A novel outlier statistic in multivariate survival models and its application to identify unusual under-five mortality sub-districts in Malawi.

Although under-five mortality (U5M) rates have declined worldwide, many countries in sub-Saharan Africa still have much higher rates. Detection of subnational areas with unusually higher U5M rates could support targeted high impact child health interventions. We propose a novel group outlier detection statistic for identifying areas with extreme U5M rates under a multivariate survival data model. The performance of the proposed statistic was evaluated through a simulation study. We applied the proposed method to an analysis of child survival data in Malawi to identify sub-districts with unusually higher or lower U5M rates. The simulation study showed that the proposed outlier statistic can detect unusual high or low mortality groups with a high accuracy of at least 90%, for datasets with at least 50 clusters of size 80 or more. In the application, at most 7 U5M outlier sub-districts were identified, based on the best fitting model as measured by the Akaike information criterion (AIC).

Motivational interviewing and problem-solving therapy intervention for patients on antiretroviral therapy for HIV in Tshwane, South Africa: A randomized controlled trial to assess the impact on alcohol consumption.

BACKGROUND AND AIMS: Reduction of alcohol consumption is important for people undergoing treatment for HIV. We tested the efficacy of a brief intervention for reducing the average volume of alcohol consumed among patients on HIV antiretroviral therapy (ART). DESIGN, SETTING AND PARTICIPANTS: This study used a two-arm multi-centre randomized controlled trial with follow-up to 6 months. Recruitment occurred between May 2016 and October 2017 at six ART clinics at public hospitals in Tshwane, South Africa. Participants were people living with HIV, mean age 40.8 years [standard deviation (SD) = 9.07], 57.5% female, and on average 6.9 years (SD = 3.62) on ART. At baseline (BL), the mean number of drinks consumed over the past 30 days was 25.2 (SD = 38.3). Of 756 eligible patients, 623 were enrolled. INTERVENTION: Participants were randomly assigned to a motivational interviewing (MI)/problem-solving therapy (PST) intervention arm (four modules of MI and PST delivered over two sessions by interventionists) or a treatment as usual (TAU) comparison arm. People assessing outcomes were masked to group assignment. MEASUREMENTS: The primary outcome was the number of standard drinks (15 ml pure alcohol) consumed during the past 30 days assessed at 6-month follow-up (6MFU). FINDINGS: Of the 305 participants randomized to MI/PST, 225 (74%) completed the intervention (all modules). At 6MFU, retention was 88% for the control and 83% for the intervention arm. In support of the hypothesis, an intention-to-treat-analysis for the primary outcome at 6MFU was -0.410 (95% confidence interval = -0.670 to -0.149) units lower on log scale in the intervention group than in the control group (P = 0.002), a 34% relative reduction in the number of drinks. Sensitivity analyses were undertaken for patients who had alcohol use disorders identification test (AUDIT) scores ≥ 8 at BL (n = 299). Findings were similar to those of the whole sample. CONCLUSIONS: In South Africa, a motivational interviewing/problem-solving therapy intervention significantly reduced drinking levels in HIV-infected patients on antiretroviral therapy at 6-month follow-up.

Estimating Unhealthy Food Effects on Childhood Overweight in Malawi Using an Observational Study.

INTRODUCTION: Consumption of unhealthy foods in children contributes to high levels of childhood obesity globally. In developing countries there is paucity of empirical studies on the association.  This study employed propensity-score methods to evaluate the effect of unhealthy foods on overweight among children in Malawi using observational data. METHODS: Data on 4625 children aged 6 to 59 months from the 2015-16 Malawi Demographic and Health Survey (MDHS) were analyzed. A multivariable logistic regression model of unhealthy foods (yes or no) on purported confounders of childhood overweight was used to obtain a child's unhealthy food propensity score. The propensity scores were then used to form matched sets of healthy and unhealthy fed children. The association between unhealthy foods and childhood overweight was assessed using the conditional logistic regression model. RESULTS: The prevalence of overweight (body mass index (BMI) z-score > 2 standard deviations) was estimated at 4.5% (3.8%, 5.3%). The proportion of children who consumed unhealthy foods was estimated at 14.6% (95% CI: 13.1%, 16.2%). Our propensity score matching achieved a balance in the distribution of the confounders between children in the healthy and unhealthy food groups. Children fed unhealthy foods were significantly more likely to be overweight than those fed healthy foods (OR = 2.5, 95% CI: (1.2, 5.2)). CONCLUSION: The findings suggest the adverse effects of unhealthy foods on childhood overweight in Malawi. Thus, efforts to reduce unhealthy food consumption among children should be implemented and supported to address the problem of childhood overweight in Malawi and the sub-Saharan African region.

Inter-Country COVID-19 Contagiousness Variation in Eight African Countries.

The estimates of contiguousness parameters of an epidemic have been used for health-related policy and control measures such as non-pharmaceutical control interventions (NPIs). The estimates have varied by demographics, epidemic phase, and geographical region. Our aim was to estimate four contagiousness parameters: basic reproduction number (R0), contact rate, removal rate, and infectious period of coronavirus disease 2019 (COVID-19) among eight African countries, namely Angola, Botswana, Egypt, Ethiopia, Malawi, Nigeria, South Africa, and Tunisia using Susceptible, Infectious, or Recovered (SIR) epidemic models for the period 1 January 2020 to 31 December 2021. For reference, we also estimated these parameters for three of COVID-19's most severely affected countries: Brazil, India, and the USA. The basic reproduction number, contact and remove rates, and infectious period ranged from 1.11 to 1.59, 0.53 to 1.0, 0.39 to 0.81; and 1.23 to 2.59 for the eight African countries. For the USA, Brazil, and India these were 1.94, 0.66, 0.34, and 2.94; 1.62, 0.62, 0.38, and 2.62, and 1.55, 0.61, 0.39, and 2.55, respectively. The average COVID-19 related case fatality rate for 8 African countries in this study was estimated to be 2.86%. Contact and removal rates among an affected African population were positively and significantly associated with COVID-19 related deaths (p-value < 0.003). The larger than one estimates of the basic reproductive number in the studies of African countries indicate that COVID-19 was still being transmitted exponentially by the 31 December 2021, though at different rates. The spread was even higher for the three countries with substantial COVID-19 outbreaks. The lower removal rates in the USA, Brazil, and India could be indicative of lower death rates (a proxy for good health systems). Our findings of variation in the estimate of COVID-19 contagiousness parameters imply that countries in the region may implement differential COVID-19 containment measures.

Evaluating the Effect of Appropriate Complementary Feeding Practices on Child Growth in Malawi Using Cross-Sectional Data: An Application of Propensity Score Matching.

Introduction: Appropriate complementary foods have been found to provide infants and young children with nutritional needs for their growth and development. In the absence of a randomized control trial (RCT), this study used observational data to evaluate the effect of appropriate complementary feeding practices on the nutritional status of children aged 6-23 months in Malawi using a propensity score matching statistical technique. Methods: Data on 4,722 children aged 6 to 23 months from the 2015-16 Malawi Demographic and Health Survey (MDHS) were analyzed. Appropriate complementary feeding practices were assessed using the core indicators recommended by the World Health Organization (WHO)/United Nations Children's Fund (UNICEF), and consist of the introduction of complementary feeding, minimum dietary diversity, minimum meal frequency and minimum acceptable diet based on a dietary intake during a most recent 24-h period. Results: The prevalence of stunting (height-for-age z-score < -2 SD) was 31.9% (95% CI: 29.3%, 34.6%), wasting (weight-for-height z-score < -2 SD) 3.5% (95% CI: 2.6%, 4.7%) and underweight (weight-for-age z-score < -2 SD) 9.9% (95% CI: 8.4%, 11.8%). Of the 4,722 children, 7.7% (95% CI: 6.9%, 8.5%) were provided appropriate complementary foods. Appropriate complementary feeding practices were found to result in significant decrease in stunting (OR = 0.7, 95% CI: 0.4, 0.95). They also resulted in the decrease of wasting (OR = 0.4, 95% CI: 0.1, 1.7) and underweight (OR = 0.6, 95% CI: 0.2, 1.7). Conclusion: Appropriate complementary feeding practices resulted in a reduction of stunting, wasting, and underweight among children 6 to 23 months of age in Malawi. We recommend the continued provision of appropriate complementary foods to infants and young children to ensure that the diet has adequate nutritional needs for their healthy growth.

A simulation study for evaluating the performance of clustering measures in multilevel logistic regression.

BACKGROUND: Multilevel logistic regression models are widely used in health sciences research to account for clustering in multilevel data when estimating effects on subject binary outcomes of individual-level and cluster-level covariates. Several measures for quantifying between-cluster heterogeneity have been proposed. This study compared the performance of between-cluster variance based heterogeneity measures (the Intra-class Correlation Coefficient (ICC) and the Median Odds Ratio (MOR)), and cluster-level covariate based heterogeneity measures (the 80% Interval Odds Ratio (IOR-80) and the Sorting Out Index (SOI)). METHODS: We used several simulation datasets of a two-level logistic regression model to assess the performance of the four clustering measures for a multilevel logistic regression model. We also empirically compared the four measures of cluster variation with an analysis of childhood anemia to investigate the importance of unexplained heterogeneity between communities and community geographic type (rural vs urban) effect in Malawi. RESULTS: Our findings showed that the estimates of SOI and ICC were generally unbiased with at least 10 clusters and a cluster size of at least 20. On the other hand, estimates of MOR and IOR-80 were less accurate with 50 or fewer clusters regardless of the cluster size. The performance of the four clustering measures improved with increased clusters and cluster size at all cluster variances. In the analysis of childhood anemia, the estimate of the between-community variance was 0.455, and the effect of community geographic type (rural vs urban) had an odds ratio (OR)=1.21 (95% CI: 0.97, 1.52). The resulting estimates of ICC, MOR, IOR-80 and SOI were 0.122 (indicative of low homogeneity of childhood anemia in the same community); 1.898 (indicative of large unexplained heterogeneity); 0.345-3.978 and 56.7% (implying that the between community heterogeneity was more significant in explaining the variations in childhood anemia than the estimated effect of community geographic type (rural vs urban)), respectively. CONCLUSION: At least 300 clusters with sizes of at least 50 would be adequate to estimate the strength of clustering in multilevel logistic regression with negligible bias. We recommend using the SOI to assess unexplained heterogeneity between clusters when the interest also involves the effect of cluster-level covariates, otherwise, the usual intra-cluster correlation coefficient would suffice in multilevel logistic regression analyses.

A Spatial Analysis of COVID-19 in African Countries: Evaluating the Effects of Socio-Economic Vulnerabilities and Neighbouring.

The ongoing highly contagious coronavirus disease 2019 (COVID-19) pandemic, which started in Wuhan, China, in December 2019, has now become a global public health problem. Using publicly available data from the COVID-19 data repository of Our World in Data, we aimed to investigate the influences of spatial socio-economic vulnerabilities and neighbourliness on the COVID-19 burden in African countries. We analyzed the first wave (January-September 2020) and second wave (October 2020 to May 2021) of the COVID-19 pandemic using spatial statistics regression models. As of 31 May 2021, there was a total of 4,748,948 confirmed COVID-19 cases, with an average, median, and range per country of 101,041, 26,963, and 2191 to 1,665,617, respectively. We found that COVID-19 prevalence in an Africa country was highly dependent on those of neighbouring Africa countries as well as its economic wealth, transparency, and proportion of the population aged 65 or older (p-value < 0.05). Our finding regarding the high COVID-19 burden in countries with better transparency and higher economic wealth is surprising and counterintuitive. We believe this is a reflection on the differences in COVID-19 testing capacity, which is mostly higher in more developed countries, or data modification by less transparent governments. Country-wide integrated COVID suppression strategies such as limiting human mobility from more urbanized to less urbanized countries, as well as an understanding of a county's social-economic characteristics, could prepare a country to promptly and effectively respond to future outbreaks of highly contagious viral infections such as COVID-19.

Discrete Survival Time Constructions for Studying Marital Formation and Dissolution in Rural South Africa.

Introduction: Marriage formation and dissolution are important life-course events which impact psychological well-being and health of adults and children experiencing the events. Family studies have usually concentrated on analyzing single transitions including Never Married to Married and Married to Divorced. This does not allow understanding and interrogation of dynamics of these life changing events and their effects on individuals and their families. The objective of this study was to assess determinants associated with transitions between and within marital states in South Africa. Methods: The population-based data available for this study consists of over 55, 000 subjects representing over 340, 000 person-years exposure from the Africa Health Research Institute (AHRI) in rural KwaZulu-Natal, South Africa. It was collected from 1 January 2004 to 31 December 2016. Multilevel multinomial, binary and competing risks regression models were used to model marital state occupation, transitions between marital states as well as investigate determinants of marital dissolution, respectively. Results: Between the years 2006 and 2007, a subject was more likely to be married than never married when compared to years 2004 - 2005. After 2007, subjects were less likely to be married than never married and the trend reduced over the years up to 2016 [with OR=0.86, CI=(0.78; 0.94), OR=0.71, CI=(0.64; 0.78), OR=0.60, CI=(0.54; 0.67), OR=0.50, CI=(0.44; 0.56), and OR = 0.43, CI = (0.38; 0.48)] for periods 2008 - 2009, 2010 - 2011, 2012 - 2013, 2014 - 2015, and 2016, respectively. In 2008 - 2009, subjects were more likely to experience a marital dissolution than in the period 2004 - 2005 and the trend slightly reduces from 2010 until 2013 [OR=24.49, CI=(5.53; 108.37)]. Raising age at first sexual debut was found to be inversely associated with a marital dissolution [OR = 0.97;CI = (0.95; 0.99)]. Highly educated subjects were more likely to stay in one marital state than those who never went to school [OR=6.43, CI=(4.89; 8.47), OR=18.86, CI=(1.14; 53.31), and OR=2.96, CI=(1.96; 4.46) for being married, separated and widowed, respectively, among subjects with tertiary education]. As the age at first marriage increased, subjects became less likely to experience a marital separation [OR = 0.06, CI = (0.00; 1.11), OR = 0.05, CI = (0.00; 0.91), and OR = 0.04, CI = (0.00; 0.76) for subjects who entered a first marriage at ages 18 - 22, 23 - 29, and 30 - 40, respectively]. Conclusion: The study found that marrying at later ages is associated with a lower rate of marital dissolution while more educated subjects tend to stay longer in one marital state. Sexual debut at later ages was associated with a lower likelihood of experiencing a marital dissolution. There could, however, be some factors that are not accounted for in the model that may lead to heterogeneity in these dynamics in our model specification which are captured by the random effects in the model. Nonetheless, we may postulate that existing programs that encourage delay in onset of sexual activity for HIV risk reduction for example, may also have a positive impact on lowering rates of marital dissolution, thus ultimately improving psychological and physical health.

Smoothed Temporal Atlases of Age-Gender All-Cause Mortality in South Africa.

Most mortality maps in South Africa and most contried of the sub-Saharan region are static, showing aggregated count data over years or at specific years. Lack of space and temporral dynamanics in these maps may adversely impact on their use and application for vigorous public health policy decisions and interventions. This study aims at describing and modeling sub-national distributions of age-gender specific all-cause mortality and their temporal evolutions from 1997 to 2013 in South Africa. Mortality information that included year, age, gender, and municipality administrative division were obtained from Statistics South Africa for the period. Individual mortality level data were grouped by three ages groups (0-14, 15-64, and 65 and over) and gender (male, female) and aggregated at each of the 234 municipalities in the country. The six age-gender all-cause mortality rates may be related due to shared common social deprivation, health and demographic risk factors. We undertake a joint analysis of the spatial-temporal variation of the six age-gender mortality risks. This is done within a shared component spatial model construction where age-gender common and specific spatial and temporal trends are estiamted using a hierarchical Bayesian spatial model. The results show municipal and temporal differentials in mortality risk profiles between age and gender groupings. High rates were seen in 2005, especially for the 15-64 years age group for both males and females. The dynamic geographical and time distributions of subnational age-gender all-cause mortality contribute to a better understanding of the temporal evolvement and geographical variations in the relationship between demographic composition and burden of diseases in South Africa. This provides useful information for effective monitoring and evaluation of public health policies and programmes targeting mortality reduction across time and sub-populations in the country.

Meta-Analysis of Effect Sizes Reported at Multiple Time Points Using General Linear Mixed Model.

Meta-analysis of longitudinal studies combines effect sizes measured at pre-determined time points. The most common approach involves performing separate univariate meta-analyses at individual time points. This simplistic approach ignores dependence between longitudinal effect sizes, which might result in less precise parameter estimates. In this paper, we show how to conduct a meta-analysis of longitudinal effect sizes where we contrast different covariance structures for dependence between effect sizes, both within and between studies. We propose new combinations of covariance structures for the dependence between effect size and utilize a practical example involving meta-analysis of 17 trials comparing postoperative treatments for a type of cancer, where survival is measured at 6, 12, 18 and 24 months post randomization. Although the results from this particular data set show the benefit of accounting for within-study serial correlation between effect sizes, simulations are required to confirm these results.

Efficacy of an alcohol-focused intervention for improving adherence to antiretroviral therapy (ART) and HIV treatment outcomes - a randomised controlled trial protocol.

BACKGROUND: Little research has examined whether alcohol reduction interventions improve antiretroviral therapy (ART) adherence and HIV treatment outcomes. This study assesses the efficacy of an intervention for reducing alcohol use among HIV patients on ART who are hazardous/harmful drinkers. Specific aims include adapting a blended Motivational Interviewing (MI) and Problem Solving Therapy (PST) intervention for use with HIV patients; evaluating the efficacy of the intervention for reducing alcohol consumption; and assessing counsellors' and participants' perceptions of the intervention. METHODS/DESIGN: A randomised controlled trial will evaluate the intervention among ART patients in public hospital-based HIV clinics in Tshwane, South Africa. We will recruit patients who are HIV-positive, on ART for at least 3 months, and classified as harmful/hazardous drinkers using the AUDIT-3. Eligible patients will be randomly assigned to one of three conditions. Patients in the experimental group will receive the MI-PST intervention to reduce harmful/hazardous alcohol use. Patients in the equal-attention wellness intervention group will receive an intervention focused on addressing health risk behaviours. Patients in the control condition will receive treatment as usual. Participants will complete an interviewer-administered questionnaire at baseline and 3, 6 and 12 months post-randomisation to assess alcohol consumption, ART adherence, physical and mental health. We will also collect biological specimens to test for recent alcohol consumption, CD4 counts and HIV RNA viral loads. The primary outcome will be reduction in the volume of alcohol consumed. Secondary outcomes include reduction in harmful/hazardous use of alcohol, reduction in biological markers of drinking, increase in adherence rates, reductions in viral loads, and increases in CD4 T-cell counts. A process evaluation will ascertain counsellors' and participants' perceptions of the acceptability and effectiveness of the interventions. DISCUSSION: We have obtained ethical approval and approval from the study sites and regional and provincial health departments. The study has implications for clinicians, researchers and policy makers as it will provide efficacy data on how to reduce harmful/hazardous alcohol consumption among HIV patients and will shed light on whether reducing alcohol consumption impacts on HIV treatment adherence and other outcomes. TRIAL REGISTRATION: Pan African Clinical Trials Register Number: PACTR201405000815100.

Pregnancy incidence and risk factors among women participating in vaginal microbicide trials for HIV prevention: systematic review and meta-analysis.

INTRODUCTION: Pregnancy is contraindicated in vaginal microbicide trials for the prevention of HIV infection in women due to the unknown maternal and fetal safety of the microbicides. Women who become pregnant are taken off the microbicide during pregnancy period but this result in reduction of the power of the trials. Strategies to reduce the pregnancy rates require an understanding of the incidence and associated risk factors of pregnancy in microbicide trials. This systematic review estimates the overall incidence rate of pregnancy in microbicide trials and describes the associated risk factors. METHODS: A comprehensive literature search was carried out to identify eligible studies from electronic databases and other sources. Two review authors independently selected studies and extracted relevant data from included studies. Meta-analysis of incidence rates of pregnancy was carried out and risk factors of pregnancy were reported narratively. RESULTS: Fifteen studies reporting data from 10 microbicide trials (N=27,384 participants) were included. A total of 4,107 participants (15.0%) fell pregnant and a meta-analysis of incidence rates of pregnancy from 8 microbicide trials (N=25,551) yielded an overall incidence rate of 23.37 (95%CI: 17.78 to 28.96) pregnancies per 100 woman-years. However, significant heterogeneity was detected. Hormonal injectable, intra-uterine device (IUD) or implants or sterilization, older age, more years of education and condom use were associated with lower pregnancy. On the other hand, living with a man, history of pregnancy, self and partner desire for future baby, oral contraceptive use, increased number of unprotected sexual acts and inconsistent use of condoms were associated with higher pregnancy. CONCLUSIONS: The incidence rate of pregnancy in microbicide trials is high and strategies for its reduction are urgently required in order to improve the sample size and power of these trials.

Divergent spatial patterns in the prevalence of the human immunodeficiency virus (HIV) and syphilis in South African pregnant women.

An analysis of the ecological association between the human immunodeficiency virus (HIV) and syphilis was undertaken using joint mapping modelling based on data from South African national HIV and syphilis sentinel surveillance surveys carried out between 2007 and 2009. The syphilis prevalence, taken as proxy for sexual behaviour and increased HIV transmission, was first used with health district-level deprivation and population density as a covariate in a HIV prevalence spatial regression model and, secondly, together with HIV as a bivariate outcome. HIV is more highly prevalent in deprived and populated areas than elsewhere, while syphilis has a high prevalence in less deprived and less populated areas. Spatially, the HIV prevalence was lowest in the southwestern and highest in the northeastern parts of the country. This was in discordance to the syphilis prevalence, which revealed negative correlations with HIV prevalence. Considerable variations across the districts remained after adjusting for the contextual covariate factors. Divergent spatial patterns between HIV and syphilis were identified, regarding both observed and unobserved covariate effects. The differential disease-specific spatial prevalence patterns may point to inconsistent successes in interventions between the two diseases. Overall, the results emphasize the need to develop and test plausible aetiological hypotheses relating to ecological correlations and causes of the disease-specific interjectory between the districts.

Investigating spatio-temporal similarities in the epidemiology of childhood leukaemia and diabetes.

Childhood acute lymphoblastic leukaemia (ALL) and Type 1 diabetes (T1D) share some common epidemiological features, including rising incidence rates and links with an infectious aetiology. Previous work has shown a significant positive correlation in incidence between the two conditions both at the international and small-area level. The aim was to extend the methodology by including shared spatial and temporal trends using a more extensive dataset among individuals diagnosed with ALL and T1D in Yorkshire (UK) aged 0-14 years from 1978-2003. Cases with ALL and T1D were ascertained from 2 high quality population-based disease registers covering the Yorkshire region of the UK and linked to an electoral ward from the 1991 UK census. A Bayesian model was fitted where similarities and differences in risk profiles of the two diseases were captured by the shared and disease-specific components using a shared-component model, with space-time interactions. The extended model revealed a positive correlation of at least 0.70 between diseases across all time periods, and an increasing risk across time for both diseases, which was more evident for T1D. Furthermore, both diseases exhibited lower rates in the more urban county of West Yorkshire and higher rates in the more rural northern and eastern part of the region. A differential effect of T1D over ALL was found in the south-eastern part of the region, which had a more pronounced association with population mixing than with population density or deprivation. Our approach has demonstrated the utility in modelling temporally and spatially varying disease incidence patterns across small geographical areas. The findings suggest searching for environmental factors that exhibit similar geographical-temporal variation in prevalence may help in the development and testing of plausible aetiological hypotheses. Furthermore, identifying environmental exposures specific to the south-eastern part of the region, especially locally varying risk factors which may differentially affect the development of T1D and ALL, may also be fruitful.

Revisiting the interaction between birth weight and current body size in the foetal origins of adult disease.

The four models proposed for exploring the foetal origins of adult disease (FOAD) hypothesis use the product term between size at birth and current size to determine the relative importance of pre- and post-natal growth on disease in later life. This is a common approach for testing the interaction between an exposure (in this instance size at birth) and an effect modifier (in this instance current size)--incorporating the product term obtained by multiplying the exposure and effect modifier variables within a statistical regression model. This study examines the mathematical basis for this approach and uses computer simulations to demonstrate two potential statistical flaws that might generate misleading findings. The first of these is that the expected value of the partial regression coefficient for the product term (between exposure and effect modifier) will be zero when the outcome, exposure and effect modifier are all continuously distributed and follow a multivariate normal distribution. This is because testing the product interaction term amounts to testing for multivariate normality among the three variables, irrespective of the pair-wise correlations amongst them. The second flaw is that it is possible to generate a statistically significant interaction between exposure and effect modifier, even when none exists, simply by categorising either or both of these variables. These flaws pose a serious challenge to the four models approach proposed for exploring the FOAD hypothesis. The interaction between exposure and effect modifier variables should be interpreted with caution both here and elsewhere in epidemiological analyses.

A full Bayesian hierarchical mixture model for the variance of gene differential expression.

BACKGROUND: In many laboratory-based high throughput microarray experiments, there are very few replicates of gene expression levels. Thus, estimates of gene variances are inaccurate. Visual inspection of graphical summaries of these data usually reveals that heteroscedasticity is present, and the standard approach to address this is to take a log2 transformation. In such circumstances, it is then common to assume that gene variability is constant when an analysis of these data is undertaken. However, this is perhaps too stringent an assumption. More careful inspection reveals that the simple log2 transformation does not remove the problem of heteroscedasticity. An alternative strategy is to assume independent gene-specific variances; although again this is problematic as variance estimates based on few replications are highly unstable. More meaningful and reliable comparisons of gene expression might be achieved, for different conditions or different tissue samples, where the test statistics are based on accurate estimates of gene variability; a crucial step in the identification of differentially expressed genes. RESULTS: We propose a Bayesian mixture model, which classifies genes according to similarity in their variance. The result is that genes in the same latent class share the similar variance, estimated from a larger number of replicates than purely those per gene, i.e. the total of all replicates of all genes in the same latent class. An example dataset, consisting of 9216 genes with four replicates per condition, resulted in four latent classes based on their similarity of the variance. CONCLUSION: The mixture variance model provides a realistic and flexible estimate for the variance of gene expression data under limited replicates. We believe that in using the latent class variances, estimated from a larger number of genes in each derived latent group, the p-values obtained are more robust than either using a constant gene or gene-specific variance estimate.

A Bayesian analysis of amalgam restorations in the Royal Air Force using the counting process approach with nested frailty effects.

Survival analysis methods are increasingly used in dental research to measure risk of tooth eruption and caries as well as life spans of amalgam restorations. Analyses have been extended to account for lack of independence in the data, which arises from the clustering of observations within units such as tooth-surfaces, teeth and subjects. There are various analytical strategies and modelling approaches now available to us in dealing with clustered dental data. In this article, the modelling strategy of Cox's proportional hazards regression is formulated using the counting process approach, which can easily be extended to include time-variant covariates as well as nested random frailty effects. A semi-parametric Bayesian method is presented for the analysis of the proposed model. The methodology is applied to an analysis of nested clustered data on life-span of amalgam restorations in the UK Royal Air Force. These data have previously been analysed using a non-Bayesian approach. The Gibbs sampler, a Markov chain Monte Carlo method, is used to generate samples from the marginal posterior distribution of the parameters of this Bayesian model.

Detecting small-area similarities in the epidemiology of childhood acute lymphoblastic leukemia and diabetes mellitus, type 1: a Bayesian approach.

Childhood acute lymphoblastic leukemia and diabetes mellitus, type 1, have common epidemiologic and etiologic features, including correlated international incidence and associations with infections. The authors examined whether the diseases' similar large-scale distributions are reflected in small geographic areas while also examining the influence of sociodemographic characteristics. Details of 299 children (0-14 years) with acute lymphoblastic leukemia and 1,551 children with diabetes diagnosed between 1986 and 1998 were extracted from two registers in Yorkshire, United Kingdom. Standardized incidence ratios across 532 electoral wards were compared using Poisson regression, confirming significant associations between population mixing and the geographic heterogeneity of both conditions. Bayesian methods analysis of spatial correlation between diseases by modeling a bivariate outcome based on their standardized incidence ratios was applied; spatial and heterogeneity components were included within a hierarchical random effects model. A positive correlation between diseases of 0.33 (95% credible interval: -0.20, 0.74) was observed, and this was reduced after control for population mixing (r = 0.18), population density (r = 0.14), and deprivation (r = 0.06). The Bayesian approach showed a modest but nonsignificant joint spatial correlation between diseases, only partially suggesting that the risk of both was associated within some electoral wards. With Bayesian methodology, population mixing remained significantly associated with both diseases. The links between diabetes and acute lymphoblastic leukemia observed for large regions are weaker for small areas. More powerful replications are needed for confirmation of these findings.