclusion.

The total fertility rate in Bangladesh declined from 6.3 children per women in 1975 to 3.3 in 1997-1999. This decline of 48 per cent over a 25-year period occurred without a substantial improvement in socio-economic status, health conditions and other factors thought to be essential for fertility decline. In this thesis it is postulated that current fertility behaviour is a manifestation of ideational change, which has occurred through mass media and interpersonal communication channels. To investigate the influence of communication on fertility behaviour and to control for demographic and socioeconomic and cultural variables, 724 married women of reptoductive age were interviewed from six rural villages of the six administrative divisions of Bangladesh. Another village was surveyed to compare the influence of religion. Data were collected in a full network basis in that one currently married woman with at least one child from each household of the entire village was interviewed. Sociometric data along with socio-economic-cultural and family planning practice data were collected using a structured questionnaire. The data have been analysed using statistical methods to construct models of factors, which influence the total number of children a woman has and those that determine the likelihood that a woman practices family planning. The main influencing variables to explain the total number of children were found to be wife's age, age at first child bom, number of family members, demand for male children, demand for female children, death of male children, place of giving birth, housing score, religion, equipment score, land property, FWA and information score. Whereas the influencing variables to explain the family planning practice were demand for male children, death of male children and variables connected with communication such as degree of interpersonal communication, mass media exposure, husband, Family Welfare Assistants (FWAs) and frequency of discussion with FWAs. Communication variables, especially interpersonal communication, were found to be most important in explaining family planning practice. More particularly, the dominant source of general information is relatives and friends. FWAs followed by friends and relatives are the main source of family planning information that along with husband influence fertility decisions. Hence, there was a need to ftu-ther understand the web of interactions among individuals, peer groups and opinion leaders using social network analysis. The web of communication links in which an individual exists and takes fertility decision was then modeled with the collected sociometric data. To do this, three matrices were constructed to reflect any communication link, the strength of these links and approval of family planning. Various centrality measures (in-degree, out-degree, betweenness and power), clique patterns and actors positions in the network were produced and analysed using Ucinet-6. This revealed that the actors who were not strongly connected or exist in the periphery of this web tended not to practice family planning. Also it was found that actors who overlap more than one clique are more likely to practice family planning. Variables created from the centrality measures were then added to the regression models for the total number of children and the use of family planning. In both the cases sociometric variables were found significant which ftirther enhanced the explanation of fertility behaviour of the women in rural Bangladesh. Using Structural Equation Models the direct and indirect effects of these variables were determined. Demographic, socio-economic-cultural variables were more directly associated in explaining total number of children while communication variables were directly associated in explaining family planning use, and family planning practice has a direct influence on the number of children born. Thus, as communication directly influences family planning practice it has an indirect influence on the Total Fertility Rate. From this work it is recommended that the service that was provided by the FWAs be reestablished and strengthened, husbands should be targeted in family planning motivation programmes and male contraceptive methods should be promoted. Also more motivational programmes should be incorporated in family planning programmes to create a positive image of female children and the extent of the social interaction among village women should be increased.

Environmental statistics are known to be important factors shaping our perceptual system. The visual and auditory systems have evolved to be effcient for processing natural images or speech. The com- mon characteristics between natural images and speech are that they are both highly structured, therefore having much redundancy. Our perceptual system may use redundancy reduction and sparse coding strategies to deal with complex stimuli every day. Both redundancy reduction and sparse coding theory emphasise the importance of high order statistics signals. This thesis includes psycho-acoustical experiments designed to inves- tigate how higher order statistics affect our speech perception. Sparse- ness can be defined by the fourth order statistics, kurtosis, and it is hypothesised that greater kurtosis should be reflected by better speech recognition performance in noise. Based on a corpus of speech mate- rial, kurtosis was found to be significantly correlated to the glimps- ing area of noisy speech, an established measure that predicts speech recognition. Kurtosis was also found to be a good predictor of speech recognition and an algorithm based on increasing kurtosis was also found to improve speech recognition score in noise. The listening experiment for the first time showed that higher order statistics are important for speech perception in noise. It is known the hearing impaired listeners have diffculty understand- ing speech in noise. Increasing kurtosis of noisy speech may be par- ticularly helpful for them to achieve better performance. Currently, neither hearing aids nor cochlear implants help hearing impaired users greatly in adverse listening enviroments, partly due to having a re- duced dynamic range of hearing. Thus there is an information bot- tleneck, whereby these devices must transform acoustical sounds with a large dynamic range into the smaller range of hearing impaired lis- teners. The limited dynamic range problem can be thought of as a communication channel with limited capacity. Information could be more effciently encoded for such a communication channel if redun- dant information could be reduced. For cochlear implant users, un- wanted channel interaction could also contribute lower speech recog- nition scores in noisy conditions. This thesis proposes a solution to these problems for cochlear im- plant users by reducing signal redundancy and making signals more sparse. A novel speech processing algorithm, SPARSE, was devel- oped and implemented. This algorithm aims to reduce redundant information and transform signals input into more sparse stimulation sequences. It is hypothesised that sparse firing patterns of neurons will be achieved, which should be more biological efficient based on sparse coding theory. Listening experiments were conducted with ten cochlear implant users who listened to speech signals in modulated and speech babble noises, either using the conventional coding strat- egy or the new SPARSE algorithm. Results showed that the SPARSE algorithm can help them to improve speech understanding in noise, particularly for those with low baseline performance. It is concluded that signal processing algorithms for cochlear implants, and possibly also for hearing aids, that increase signal sparseness may deliver ben- efits for speech recognition in noise. A patent based on the algorithm has been applied for.

This thesis aims to explore the measurement of and the correlation between risky sexual behaviour and chlamydia and gonorrhoea infection in the UK in three chapters. The first of these explores methods of calculating rates of Chlamydia and gonorrhoea infection at UK genitourinary medicine (GUM) clinics. Data from KC60 returns from clinics in the Northwest, Southwest and East Midlands of England are used to provide a numerator for the rates and three methods are tested to derive the denominator: Thiessen polygons, 15 mile boundaries, and 30 minute drive times. The study finds that the rates calculated are relatively insensitive to the method chosen and thus the simplest approach, the Thiessen polygons, is recommended. The analysis also highlights substantial regional differences in GUM service accessibility. The second chapter uses latent class analysis to derive a measure of risky sexual behaviour with respect to chlamydia and gonorrhoea infection. Data from the National Survey of Sexual Attitudes and Lifestyles II, a nationally representative survey of sexual behaviour in Britain, has been analysed in order to identify patterns of behaviours associated with increased disease risk A 3-class solution is obtained, with individuals classified on the basis of the number of partners they have had in the last 12 months. iii The third chapter examines the relationship between the rates of chlamydia and gonorrhoea infection and the measure of risky sexual behaviour. Small area estimates of risky behaviour are obtained for all wards in England using synthetic regression methods. These are then aggregated in line with the Thiessen polygons in order to explore the correlation with the rates of chlamydia and gonorrhoea infection. There is a positive correlation for both infections, but far stronger for gonorrhoea than chlamydia (r=0.70 and r=0.41 respectively), suggesting that although risky behaviour may explain some of the observed variation, further research is need to explore other possible explanations.

This study investigates whether there is an association between economic activity in women and union dissolution in the UK. This study looks at both individual-level and aggregate-level trends by posing a number of research questions. Using a series of Cox Proportional Hazard and Piecewise Constant models to analyse individual-level data from the British Household Panel Survey and Understanding Society surveys, this study has found only weak and inconsistent evidence of an association between women’s economic activity and union dissolution. Examining these data for separate union cohorts, this study has found some initial evidence that the relationship between economic activity and union dissolution may be changing over time. The final stage of the analysis in this study looked at aggregate trends in economic activity and divorce and found some evidence of an association at the aggregate level, although due to data restrictions this was not conclusive. Following a discussion of the changing status of women and the changing legal, social and cultural context within which unions are formed and dissolved, this study concluded more evidence is found for an association at the aggregate level, leading to the hypothesis that economic activity is contributing to wider social changes and that these social changes are influencing the risk of union dissolution.

Data sets commonly used in the social sciences are often obtained by sample surveys with complex designs. These designs usually incorporate a multistage selection from a population with a natural hierarchical structure. In addition, these surveys can also be carried out in a repeated manner including a rotating panel design, which is a source of planned non-response. Unplanned non-response is also present in panel data in the form of panel attrition and intermittent nonresponse. Methods are developed to handle this type of data complexity. These methods follow the Multilevel Model framework which is reviewed. Longitudinal growth curve models accounting for the complex data hierarchy are tted. Recognizing the need to account for the complex correlation structure present in the data, multivariate multilevel models are then adopted. Alternative modied correlation structures accounting for the rotating sample design are proposed. Multivariate multilevel models are tted utilizing these alternative correlation structures. In addition, models estimated using robust methods are compared with those estimated using standard methods. A method for calculating a set of longitudinal sample weights that accounts for attrition is proposed. Models utilising the conditional sample weights and longitudinal weights are tted using the Probability-weighted Iterative Generalized Least Squares (PWIGLS) estimation method. Furthermore, an extension to PWIGLS for multivariate multilevel models is developed. Models tted through dierent estimation methods are compared and the best approaches are suggested. Data from the Brazilian labour force survey, Pesquisa Mensal de Emprego (PME) are used. The PME has a complex sampling design that includes a multistage selection of the sample units and a rotating panel design characterised as 4-8-4. The methods developed are used to investigate the labour income dynamics of employed heads of households in the PME survey.

The proportion of children entering primary school at the stipulated age in 2010 in Sub-Saharan Africa was 57%. For the same year, the net attendance ratios for primary and lower secondary education were 76% and 47% respectively. These figures are correlated in that delayed school enrolment increases the risk of dropout which in turn shortens the school life expectancy for children. These observations are the motivation behind this research. By writing this thesis, three substantive research questions have been explored: (1) what is Sierra Leone’s progress towards achieving universal basic education (2) what are the determinants of school attendance at basic education in West Africa and (3) does living in a community with more educated mothers enhance children’s school attendance at basic education. Three countries have been used: Sierra Leone, Liberia, and Ghana. Sierra Leone and Liberia have been used to reflect poor and post-conflict states with transitional and premature education systems respectively. Ghana is representative of middle income and politically stable countries with more advanced education systems in the region. The most recent Demographic and Health Survey for the three countries are used for analysis. Four empirical chapters are presented. The first chapter addresses research question 1. It applies simple statistical analyses to United Nations indicators for evaluating progress towards universal education. The second and third chapters answer the second research question and the final chapter answers the third research question. These three chapters employ multilevel statistical techniques to model the determinants of primary and junior secondary school attendance. The second empirical chapter focuses on the interaction between household and community poverty with the aim of investigating whether the attendance of poor children suffers more than affluent children by residing in a poor community. The third empirical chapter explores the determinants of junior secondary school attendance with the aim of deducing whether there are significant differences between post-conflict countries and more stable countries. The final chapter focuses on the relationship between mothers’ education and school attendance at basic education, arguing that living in a community with a high proportion of more educated mothers enhances the likelihood that a child will attend school, irrespective of the child’s background. The results from the first chapter show that the realisation of UBE is distant in Sierra Leone. There has been a decline in the number of children entering primary education; junior secondary education has however doubled although it remains low at 21%. Children from the poorest households are the most excluded from school followed by rural children and girls. The results from the second empirical chapter showed that there is a significant interaction between household and community poverty where poor children living in poor communities experience a greater depreciation in their probability of attending school than more affluent children who live in the same deprived environment in Sierra Leone. No such interaction was found in Liberia or Ghana. In the third empirical chapter, the sex of the child, agricultural livelihood within a community, household wealth and area of residence were significant in Sierra Leone and Liberia. In Ghana, sex of the household head and maternal orphanhood were significant. The hypothesis of the relationship between mothers’ community education and children’s school attendance for the final empirical chapter was confirmed.

There is limited understanding of how both trends and determinants of neonatal mortality vary from post-neonatal mortality, and more specifically how health care variables are associated with deaths in the first month of life. In particular the association between care at delivery and neonatal mortality is difficult to determine: in developing countries many women only seek skilled care once complications arise, making poor outcomes more probable. It is therefore inappropriate to directly compare outcomes from those who did and did not receive care at delivery due to this heterogeneity between the groups. This three-paper PHD thesis attempts to address some of these issues. Chapter 1 provides an overview of what is known about the determinants of neonatal and child mortality, before developing a conceptual framework for the analysis of neonatal and post-neonatal deaths. Chapter 2 (paper 1) provides a comprehensive analysis of the quality of Demographic & Household Surveys (DHS) data, before describing how trends in neonatal mortality differ from post-neonatal mortality over the short- and medium- term. It then examines how the associations between gross domestic product and neonatal, post-neonatal and early childhood mortality at national level differ using both cross-sectional and longitudinal data. Chapter 3 (paper 2) uses DHS data from Bangladesh to carry out bivariate and multivariate analysis to determine how the determinants of neonatal mortality vary from those of postneonatal mortality. It also tries to identify groups of women who are at ‘high’ or ‘low’ risk from institutional deliveries and compares rates of neonatal mortality. The risk categories are based on socio-economic, maternal health and health care utilisation factors that influence whether or not they are likely to have planned their delivery care or sought hospital care only in the event of complications. Chapter 4 (paper 3) furthers this work using Indian DHS data by examining how the association between health care determinants and neonatal mortality differ by asset quintile, mother’s education and state-level access to professional attendant at delivery. In this chapter I also use instrumental variable methodology to overcome the problem of endogeneity between delivery care variables and neonatal mortality. This technique enables me to examine the association between professional assistance at delivery while adjusting for the heterogeneity between women who do and do not seek such care. Chapter 5 concludes with a summary of key findings, as well as outlining areas for further research in this area.

This thesis examines health inequalities by area-level socioeconomic deprivation, and health in later life in New Zealand. It identifies whether expansion or compression of morbidity is occurring at the end of life. It asks if overall morbidity at a population level is likely to increase or decrease in future as life expectancy increases, and if the same trend is seen for more and less deprived areas. The focus of this research is the identification and dissemination of mortality and morbidity patterns present in two large datasets, using powerful but relatively simple techniques. Large administrative datasets on morbidity and public hospital discharges in New Zealand between 1974 and 2006 are used in the analyses. The thesis consists of three papers. Each paper uses the same datasets, but addresses separate research questions using different methods. The first paper is an exploratory analysis of age-specific and age-standardised mortality and hospital bed day rates, which are used as a proxy for morbidity. The second paper explores lifetime morbidity by using period-prevalence life table functions including Hospital Utilisation Expectancies: a variation of health expectancies. The third paper uses individual record linkage between the mortality and hospital datasets to examine hospital use in the last few months of life. Hospital bed day and mortality rates declined over the time period, and convergence was seen between more and less deprived areas. Individuals at the oldest ages (80 years and over) saw little variation in hospital or mortality rates by area deprivation. Strong evidence for compression of morbidity was observed, particularly at older ages. This was in the absence of evidence for rectangularisation of the survival curve, considered by some to be a prerequisite for compression of morbidity. Rectangularisation of the survival curve would be denoted by life expectancy increases slowing, indicating the nearing of a limit to life expectancy. Instead, compression of morbidity was achieved through a decline in the severity of morbidity in the months prior to death. No evidence of a change in the point at onset of morbidity prior to death was observed. There was however some evidence that the decline in hospital utilisation prior to death (particularly for deaths at older ages) may be partly artefactual. Further research using a different measure of morbidity is required to either support or disprove this theory.