Search

This note presents an alternative to multiple imputation and other approaches to regression analysis in the presence of missing covariate data. Our recommendation, based on factorial and fractional factorial arrangements, is more faithful to ancillarity considerations of regression analysis and involves assessing the sensitivity of inference on each regression parameter to missingness in each of the explanatory variables. The ideas are illustrated on a medical example concerned with the success of hematopoietic stem cell transplantation in children, and on a sociological example concerned with socio-economic inequalities in educational attainment., (© 2023 The Authors.)

The simplest form of retrospective study allows the reconstruction of the dependence between a binary outcome, Y , representing the contrast between cases and controls, and one or more explanatory variables. A different objective for such situations is considered, in which there are distinct explanatory variables, say ( W , X ) determining Y . Reconstruction of the originating distribution of ( W , X ) from the case-control data is considered for both continuous and binary variables. Emphasis is on the linear regression coefficient of W on X . That coefficient, but not the relevant intercept, shows considerable stability, as shown by theory and simulations. An approximation to the value of the coefficient not conditioning on Y is given., (© 2020 The Author(s).)

The analysis of binary response data commonly uses models linear in the logistic transform of probabilities. This paper considers some of the advantages and disadvantages of simple least-squares estimates based on a linear representation of the probabilities themselves, this in particular sometimes allowing a more direct empirical interpretation of underlying parameters. A sociological study is used in illustration., Competing Interests: The authors confirm that there are no competing interests.

Recently, Cox and Battey (2017 Proc. Natl Acad. Sci. USA 114 , 8592-8595 (doi:10.1073/pnas.1703764114)) outlined a procedure for regression analysis when there are a small number of study individuals and a large number of potential explanatory variables, but relatively few of the latter have a real effect. The present paper reports more formal statistical properties. The results are intended primarily to guide the choice of key tuning parameters.

A broad review is given of the impact of big data on various aspects of investigation. There is some but not total emphasis on issues in epidemiological research.

Data with a relatively small number of study individuals and a very large number of potential explanatory features arise particularly, but by no means only, in genomics. A powerful method of analysis, the lasso [Tibshirani R (1996) J Roy Stat Soc B 58:267-288], takes account of an assumed sparsity of effects, that is, that most of the features are nugatory. Standard criteria for model fitting, such as the method of least squares, are modified by imposing a penalty for each explanatory variable used. There results a single model, leaving open the possibility that other sparse choices of explanatory features fit virtually equally well. The method suggested in this paper aims to specify simple models that are essentially equally effective, leaving detailed interpretation to the specifics of the particular study. The method hinges on the ability to make initially a very large number of separate analyses, allowing each explanatory feature to be assessed in combination with many other such features. Further stages allow the assessment of more complex patterns such as nonlinear and interactive dependences. The method has formal similarities to so-called partially balanced incomplete block designs introduced 80 years ago [Yates F (1936) J Agric Sci 26:424-455] for the study of large-scale plant breeding trials. The emphasis in this paper is strongly on exploratory analysis; the more formal statistical properties obtained under idealized assumptions will be reported separately., Competing Interests: The authors declare no conflict of interest.

Statistical science provides a wide range of concepts and methods for studying situations subject to unexplained variability. Such considerations enter fields ranging from particle physics and astrophysics to genetics, sociology and economics, and beyond; to associated areas of application such as engineering, agriculture, and medicine, in particular in clinical trials. Successful application hinges on absorption of statistical thinking into the subject matter and, hence, depends strongly on the field in question and on the individual investigators. It is the job of theoretical statisticians both to be alive to the challenges of specific applications and, at the same time, to develop methods and concepts that, with good fortune, will be broadly applicable.

Background: Badgers are involved in the transmission to cattle of bovine tuberculosis (TB), a serious problem for the UK farming industry. Cross-sectional studies have shown an association between bite wounds and TB infection in badgers which may have implications for M. bovis transmission and control, although the sequence of these two events is unclear. Transmission during aggressive encounters could potentially reduce the effectiveness of policies which increase the average range of a badger and thus its opportunities for interaction with other social groups., Methods: Data were obtained on badgers captured during a long term study at Woodchester Park, UK (1998-2006). Many badgers had multiple observations. At each observation, the badger was assigned a "state" depending on presence of bite wounds and/or TB infection. Hence each badger had a "transition" from the previous state to the current state. We calculated the numbers of each type of transition and the time spent in each state. Transition rates were calculated for each transition category, dividing the number of such transitions by the total time at risk. We compared the rate of bite wound acquisition in infected badgers with that for uninfected badgers and the rate of positive M.bovis test results in bitten badgers with that in unbitten badgers., Results: The rate of bite wound acquisition in infected badgers (0.291 per year) was 2.09 (95% CI: 1.41, 3.08) times that in uninfected badgers (0.139 per year). The rate of positive M.bovis test results in bitten badgers (0.097 per year) was 2.45 (95% CI: 1.29, 4.65) times that in unbitten badgers (0.040 per year)., Conclusions: We found strong evidence of both potential sequences of events consistent with transmission via bite wounds and distinctive behaviour in infected badgers. The complex relationship between behaviour and infection must be considered when planning TB control strategies.

Objectives: We present the results of a 2005 case-control study of bovine tuberculosis (bTB) breakdowns in English and Welsh herds. The herd management, farming practices, and environmental factors of 401 matched pairs of case and control herds were investigated to provide a picture of herd-level risk factors in areas of varying bTB incidence., Methods: A global conditional logistic regression model, with region-specific variants, was used to compare case herds that had experienced a confirmed bTB breakdown to contemporaneous control herds matched on region, herd type, herd size, and parish testing interval., Results: Contacts with cattle from contiguous herds and sourcing cattle from herds with a recent history of bTB were associated with an increased risk in both the global and regional analyses. Operating a farm over several premises, providing cattle feed inside the housing, and the presence of badgers were also identified as significantly associated with an increased bTB risk., Conclusions: Steps taken to minimize cattle contacts with neighboring herds and altering trading practices could have the potential to reduce the size of the bTB epidemic. In principle, limiting the interactions between cattle and wildlife may also be useful; however this study did not highlight any specific measures to implement., (Copyright © 2011 International Society for Infectious Diseases. All rights reserved.)

Lung transplantation is a complex, high-risk, potentially life-saving therapy for the end-stage lung disease of cystic fibrosis (CF). The decision to pursue transplantation involves comparing the likelihood of survival with and without transplantation as well as assessing the effect of wait-listing and transplantation on the patient's quality of life. Although recent population-based analyses of the US lung allocation system for the CF population have raised controversies about the survival benefits of transplantation, studies from the United Kingdom and Canada have suggested a definite survival advantage for those receiving transplants. In response to these and other controversies, leaders in transplantation and CF met together in Lansdowne, Virginia, to consider the state of the art in lung transplantation for CF in an international context, focusing on advances in surgical technique, measurement of outcomes, use of prognostic criteria, variations in local control over listing, and prioritization among the United States, Canada, the United Kingdom, and The Netherlands, patient adherence before and after transplantation and other issues in the broader context of lung transplantation. Finally, the conference members carefully considered how efforts to improve outcomes for lung transplantation for CF lung disease might best be studied. This Roundtable seeks to communicate the substance of our discussions.

1. In most social animals, the prevalence of directly transmitted pathogens increases in larger groups and at higher population densities. Such patterns are predicted by models of Mycobacterium bovis infection in European badgers (Meles meles). 2. We investigated the relationship between badger abundance and M. bovis prevalence, using data on 2696 adult badgers in 10 populations sampled at the start of the Randomized Badger Culling Trial. 3. M. bovis prevalence was consistently higher at low badger densities and in small social groups. M. bovis prevalence was also higher among badgers whose genetic profiles suggested that they had immigrated into their assigned social groups. 4. The association between high M. bovis prevalence and small badger group size appeared not to have been caused by previous small-scale culling in study areas, which had been suspended, on average, 5 years before the start of the current study. 5. The observed pattern of prevalence might occur through badgers in smaller groups interacting more frequently with members of neighbouring groups; detailed behavioural data are needed to test this hypothesis. Likewise, longitudinal data are needed to determine whether the size of infected groups might be suppressed by disease-related mortality. 6. Although M. bovis prevalence was lower at high population densities, the absolute number of infected badgers was higher. However, this does not necessarily mean that the risk of M. bovis transmission to cattle is highest at high badger densities, since transmission risk depends on badger behaviour as well as on badger density.

Bovine tuberculosis (TB) is a zoonotic disease that can have serious consequences for cattle farming and, potentially, for public health. In Britain, failure to control bovine TB has been linked to persistent infection of European badger (Meles meles) populations. However, culling of badgers in the vicinity of recent TB outbreaks in cattle has failed to reduce the overall incidence of cattle TB. Using data from a large-scale study conducted in 1998-2005, we show that badgers collected on such localized culls had elevated prevalence of Mycobacterium bovis, the causative agent of bovine TB, suggesting that infections in cattle and badgers were indeed associated. Moreover, there was a high degree of similarity in the M. bovis strain types isolated from cattle and associated badgers. This similarity between strain types appeared to be unaffected by time lags between the detection of infection in cattle and culling of badgers, or by the presence of purchased cattle that might have acquired infection elsewhere. However, localized culling appeared to prompt an increase in the prevalence of M. bovis infection in badgers, probably by disrupting ranging and territorial behavior and hence increasing intraspecific transmission rates. This elevated prevalence among badgers could offset the benefits, for cattle, of reduced badger densities and may help to explain the failure of localized culling to reduce cattle TB incidence.

The Randomized Badger Culling Trial (RBCT) began in 1998 to determine the impact of badger culling in controlling bovine tuberculosis in cattle. A total of 1166 badgers (14% of total) proactively culled during the RBCT were found to be tuberculous, offering a unique opportunity to study the pathology caused by Mycobacterium bovis in a large sample of badgers. Of these, 39% of adults (approximately 6% of all adults culled) had visible lesions (detectable at necropsy) of bovine tuberculosis; cubs had a lower prevalence of infection (9%) but a higher percentage of tuberculous cubs (55.5%) had visible lesions. Only approximately 1% of adult badgers had extensive, severe pathology. Tuberculous badgers with recorded bite wounds (approximately 5%) had a higher prevalence of visible lesions and a different distribution of lesions, suggesting transmission via bite wounds. However, the predominance of lesions in the respiratory tract indicates that most transmission occurs by the respiratory route.

Background: Bovine tuberculosis (TB) has re-emerged as a major problem for British cattle farmers. Failure to control the infection has been linked to transmission from European badgers; badger culling has therefore formed a component of British TB control policy since 1973., Objectives and Design: To investigate the impact of repeated widespread badger culling on cattle TB, the Randomised Badger Culling Trial compared TB incidence in cattle herds in and around ten culling areas (each 100 km2) with those in and around ten matched unculled areas., Results: Overall, cattle TB incidence was 23.2% lower (95% confidence interval (CI) 12.4-32.7% lower) inside culled areas, but 24.5% (95% CI 0.6% lower-56.0% higher) higher on land

Human and livestock diseases can be difficult to control where infection persists in wildlife populations. For three decades, European badgers (Meles meles) have been culled by the British government in a series of attempts to limit the spread of Mycobacterium bovis, the causative agent of bovine tuberculosis (TB), to cattle. Despite these efforts, the incidence of TB in cattle has risen consistently, re-emerging as a primary concern for Britain's cattle industry. Recently, badger culling has attracted controversy because experimental studies have reached contrasting conclusions (albeit using different protocols), with culled areas showing either markedly reduced or increased incidence of TB in cattle. This has confused attempts to develop a science-based management policy. Here we use data from a large-scale, randomized field experiment to help resolve these apparent differences. We show that, as carried out in this experiment, culling reduces cattle TB incidence in the areas that are culled, but increases incidence in adjoining areas. These findings are biologically consistent with previous studies but will present challenges for policy development.

As an aid to the study of bovine tuberculosis (TB), a simple model has been developed of an epidemic involving two species, cattle and badgers. Each species may infect the other. The proportion of animals affected is assumed relatively small so that the usual nonlinear aspects of epidemic theory are avoided. The model is used to study the long-run and transient effect on cattle of culling badgers and the effect of a period without routine testing for TB, such as occurred during the 2001 epidemic of foot-and-mouth disease in Great Britain. Finally, by examining the changes in cattle TB over the last 15 years, and with some other working assumptions, it is estimated that the net reproduction number of the epidemic is approximately 1.1. The implications for controlling the disease are discussed.

During the course of an epidemic of a potentially fatal disease, it is important that the case fatality ratio be well estimated. The authors propose a novel method for doing so based on the Kaplan-Meier survival procedure, jointly considering two outcomes (death and recovery), and evaluate its performance by using data from the 2003 epidemic of severe acute respiratory syndrome in Hong Kong, People's Republic of China. They compare this estimate obtained at various points in the epidemic with the case fatality ratio eventually observed; with two commonly quoted, naïve estimates derived from cumulative incidence and mortality statistics at single time points; and with estimates in which a parametric mixture model is used. They demonstrate the importance of patient characteristics regarding outcome by analyzing subgroups defined by age at admission to the hospital.

Social class differentials in educational attainment have been extensively studied in numerous countries. In this paper, we begin by examining class differentials in the progression to higher secondary education among 16-year-old children in England and Wales. As has been shown for other countries, the differentials result both from the primary effects of differing levels of academic performance of children of different class background and from the secondary effects of differences in the educational choices that these children make at given levels of performance. Through counterfactual analyses in which the performance distribution of one class is combined with the choice distribution of another, primary and secondary effects are decomposed and the former are shown to be roughly three times the size of the latter.

Suppose measurements of a particular feature are collected at baseline and at a number of subsequent time points and that for each individual there is a roughly linear trend in time. This paper takes three approaches to testing whether there is a relation between the initial value and the slope. It also considers whether the initial value for an individual is a useful predictor of the slope for that individual. The problems are formulated in terms of regression models with random coefficients. The solutions are illustrated using data from an observational study of clinical correlates of disability and progression in Huntington's disease.

A case-control study of the factors associated with the risk of a bovine tuberculosis (TB) breakdown in cattle herds was undertaken within the randomized badger culling trial (RBCT). TB breakdowns occurring prior to the 2001 foot-and-mouth disease epidemic in three RBCT triplets were eligible to be cases; controls were selected from the same RBCT area. Data from 151 case farms and 117 control farms were analysed using logistic regression. The strongest factors associated with an increased TB risk were movement of cattle onto the farm from markets or farm sales, operating a farm over multiple premises and the use of either covered yard or 'other' housing types. Spreading artificial fertilizers or farmyard manure on grazing land were both associated with decreased risk. These first case-control results from the RBCT will be followed by similar analyses as more data become available.

Simple tests are given for consistency of the data with additive and with multiplicative effects of two risk factors on a binary outcome. A combination of the procedures will show whether data are consistent with neither, one or both of the models of no additive or no multiplicative interaction. Implications for the size of the study needed to detect differences between the models are also addressed. Because of the simple form of the test statistics, combination of evidence from different studies or strata is straightforward. Illustration of how the method could be extended to data from a 2xRxC table is also given.

The application of regular herd testing to identify and remove infected animals has proved to be a highly successful method of controlling bovine tuberculosis (TB) in many parts of the world. However, in some countries, notably the United Kingdom, Ireland and New Zealand, the disease has continued to pose a significant problem, despite intensive herd testing. Persistence of disease in these countries is associated with the presence of wildlife reservoirs of infection. Attempts to control bovine TB by culling of wildlife have been, at best, only partially successful and have proved difficult to sustain. This has led to considering of vaccination either of wildlife or cattle as a potential control measure. However, there are a number of obstacles that need to be overcome before vaccination can be considered a practical option. Vaccine efficacy, methods used for vaccine delivery in wildlife, potential interference of vaccination with diagnostic tests for cattle and appropriate design of field trials are among the issues that need to be addressed.

Pathogens that are transmitted between wildlife, livestock and humans present major challenges for the protection of human and animal health, the economic sustainability of agriculture, and the conservation of wildlife. Mycobacterium bovis, the aetiological agent of bovine tuberculosis (TB), is one such pathogen. The incidence of TB in cattle has increased substantially in parts of Great Britain in the past two decades, adversely affecting the livelihoods of cattle farmers and potentially increasing the risks of human exposure. The control of bovine TB in Great Britain is complicated by the involvement of wildlife, particularly badgers (Meles meles), which appear to sustain endemic infection and can transmit TB to cattle. Between 1975 and 1997 over 20,000 badgers were culled as part of British TB control policy, generating conflict between conservation and farming interest groups. Here we present results from a large-scale field trial that indicate that localized badger culling not only fails to control but also seems to increase TB incidence in cattle.

This paper deals with the synthesis of information from different studies when there is lack of independence in some of the contrasts to be combined. This problem can arise in several different situations in both case-control studies and clinical trials. For efficient estimation we appeal to the method of generalized least squares to estimate the summary effect and its standard error. This method requires estimates of the covariances between those contrasts that are not independent. Although it is not possible to estimate the covariance between effects that have been adjusted for confounding factors we present a method for finding upper and lower bounds for this covariance. In the simplest discussion homogeneity of the relative risks is assumed but the method is then extended to allow for heterogeneity in an overall estimate. We then illustrate the method with several examples from an analysis in which case-control studies of cervical cancer and oral contraceptive use are synthesized.

Some of the many statistical aspects of floods are discussed and some new results are given on a number of features. The probability theory of extreme values is briefly reviewed and its potential for applications outlined. The peaks-over-threshold method of estimation is compared with the direct use of annual maxima and some theoretical comparisons of efficiency are given. The effect of trend on the distribution of maxima is analysed in terms of a simple theoretical model distinguishing the effects of trend in mean level and of trend in dispersion. An empirical Bayes method for pooling information from a number of sources is described and illustrated, and related to the procedures recommended in the Flood estimation handbook. In the final section, a range of further issues is outlined.

Background: Several studies implicate polymorphisms in the human beta-adrenergic receptor gene (ADRB2) in the susceptibility to hypertension. We sought to replicate these results in a population of Chinese origin primarily from Taiwan and the San Francisco Bay area., Methods: We genotyped >800 hypertensive subjects and individuals with low-normal blood pressure that were derived largely from the same families as the hypertensive patients for three polymorphisms in the ADRB2 gene: a C/T transition at position 47 (C-47T) in the 5' leader cistron; another C/T transition that results in a glycine/ arginine substitution at codon 16 (Gly16Arg), and a G/C transversion that causes a glutamate/glutamine substitution at codon 27 (Glu27Gln)., Results: The Gly16Arg was significantly associated with hypertension (P < .03). Under a dominant model, for hypertension the relative risk for the Gly/Gly and Gly/Arg genotypes versus the Arg/Arg genotype was 1.35 (95% confidence limits [CL] 1.08, 1.70); for low-normal blood pressure the relative risk was 0.79 (95% CL 0.66, 0.94). This polymorphism explained approximately 1% of the variance in systolic and diastolic blood pressures in our study population. There was no evidence of association between the C-47T and Glu27Gln polymorphisms and hypertension in this population., Conclusions: The Glyl6 allele in the beta2-adrenergic receptor gene is a susceptibility allele for essential hypertension in a population of Chinese origin.

Global patterns of human DNA sequence variation (haplotypes) defined by common single nucleotide polymorphisms (SNPs) have important implications for identifying disease associations and human traits. We have used high-density oligonucleotide arrays, in combination with somatic cell genetics, to identify a large fraction of all common human chromosome 21 SNPs and to directly observe the haplotype structure defined by these SNPs. This structure reveals blocks of limited haplotype diversity in which more than 80% of a global human sample can typically be characterized by only three common haplotypes.

The mineralocorticoid hormone, aldosterone, is known to play a role in sodium homeostasis. We serendipitously found, however, highly significant association between single-nucleotide polymorphisms in the aldosterone synthase gene and plasma glucose levels in a large population of Chinese and Japanese origin. Two polymorphisms--one in the putative promoter (T-344C) and another resulting in a lysine/arginine substitution at amino acid 173, which are in complete linkage disequilibrium in this population--were associated with fasting plasma glucose levels (P = 0.000017) and those 60 (P = 0.017) and 120 (P = 0.0019) min after an oral glucose challenge. A C/T variant in intron 1, between these polymorphisms, was not associated with glucose levels. Arg-173 and -344C homozygotes were most likely to be diabetic [odds ratio 2.51; 95% confidence interval (C.I.) 1.39-3.92; P = 0.0015] and have impaired fasting glucose levels (odds ratio 3.53; 95% C.I. 2.02-5.5; P = 0.0000036). These results suggest a new role for aldosterone in glucose homeostasis.

One approach to identify potentially important segments of the human genome is to search for DNA regions with nonrandom patterns of human sequence variation. Previous studies have investigated these patterns primarily in and around candidate gene regions. Here, we determined patterns of DNA sequence variation in 2.5 Mb of finished sequence from five regions on human chromosome 21. By sequencing 13 individual chromosomes, we identified 1460 single-nucleotide polymorphisms (SNPs) and obtained unambiguous haplotypes for all chromosomes. For all five chromosomal regions, we observed segments with high linkage disequilibrium (LD), extending from 1.7 to>81 kb (average 21.7 kb), disrupted by segments of similar or larger size with no significant LD between SNPs. At least 25% of the contig sequences consisted of segments with high LD between SNPs. Each of these segments was characterized by a restricted number of observed haplotypes,with the major haplotype found in over 60% of all chromosomes. In contrast, the interspersed segments with low LD showed significantly more haplotype patterns. The position and extent of the segments of high LD with restricted haplotype variability did not coincide with the location of coding sequences. Our results indicate that LD and haplotype patterns need to be investigated with closely spaced SNPs throughout the human genome, independent of the location of coding sequences, to reliably identify regions with significant LD useful for disease association studies.

Comparison of genomic DNA sequences from human and mouse revealed a new apolipoprotein (APO) gene (APOAV) located proximal to the well-characterized APOAI/CIII/AIV gene cluster on human 11q23. Mice expressing a human APOAV transgene showed a decrease in plasma triglyceride concentrations to one-third of those in control mice; conversely, knockout mice lacking Apoav had four times as much plasma triglycerides as controls. In humans, single nucleotide polymorphisms (SNPs) across the APOAV locus were found to be significantly associated with plasma triglyceride levels in two independent studies. These findings indicate that APOAV is an important determinant of plasma triglyceride levels, a major risk factor for coronary artery disease.

Comparison of human sequences with the DNA of other mammals is an excellent means of identifying functional elements in the human genome. Here we describe the utility of high-density oligonucleotide arrays as a rapid approach for comparing human sequences with the DNA of multiple species whose sequences are not presently available. High-density arrays representing approximately 22.5 Mb of nonrepetitive human chromosome 21 sequence were synthesized and then hybridized with mouse and dog DNA to identify sequences conserved between humans and mice (human-mouse elements) and between humans and dogs (human-dog elements). Our data show that sequence comparison of multiple species provides a powerful empiric method for identifying actively conserved elements in the human genome. A large fraction of these evolutionarily conserved elements are present in regions on chromosome 21 that do not encode known genes.

The kidney, by regulating the volume of fluid in the body, plays a key role in regulating blood pressure (BP). The kidney uses primarily sodium and, to a lesser extent, urea to maintain the appropriate volume of fluid. Genetic variation in proteins that determine sodium reabsorption and excretion is known to significantly influence BP. However, the influence of genetic variation in urea transporters on BP has not been examined. We determined therefore whether nucleotide variation in the kidney-specific human urea transporter, HUT2, is associated with variation in BP. After determining the genomic structure of the coding sequence, seven single nucleotide polymorphisms (SNPs) were identified. Two of the SNPs result in Val/Ile and Ala/Thr amino acid substitutions at positions 227 and 357 in the HUT2 open reading frame, respectively. Another SNP is silent and four others are in introns or the 3' untranslated region. Over 1000 hypertensive and low-normotensive individuals of Chinese origin were typed for five of these SNPs using a high-throughput genotyping method. The Ile227 and Ala357 alleles were associated with low diastolic BP in men but not women, with odds ratios 2.1 [95% confidence interval (CI) 1.5-2.7, P < 0.001] and 1.5 (95% CI 1.2-1.8, P < 0.001), respectively. There was a similar trend for systolic BP, and odds ratios for the Ile227 and Ala357 alleles were 1.7 (95% CI 1.2-2.3, P = 0.002) and 1.3 (95% CI 1.1-1.6, P = 0.007), respectively, in men.

To make large-scale association studies a reality, automated high-throughput methods for genotyping with single-nucleotide polymorphisms (SNPs) are needed. We describe PCR conditions that permit the use of the TaqMan or 5' nuclease allelic discrimination assay for typing large numbers of individuals with any SNP and computational methods that allow genotypes to be assigned automatically. To demonstrate the utility of these methods, we typed >1600 individuals for a G-to-T transversion that results in a glutamate-to-aspartate substitution at position 298 in the endothelial nitric oxide synthase gene, and a G/C polymorphism (newly identified in our laboratory) in intron 8 of the 11-beta hydroxylase gene. The genotyping method is accurate-we estimate an error rate of fewer than 1 in 2000 genotypes, rapid-with five 96-well PCR machines, one fluorescent reader, and no automated pipetting, over one thousand genotypes can be generated by one person in one day, and flexible-a new SNP can be tested for association in less than one week. Indeed, large-scale genotyping has been accomplished for 23 other SNPs in 13 different genes using this method. In addition, we identified three "pseudo-SNPs" (WIAF1161, WIAF2566, and WIAF335) that are probably a result of duplication.

The traditional exploration of large contingency tables leads to multiple comparisons with the inherent generation of chance associations. To allow for this, a simple empirical Bayesian approach is used here to derive estimates of association 'shrunk' towards a global mean. Estimates are displayed on ordered normal plots, to allow visual detection of outliers, with the addition of 'guide rails', derived from simulation, to facilitate their detection. The methods, and the interpretation of results, are illustrated using a large table of occupations for cancer registrations in England and Wales for 1971-90.

Some of the many ways in which mathematical biology and statistics have been used in investigating the acquired immunodeficiency syndrome (AIDS) epidemic are reviewed. Aspects of the spread of the disease via social and sexual networks are discussed. The different kinds of data involved are critically compared. Some studies of the incubation period are briefly reviewed and some comments made on the role of adherence to therapy.

A postal survey of British sheep farmers provided information on the proportion of farms that experienced their first case of scrapie in each year between 1962 and 1998. We found no evidence of a large increase in the proportion of scrapie-affected farms prior to, during or following the epidemic of BSE in British cattle. After correcting for between-farm heterogeneity in the probability of acquiring scrapie, we estimated the yearly between-flock force of infection since 1962. The current force of infection is estimated at approximately 0.0045 per farm per year and combined with a simple model of scrapie spread provides an estimate of the average duration of a scrapie outbreak on an individual farm. Considering all farms, the average outbreak lasts for five years, but if only those farms that have cases in animals born on the farm are considered, it lasts 15 years. We use these parameter estimates to compare the proportion of farms with scrapie in time periods of different lengths. In the survey, 2.7% of farms had a case in 1998. The 5.3% of farms reporting having a case between 1993 and 1997 is consistent with the hypothesis that the scrapie force of infection remained constant over this period.

We have constructed a physical map of the human genome by using a panel of 90 whole-genome radiation hybrids (the TNG panel) in conjunction with 40,322 sequence-tagged sites (STSs) derived from random genomic sequences as well as expressed sequences. Of 36,678 STSs on the TNG radiation hybrid map, only 3604 (9.8%) were absent from the unassembled draft sequence of the human genome. Of 20,030 STSs ordered on the TNG map as well as the assembled human genome draft sequence and the Celera assembled human genome sequence, 36% of the STSs had a discrepant order between the working draft sequence and the Celera sequence. The TNG map order was identical to one of the two sequence orders in 60% of these discrepant cases.

The human genome holds an extraordinary trove of information about human development, physiology, medicine and evolution. Here we report the results of an international collaboration to produce and make freely available a draft sequence of the human genome. We also present an initial analysis of the data, describing some of the insights that can be gleaned from the sequence.

The human genome is by far the largest genome to be sequenced, and its size and complexity present many challenges for sequence assembly. The International Human Genome Sequencing Consortium constructed a map of the whole genome to enable the selection of clones for sequencing and for the accurate assembly of the genome sequence. Here we report the construction of the whole-genome bacterial artificial chromosome (BAC) map and its integration with previous landmark maps and information from mapping efforts focused on specific chromosomal regions. We also describe the integration of sequence data with the map.

We have placed 7,600 cytogenetically defined landmarks on the draft sequence of the human genome to help with the characterization of genes altered by gross chromosomal aberrations that cause human disease. The landmarks are large-insert clones mapped to chromosome bands by fluorescence in situ hybridization. Each clone contains a sequence tag that is positioned on the genomic sequence. This genome-wide set of sequence-anchored clones allows structural and functional analyses of the genome. This resource represents the first comprehensive integration of cytogenetic, radiation hybrid, linkage and sequence maps of the human genome; provides an independent validation of the sequence map and framework for contig order and orientation; surveys the genome for large-scale duplications, which are likely to require special attention during sequence assembly; and allows a stringent assessment of sequence differences between the dark and light bands of chromosomes. It also provides insight into large-scale chromatin structure and the evolution of chromosomes and gene families and will accelerate our understanding of the molecular bases of human disease and cancer.

In this study we quantify the features of meiotic recombination on the long arm of human chromosome 21. We constructed a 67. 3-centimorgan (cM) high-resolution, comprehensive, and accurate genetic linkage map of chromosome 21q using 187 highly polymorphic markers covering almost the entire long arm; 46 loci, consisting of mutually recombining marker sets, were ordered with greater than 1000:1 odds and with average interlocus distance of 1.46 cM. These markers were used to accurately identify all exchanges in 186 female and 160 male meioses and to show (1) significant excess of recombination in female versus male meioses, (2) an overall decline in female:male recombination between the centromere and the telomere, (3) greater positive chiasma interference in male than in female meioses, and (4) lack of correlation between exchange frequency and parental age. By comparing the genetic map with the 21q sequence map, we show a general trend of increasing male, but near-constant female, recombination versus physical distance across 21q, explaining the gender-specific recombination effect. The recombination rate varies considerably between genders across 21q but is the greatest (eightfold) in the pericentromeric region, with a rate of approximately 250 kb/cM in females and approximately 2125 kb/cM in males. We used information on the locations of all exchanges to construct an empirical map function that confirms the statistical findings of positive interference. These analyses reveal that occurrence of recombination on 21q is not only gender-specific but also region-specific and that recombination suppression at the centromere is not universal. We also find evidence that male exchange location is highly correlated with gene density.