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Background: cystic fibrosis (CF) is a life-threatening genetic disease, affecting around 10 500 people in the UK. Precision medicines have been developed to treat specific CF-gene mutations. The newest, elexacaftor/tezacaftor/ivacaftor (ELEX/TEZ/IVA), has been found to be highly effective in randomised controlled trials (RCTs) and became available to a large proportion of UK CF patients in 2020. Understanding the potential health economic impacts of ELEX/TEZ/IVA is vital to planning service provision.Methods: we combined observational UK CF Registry data with RCT results to project the impact of ELEX/TEZ/IVA on total days of intravenous (IV) antibiotic treatment at a population level. Registry data from 2015 to 2017 were used to develop prediction models for IV days over a 1-year period using several predictors, and to estimate 1-year population total IV days based on standards of care pre-ELEX/TEZ/IVA. We considered two approaches to imposing the impact of ELEX/TEZ/IVA on projected outcomes using effect estimates from RCTs: approach 1 based on effect estimates on FEV1% and approach 2 based on effect estimates on exacerbation rate.Results: ELEX/TEZ/IVA is expected to result in significant reductions in population-level requirements for IV antibiotics of 16.1% (~17 800 days) using approach 1 and 43.6% (~39 500 days) using approach 2. The two approaches require different assumptions. Increased understanding of the mechanisms through which ELEX/TEZ/IVA acts on these outcomes would enable further refinements to our projections.Conclusions: this work contributes to increased understanding of the changing healthcare needs of people with CF and illustrates how Registry data can be used in combination with RCT evidence to estimate population-level treatment impacts.

The existing framework of Mendelian randomization (MR) infers the causal effect of one or multiple exposures on one single outcome. It is not designed to jointly model multiple outcomes, as would be necessary to detect causes of more than one outcome and would be relevant to model multimorbidity or other related disease outcomes. Here, we introduce Multi-response Mendelian randomization (MR2), a novel MR method specifically designed for multiple outcomes to identify exposures that cause more than one outcome or, conversely, exposures that exert their effect on distinct responses. MR2uses a sparse Bayesian Gaussian copula regression framework to detect causal effects while estimating the residual correlation between summary-level outcomes, i.e., the correlation that cannot be explained by the exposures, andviceversa. We show both theoretically and in a comprehensive simulation study how unmeasured shared pleiotropy induces residual correlation. We also reveal how non-genetic factors that affect more than one outcome contribute to their correlation. We demonstrate that by accounting for residual correlation, MR2has higher power to detect shared exposures causing more than one outcome. It also provides more accurate causal effect estimates than existing methods that ignore the dependence between related responses. Finally, we illustrate how MR2detects shared and distinct causal exposures for five cardiovascular diseases in two applications considering cardiometabolic and lipidomic exposures and uncovers residual correlation between summary-level outcomes reflecting known relationships between cardiovascular diseases.

The Centre of Excellence for Development Impact and Learning (CEDIL) has recently funded several studies that use machine learning methods to enhance the inferences made from impact evaluations. These studies focus on assessing the impact of complex development interventions, which can be expected to have impacts in different domains, possibly over an extended period of time. These studiestherefore involve study participants being followed up at multiple time-points after the intervention, and typically collect large numbers of variables at each follow-up. The hope is that machine learning approaches can uncover new insights into the variation in responses to interventions, and possible causal mechanisms, which in turn can highlight potential areas that policy and planning can focus on. This paper describes these studies using machine learning methods, gives an overview of the common aims and methodological approaches used in impact evaluations, and highlights some lessons and important caveats.

The microbiome plays a key role in the health of the human body. Interest often lies in finding features of the microbiome, alongside other covariates, which are associated with a phenotype of interest. One important property of microbiome data, which is often overlooked, is its compositionality as it can only provide information about the relative abundance of its constituting components. Typically, these proportions vary by several orders of magnitude in datasets of high dimensions. To address these challenges we develop a Bayesian hierarchical linear log-contrast model which is estimated by mean field Monte-Carlo coordinate ascent variational inference (CAVI-MC) and easily scales to high dimensional data. We use novel priors which account for the large differences in scale and 1 constrained parameter space associated with the compositional covariates. A reversible jump Monte Carlo Markov chain guided by the data through univariate approximations of the variational posterior probability of inclusion, with proposal parameters informed by approximating variational densities via auxiliary parameters, is used to estimate intractable marginal expectations. We demonstrate that our proposed Bayesian method performs favourably against existing frequentist state of the art compositional data analysis methods. We then apply the CAVI-MC to the analysis of real data exploring the relationship of the gut microbiome to body mass index.

Background It has been hypothesised that greater maternal adiposity before or during pregnancy causes greater offspring adiposity in childhood and adulthood, via causal intrauterine or periconceptional mechanisms. Previous Mendelian randomization (MR) estimates were imprecise, with wide confidence intervals that included potentially important protective or adverse effects, and may have been biased by collider effects or imperfect adjustment for genetic inheritance. Here we use an improved MR approach to investigate whether associations between maternal pre-/early pregnancy body mass index (BMI) and offspring adiposity from birth to adolescence are causal, or are instead due to confounding. Methods and findings We undertook confounder adjusted multivariable (MV) regression and Mendelian randomization (MR) using mother-offspring pairs from two UK cohorts: Avon Longitudinal Study of Parents and Children (ALSPAC) and Born in Bradford (BiB). In ALSPAC and BiB the outcomes were birthweight (BW; N = 9339) and BMI at age 1 (N = 8659) and 4 years (N = 7575), and in ALSPAC only we investigated BMI at 10 (N = 4476) and 15 years (N = 4112) and dual-energy X-ray absorptiometry (DXA) determined fat mass index (FMI) from age 10– 18 years (N = 2659 to 3855). We compared MR results from several polygenic risk scores (PRS), calculated from maternal non-transmitted alleles at between 29 and 80,939 single nucleotide polymorphisms (SNPs). MV and MR showed a consistent positive association of maternal BMI with BW, but for adiposity at most older ages MR estimates were weaker than MV estimates. In MV regression a one standard deviation (SD) higher maternal BMI was associated with a 0.13 (95% confidence interval [CI]: 0.10, 0.16) SD increase in offspring BW. The corresponding MR estimate from the strongest PRS (including up to 80,939 SNPs) was 0.14 (95% CI: 0.05, 0.23), with no difference between the two estimates (Pdifference = 0.84). For 15 year BMI the MV and MR estimates (80,939 SNPs) were 0.32 (95% CI: 0.29, 0.36) and 0.13 (95% CI: 0.01, 0.24) respectively (Pdifference = 1.0e-3). Results for FMI were similar to those for adolescent BMI. As the number of SNPs included in the PRS increased, the MR confidence intervals narrowed and the effect estimates for adolescent adiposity became closer to the MV estimates. Sensitivity analyses suggested the stronger effects with more SNPs were explained by horizontal pleiotropic bias away from zero. Consequently, the unbiased difference between the MV and MR estimates is probably greater than shown in our main analyses. Furthermore, MR estimates from IVs with fewer SNPs provided no strong evidence for a causal effect on adolescent adiposity. Conclusions Our results suggest that higher maternal pre-/early-pregnancy BMI is not a key driver of higher adiposity in the next generation. Thus, they support interventions that target the whole population for reducing overweight and obesity, rather than a specific focus on women of reproductive age.

Background Maternal pre-pregnancy body mass index (BMI) is positively associated with offspring birth weight (BW) and BMI in childhood and adulthood. Each of these associations could be due to causal intrauterine effects, or confounding (genetic or environmental), or some combination of these. Here we estimate the extent to which the association between maternal BMI and offspring body size is explained by offspring genotype, as a first step towards establishing the importance of genetic confounding. Methods We examined the associations of maternal pre-pregnancy BMI with offspring BW and BMI at 1, 5, 10 and 15 years, in three European birth cohorts (n ≤11 498). Bivariate Genomic-relatedness-based Restricted Maximum Likelihood implemented in the GCTA software (GCTA-GREML) was used to estimate the extent to which phenotypic covariance was explained by offspring genotype as captured by common imputed single nucleotide polymorphisms (SNPs). We merged individual participant data from all cohorts, enabling calculation of pooled estimates. Results Phenotypic covariance (equivalent here to Pearson’s correlation coefficient) between maternal BMI and offspring phenotype was 0.15 [95% confidence interval (CI): 0.13, 0.17] for offspring BW, increasing to 0.29 (95% CI: 0.26, 0.31) for offspring 15 year BMI. Covariance explained by offspring genotype was negligible for BW [–0.04 (95% CI: –0.09, 0.01)], but increased to 0.12 (95% CI: 0.04, 0.21) at 15 years, which is equivalent to 43% (95% CI: 15%, 72%) of the phenotypic covariance. Sensitivity analyses using weight, BMI and ponderal index as the offspring phenotype at all ages showed similar results. Conclusions Offspring genotype explains a substantial fraction of the covariance between maternal BMI and offspring adolescent BMI. This is consistent with a potentially important role for genetic confounding as a driver of the maternal BMI–offspring BMI association.

BACKGROUND: Psychological stress is commonly cited as a risk factor for melanoma, but clinical evidence is limited. OBJECTIVES: This study aimed to evaluate the association between partner bereavement and (i) first-time melanoma diagnosis and (ii) mortality in patients with melanoma. METHODS: We conducted two cohort studies using data from the U.K. Clinical Practice Research Datalink (1997-2017) and Danish nationwide registries (1997-2016). In study 1, we compared the risk of first melanoma diagnosis in bereaved vs. matched nonbereaved people using stratified Cox regression. In study 2 we estimated hazard ratios (HRs) for death from melanoma in bereaved compared with nonbereaved individuals with melanoma using Cox regression. We estimated HRs separately for the U.K. and for Denmark, and then pooled the data to perform a random-effects meta-analysis. RESULTS: In study 1, the pooled adjusted HR for the association between partner bereavement and melanoma diagnosis was 0·88 [95% confidence interval (CI) 0·84-0·92] across the entire follow-up period. In study 2, we observed increased melanoma-specific mortality in people experiencing partner bereavement across the entire follow-up period (HR 1·17, 95% CI 1·06-1·30), with the peak occurring during the first year of follow-up (HR 1·31, 95% CI 1·07-1·60). CONCLUSIONS: We found decreased risk of melanoma diagnosis, but increased mortality associated with partner bereavement. These findings may be partly explained by delayed detection resulting from the loss of a partner who could notice skin changes. Stress may play a role in melanoma progression. Our findings indicate the need for a low threshold for skin examination in individuals whose partners have died. What is already known about this topic? Psychological stress has been proposed as a risk factor for the development and progression of cancer, including melanoma, but evidence is conflicting. Clinical evidence is limited by small sample sizes, potential recall bias associated with self-report, and heterogeneous stress definitions. What does this study add? We found a decreased risk of melanoma diagnosis, but increased mortality associated with partner bereavement. While stress might play a role in the progression of melanoma, an alternative explanation is that bereaved people no longer have a close person to help notice skin changes, leading to delayed melanoma detection. Linked Comment: Talaganis et al. Br J Dermatol 2020; 183:607-608.

© 2019 The Authors. Background: The contingent valuation (CV) method is used to estimate the willingness to pay (WTP) for services and products to inform cost benefit analyses (CBA). A long-standing criticism that stated WTP estimates may be poor indicators of actual WTP, calls into question their validity and the use of such estimates for welfare evaluation, especially in the health sector. Available evidence on the validity of CV studies so far is inconclusive. We systematically reviewed the literature to (1) synthesize the evidence on the criterion validity of WTP/willingness to accept (WTA), (2) undertake a meta-analysis, pooling evidence on the extent of variation between stated and actual WTP values and, (3) explore the reasons for the variation. Methods: Eight electronic databases were searched, along with citations and reference reviews. 50 papers detailing 159 comparisons were identified and reviewed using a standard proforma. Two reviewers each were involved in the paper selection, review and data extraction. Meta-analysis was conducted using random effects models for ratios of means and percentage differences separately. Meta-bias was investigated using funnel plots. Results: Hypothetical WTP was on average 3.2 times greater than actual WTP, with a range of 0.7–11.8 and 5.7 (0.0–13.6) for ratios of means and percentage differences respectively. However, key methodological differences between surveys of hypothetical and actual values were found. In the meta-analysis, high levels of heterogeneity existed. The overall effect size for mean summaries was 1.79 (1.56–2.04) and 2.37 (1.93–2.80) for percent summaries. Regression analyses identified mixed results on the influence of the different experimental protocols on the variation between stated and actual WTP values. Results indicating publication bias did not account for differences in study design. Conclusions: The evidence on the criterion validity for CV studies is more mixed than authors are representing because substantial differences in study design between hypothetical and actual WTP/WTA surveys are not accounted for. Brunel University London, Health Economics Research Group.

BackgroundThere are various maternal prenatal biopsychosocial (BPS) predictors of birth weight, making it difficult to quantify their cumulative relationship.MethodsWe studied two birth cohorts: Northern Finland Birth Cohort 1986 (NFBC1986) born in 1985–1986 and the Generation R Study (from the Netherlands) born in 2002–2006. In NFBC1986, we selected variables depicting BPS exposure in association with birth weight and performed factor analysis to derive latent constructs representing the relationship between these variables. In Generation R, the same factors were generated weighted by loadings of NFBC1986. Factor scores from each factor were then allocated into tertiles and added together to calculate a cumulative BPS score. In all cases, we used regression analyses to explore the relationship with birth weight corrected for sex and gestational age and additionally adjusted for other factors.ResultsFactor analysis supported a four-factor structure, labelled closely to represent their characteristics as ‘Factor1-BMI’ (body mass index), ‘Factor2-DBP’ (diastolic blood pressure), ‘Factor3-Socioeconomic-Obstetric-Profile’ and ‘Factor4-Parental-Lifestyle’. In both cohorts, ‘Factor1-BMI’ was positively associated with birth weight, whereas other factors showed negative association. ‘Factor3-Socioeconomic-Obstetric-Profile’ and ‘Factor4-Parental-Lifestyle’ had the greatest effect size, explaining 30% of the variation in birth weight. Associations of the factors with birth weight were largely driven by ‘Factor1-BMI’. Graded decrease in birth weight was observed with increasing cumulative BPS score, jointly evaluating four factors in both cohorts.ConclusionOur study is a proof of concept for maternal prenatal BPS hypothesis, highlighting the components snowball effect on birth weight in two different European birth cohorts.

This project received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 633595

Funder: Victorian Government’s Operational Infrastructure Support Program, Our work is motivated by the search for metabolite quantitative trait loci (QTL) in a cohort of more than 5000 people. There are 158 metabolites measured by NMR spectroscopy in the 31‐year follow‐up of the Northern Finland Birth Cohort 1966 (NFBC66). These metabolites, as with many multivariate phenotypes produced by high‐throughput biomarker technology, exhibit strong correlation structures. Existing approaches for combining such data with genetic variants for multivariate QTL analysis generally ignore phenotypic correlations or make restrictive assumptions about the associations between phenotypes and genetic loci. We present a computationally efficient Bayesian seemingly unrelated regressions model for high‐dimensional data, with cell‐sparse variable selection and sparse graphical structure for covariance selection. Cell sparsity allows different phenotype responses to be associated with different genetic predictors and the graphical structure is used to represent the conditional dependencies between phenotype variables. To achieve feasible computation of the large model space, we exploit a factorisation of the covariance matrix. Applying the model to the NFBC66 data with 9000 directly genotyped single nucleotide polymorphisms, we are able to simultaneously estimate genotype–phenotype associations and the residual dependence structure among the metabolites. The R package BayesSUR with full documentation is available at https://cran.r‐project.org/web/packages/BayesSUR/

ObjectivesAn effectiveness and cost-effectiveness analyses of two-staged community sports interventions; taster sports sessions compared with portfolio of community sport sessions.DesignQuasi-experiment using an interrupted time series design.SettingCommunity sports projects delivered by eight lead partners in London Borough of Hounslow, UK.ParticipantsInactive people aged 14 plus years (n=246) were recruited between May 2013 and February 2014.InterventionsCommunity sports interventions delivered in two stages, 6-week programme of taster sport sessions (stage 1) and 6-week programme of portfolio of community sporting sessions delivered by trained coaches (stage 2).Outcome measures(a) Change in days with ≥30 min of self-reported vigorous intensity physical activity (PA), moderate intensity PA, walking and sport; and (b) change in subjective well-being and EQ5D5L quality-adjusted life-years (QALYs).MethodsInterrupted time series analysis evaluated the effectiveness of the two-staged sports programmes. Cost-effectiveness analysis compares stage 2 with stage 1 from a provider’s perspective, reporting outcomes of incremental cost per QALY (2015/2016 price year). Uncertainty was assessed using deterministic and probabilistic sensitivity analyses.ResultsCompared with stage 1, counterfactual change at 21 days in PA was lower for vigorous (log odds: −0.52; 95% CI −1 to –0.03), moderate PA (−0.50; 95% CI 0.94 to 0.05) and sport(−0.56; 95% CI −1.02 to –0.10). Stage 2 increased walking (0.28; 95% CI 0.3 to 0.52). Effect overtime was similar. Counterfactual change at 21 days in well-being was positive particularly for ‘happiness’ (0.29; 95% CI 0.06 to 0.51). Stage 2 was more expensive (£101 per participant) but increased QALYs (0.001; 95% CI −0.034 to 0.036). Cost per QALY for stage 2 was £50 000 and has 29% chance of being cost-effective (£30 000 threshold).ConclusionCommunity-based sport interventions could increase PA among inactive people. Less intensive sports sessions may be more effective and cost-effective.

Introduction Young children commonly wheeze but only some have asthma later in life. Asthma prediction tools have poor predictive performance and few have been validated. We aimed to develop a robust tool for the prediction of asthma at age 10–14 years using readily available information. Methods we studied 5 UK birth cohorts (the STELAR consortium) and considered two groups: 1. all children recruited at birth and 2. high-risk children on the basis of reported wheezing at 2/3 or 5 years. Two comparable cohorts (Ashford and ALSPAC) were used to select predictors (training sample) and the SEATON, MAAS and Isle of Wight studies to assess predictive performance (validation sample). We included 16 187 and 814 children from groups 1 and 2 respectively in the training sample and validated the developed predictive tools in 5320 and 285 children from the validation sample. We considered 40 potential predictors collected at recruitment and at 1, 2/3 and 5 years of age: demographic and perinatal information, eczema, hay-fever, respiratory symptoms, environmental and family-related factors. We defined asthma at 10–14 years by the presence of both current wheeze and asthma treatment. We compared 5 statistical methods to select variables and estimate coefficients: stepwise regression, classical (LASSO and Elastic-Net, EN), empirical Bayes (EB) and Bayesian (BM) regularisation Methods Predictive performance was assessed using calibration and discrimination measures including area under the ROC curve (AUC). Results Asthma prevalence at age 10–14 ranged from 7%–18% in group 1 and from 32%–52% in group 2. Frequency of early wheezing, eczema, and paternal asthma were important predictors in all models and both groups. Other selected predictors included birth order, maternal asthma and domestic pets. Specificity and negative predictive value (NPV) were higher in the general population, while sensitivity and positive predictive value (PPV) were higher in high-risk group. BM (AUC 0.77, specificity 0.84 and NPV 0.93) and EN (AUC 0.74, sensitivity 0.71 and PPV 0.65) provided the highest accuracy and discriminative ability predictive ability in the 2 groups, respectively. Conclusion The use of sophisticated statistical methods in a large, multicentre population demonstrated promising Results in developing an asthma predictive tool.

During aging, intracranial volume remains unchanged and represents maximally attained brain size, while various interacting biological phenomena lead to brain volume loss. Consequently, intracranial volume and brain volume in late life reflect different genetic influences. Our genome-wide association study (GWAS) in 8,175 community-dwelling elderly persons did not reveal any associations at genome-wide significance (P < 5 × 10 -8) for brain volume. In contrast, intracranial volume was significantly associated with two loci: rs4273712 (P = 3.4 × 10 -11), a known height-associated locus on chromosome 6q22, and rs9915547 (P = 1.5 × 10 -12), localized to the inversion on chromosome 17q21. We replicated the associations of these loci with intracranial volume in a separate sample of 1,752 elderly persons (P = 1.1 × 10 -3 for 6q22 and 1.2 × 10 -3 for 17q21). Furthermore, we also found suggestive associations of the 17q21 locus with head circumference in 10,768 children (mean age of 14.5 months). Our data identify two loci associated with head size, with the inversion at 17q21 also likely to be involved in attaining maximal brain size. © 2012 Nature America, Inc. All rights reserved.

Fuzzy multiple comparisons procedures are introduced as a solution to the problem of multiple comparisons for discrete test statistics. The critical function of the randomized p-values is proposed as a measure of evidence against the null hypotheses. The classical concept of randomized tests is extended to multiple comparisons. This approach makes all theory of multiple comparisons developed for continuously distributed statistics automatically applicable to the discrete case. Examples of familywise error rate and false discovery rate procedures are discussed and an application to linkage disequilibrium testing is given. Software for implementing the procedures is available. Copyright 2009, Oxford University Press.

Whitening, or sphering, is a common preprocessing step in statistical analysis to transform random variables to orthogonality. However, due to rotational freedom there are infinitely many possible whitening procedures. Consequently, there is a diverse range of sphering methods in use, for example based on principal component analysis (PCA), Cholesky matrix decomposition and zero-phase component analysis (ZCA), among others. Here we provide an overview of the underlying theory and discuss five natural whitening procedures. Subsequently, we demonstrate that investigating the cross-covariance and the cross-correlation matrix between sphered and original variables allows to break the rotational invariance and to identify optimal whitening transformations. As a result we recommend two particular approaches: ZCA-cor whitening to produce sphered variables that are maximally similar to the original variables, and PCA-cor whitening to obtain sphered variables that maximally compress the original variables., Comment: 14 pages, 2 tables

Previous studies have raised concerns about possible excess risks of bladder, brain and hepatobiliary cancers and leukaemias near landfill sites. Several cancers have been implicated, but no consistent pattern has emerged. We present a large nationwide analysis of selected cancers near landfill sites in Great Britain. The base population comprised people living within 2 km of 9565 (from a total of 19 196) landfill sites that were operational at some time from 1982 to 1997, with populations living more than 2 km from a landfill as reference. Risks of cancers at the above sites were computed with adjustment for age, sex, year of diagnosis, region and deprivation. National post-coded registers provided a total of 341 856 640 person–years for the adult cancer analyses and 113 631 443 person–years for childhood leukaemia. There were 89 786 cases of bladder cancer, 36 802 cases of brain cancer, 21 773 cases of hepatobiliary cancer, 37 812 cases of adult leukaemia and 3973 cases of childhood leukaemia. In spite of the very large scale of this national study, we found no excess risks of cancers of the bladder and brain, hepatobiliary cancer or leukaemia, in populations living within 2 km of landfill sites. The results were similar if the analysis were restricted to landfill sites licensed to carry special (hazardous) waste. Our results do not support suggestions of excess risks of cancer associated with landfill sites reported in other studies. British Journal of Cancer (2002) 86, 1732–1736. doi:10.1038/sj.bjc.6600311 www.bjcancer.com © 2002 Cancer Research UK

Background RNA Biology A common and important aim in the field of genomics is the characterization of populations of RNA molecules. Investigators within the field typically wish to uncover the sequence and concentration of each RNA in a set of samples, either as an objective in its own right or as an early step in a larger analysis pipeline. Later steps might include the identification of differentially expressed genes between treatment and control groups, the clustering of genes into sets sharing putative, common regulatory pathways, or the association of genomic polymorphisms with patterns of expression. Roughly 4% of the RNAs in a typical unprocessed RNA sample consists of messenger RNAs (mRNAs), which code for proteins. Non-coding RNAs largely comprise ribosomal and transfer RNAs, which are involved in protein synthesis but do not code for proteins themselves. The remainder of the non-coding RNAs include a set of less abundant types of molecules with diverse functions. As a result of their direct role in protein synthesis, mRNAs have been in the limelight of genomic research. Protein-coding genes are transcribed by RNA polymerase from their 5′ (upstream) end to their 3′ (downstream) end to produce pre-mRNA. As this process takes place, certain regions may be spliced out from the pre-mRNA and discarded, leaving behind only an mRNA sequence of connected exons, known as an isoform. Multiple combinations of exons may be produced, which is known as alternative splicing, and different isoforms may have different 5′ and 3′ transcript start and end sites. This allows a single gene to produce multiple distinct transcripts and contributes to the phenotypic complexity of eukaryotes. The collection of possible transcripts produced by a single gene is known as the gene model.

This paper concerns several important points when testing for Hardy-Weinberg equilibrium (HWE) and linkage disequilibrium (LD) in genetics. First, we challenge the necessity of using exclusively two-sided tests for LD. Next, we show that the exact 2-sided tests based on the most popular measures of LD are not equivalent, and neither are the standard statistical tests even though the 1-sided tests are equivalent. We show how this results in different inference about LD for two data sets consisting of small groups of markers. Finally, we advocate the use of the conditional p-value for both LD and HWE testing. An important advantage of this p-value is that equivalent 1-sided tests are transformed into equivalent 2-sided tests.

Affymetrix has recently developed whole-transcript GeneChips-'Gene' and 'Exon' arrays-which interrogate exons along the length of each gene. Although each probe on these arrays is intended to hybridize perfectly to only one transcriptional target, many probes match multiple transcripts located in different parts of the genome or alternative isoforms of the same gene. Existing statistical methods for estimating expression do not take this into account and are thus prone to producing inflated estimates. We propose a method, Multi-Mapping Bayesian Gene eXpression (MMBGX), which disaggregates the signal at 'multi-match' probes. When applied to Gene arrays, MMBGX removes the upward bias of gene-level expression estimates. When applied to Exon arrays, it can further disaggregate the signal between alternative transcripts of the same gene, providing expression estimates of individual splice variants. We demonstrate the performance of MMBGX on simulated data and a tissue mixture data set. We then show that MMBGX can estimate the expression of alternative isoforms within one experimental condition, confirming our results by RT-PCR. Finally, we show that our method for detecting differential splicing has a lower error rate than standard exonlevel approaches on a previously validated colon cancer data set. © The Author(s) 2009. Published by Oxford University Press. EU (grant FP6-36495); BBSRC (grants BBG0003521 and BBC5196701). Funding for open access charge: BBSRC.

We review the use of Bayesian methods for analyzing gene expression data. We focus on methods which select groups of genes on the basis of their expression in RNA samples derived under different experimental conditions. We first describe Bayesian methods for estimating gene expression level from the intensity measurements obtained from analysis of microarray images. We next discuss the issues involved in assessing differential gene expression between two conditions at a time, including models for classifying the genes as differentially expressed or not. In the last two sections, we present models for grouping gene expression profiles over different experimental conditions, in order to find co-expressed genes, and multivariate models for finding gene signatures, i.e. for selecting a parsimonious group of genes that discriminate between entities such as subtypes of disease.

Background Gene Ontology (GO) terms are often used to assess the results of microarray experiments. The most common way to do this is to perform Fisher's exact tests to find GO terms which are over-represented amongst the genes declared to be differentially expressed in the analysis of the microarray experiment. However, due to the high degree of dependence between GO terms, statistical testing is conservative, and interpretation is difficult. Results We propose testing groups of GO terms rather than individual terms, to increase statistical power, reduce dependence between tests and improve the interpretation of results. We use the publicly available package POSOC to group the terms. Our method finds groups of GO terms significantly over-represented amongst differentially expressed genes which are not found by Fisher's tests on individual GO terms. Conclusion Grouping Gene Ontology terms improves the interpretation of gene set enrichment for microarray data.

We present a Bayesian hierarchical model for detecting differentially expressing genes that includes simultaneous estimation of array effects, and show how to use the output for choosing lists of genes for further investigation. We give empirical evidence that expression-level dependent array effects are needed, and explore different nonlinear functions as part of our model-based approach to normalization. The model includes gene-specific variances but imposes some necessary shrinkage through a hierarchical structure. Model criticism via posterior predictive checks is discussed. Modeling the array effects (normalization) simultaneously with differential expression gives fewer false positive results. To choose a list of genes, we propose to combine various criteria (for instance, fold change and overall expression) into a single indicator variable for each gene. The posterior distribution of these variables is used to pick the list of genes, thereby taking into account uncertainty in parameter estimates. In an application to mouse knockout data, Gene Ontology annotations over- and underrepresented among the genes on the chosen list are consistent with biological expectations.

We consider the consequences of an observed Cosmic Microwave Background (CMB) temperature anisotropy spectrum containing no secondary oscillations. While such a spectrum is generally considered to be a robust signature of active structure formation, we show that such a spectrum {\em can} be produced by (very unusual) inflationary models or other passive evolution models. However, we show that for all these passive models the characteristic oscillations would show up in other observable spectra. Our work shows that when CMB polarization and matter power spectra are taken into account secondary oscillations are indeed a signature of even these very exotic passive models. We construct a measure of the observability of secondary oscillations in a given experiment, and show that even with foregrounds both the MAP and \pk satellites should be able to distinguish between models with and without oscillations. Thus we conclude that inflationary and other passive models can {\em not} evade the secondary oscillation test., Final version accepted for publication in PRD. Minor improvements have been made to the discussion and new data has been included. The conclusions are unchagned

In this paper we propose a new statistic capable of detecting non-Gaussianity in the CMB. The statistic is defined in Fourier space, and therefore naturally separates angular scales. It consists of taking another Fourier transform, in angle, over the Fourier modes within a given ring of scales. Like other Fourier space statistics, our statistic outdoes more conventional methods when faced with combinations of Gaussian processes (be they noise or signal) and a non-Gaussian signal which dominates only on some scales. However, unlike previous efforts along these lines, our statistic is successful in recognizing multiple non-Gaussian patterns in a single field. We discuss various applications, in which the Gaussian component may be noise or primordial signal, and the non-Gaussian component may be a cosmic string map, or some geometrical construction mimicking, say, small scale dust maps., 8 pages, 14 figures Corrected typos

We present a Bayesian hierarchical model for detecting differentially expressed genes using a mixture prior on the parameters representing differential effects. We formulate an easily interpretable 3-component mixture to classify genes as over-expressed, under-expressed and non-differentially expressed, and model gene variances as exchangeable to allow for variability between genes. We show how the proportion of differentially expressed genes, and the mixture parameters, can be estimated in a fully Bayesian way, extending previous approaches where this proportion was fixed and empirically estimated. Good estimates of the false discovery rates are also obtained.Different parametric families for the mixture components can lead to quite different classifications of genes for a given data set. Using Affymetrix data from a knock out and wildtype mice experiment, we show how predictive model checks can be used to guide the choice between possible mixture priors. These checks show that extending the mixture model to allow extra variability around zero instead of the usual point mass null fits the data better.A software package for R is available.