Large numbers of explanatory variables, a semi-descriptive analysis.

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.

Big data: Some statistical issues.

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.

A potassium channel mutation in weaver mice implicates membrane excitability in granule cell differentiation.

Early events in neuronal differentiation are generally considered to be regulated by factors independent of alterations in membrane permeability. Weaver mice harbour a mutation that blocks neuronal differentiation just after cessation of cell division, prior to cell migration and synaptogenesis. Cerebellar granule cells in homozygous weaver mice fail to differentiate, either because intrinsic cues are absent or because the granule cells are unable to respond to those cues. We now report that weaver mice have a missense mutation in a gene encoding a G-protein coupled inward rectifier potassium channel. The mutation alters the putative ion-permeable, pore-forming domain of the protein, suggesting that granule cell differentiation is regulated by changes in membrane permeability.

Regression Reconstruction from a Retrospective Sample.

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.

Missing observations in regression: a conditional approach.

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.

Positive and negative effects of widespread badger culling on tuberculosis in cattle.

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.

Stem cell deficiencies and thymic abnormalities in fetal mouse trisomy 16.

Mouse fetuses with trisomy 16 have severe abnormalities of several hematopoietic stem cell and precursor populations. The thymus is extremely hypoplastic, with a greater than or equal to 80% reduction in the number of thymocytes. This cellular deficiency appears to be the result of a deficiency in the number of precursor cells in the early thymus, since the rate of proliferation of thymocytes in explanted day-14 thymuses was normal. However, the functional maturation of thymocytes was delayed in vitro in day-17 organ explants, although the maximal response to the mitogenic and interleukin 2-stimulating effects of concanavalin A are quantitatively normal. B cells and pre-B cells in the fetal liver were moderately decreased, but the ability of fetal liver cells to be transformed by Abelson murine leukemia virus was nearly totally lost. There were also significant relative and absolute decreases in the number of spleen, culture, and erythroid colony-forming units (CFU-S, CFU-C, CFU-E) and of erythroid burst-forming units (BFU-E) in the trisomic liver, and the trisomic animals were anemic with small spleens and livers. However, unlike other genetically caused anemias, there was no reduction in the number of germ cells. The hematopoietic abnormalities in the trisomy 16 mouse, involving the lymphoid, myeloid, and erythroid cell lineages, are much more generalized than the abnormalities in any of the other described genetically caused immunodeficiencies or anemias in the mouse. They are also more severe than those in human trisomy 21 (Down syndrome), for which mouse trisomy 16 is a genetic model, but there does exist an interesting parallel between the thymic abnormalities in the two species.

Impact of localized badger culling on tuberculosis incidence in British cattle.

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.

Radiation hybrid mapping: a somatic cell genetic method for constructing high-resolution maps of mammalian chromosomes.

Radiation hybrid (RH) mapping, a somatic cell genetic technique, was developed as a general approach for constructing long-range maps of mammalian chromosomes. This statistical method depends on x-ray breakage of chromosomes to determine the distances between DNA markers, as well as their order on the chromosome. In addition, the method allows the relative likelihoods of alternative marker orders to be determined. The RH procedure was used to map 14 DNA probes from a region of human chromosome 21 spanning 20 megabase pairs. The map was confirmed by pulsed-field gel electrophoretic analysis. The results demonstrate the effectiveness of RH mapping for constructing high-resolution, contiguous maps of mammalian chromosomes.

Gene encoding the beta subunit of S100 protein is on chromosome 21: implications for Down syndrome.

S100 protein is a calcium-binding protein found predominantly in the vertebrate nervous system. Genomic and complementary DNA probes were used in conjunction with a panel of rodent-human somatic cell hybrids to assign the gene for the beta subunit of S100 protein to the distal half of the long arm of human chromosome 21. This gene was identified as a candidate sequence which, when expressed in the trisomic state, may underlie the neurologic disturbances in Down syndrome.

An apolipoprotein influencing triglycerides in humans and mice revealed by comparative sequencing.

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.

Human homolog of patched, a candidate gene for the basal cell nevus syndrome.

The basal cell nevus syndrome (BCNS) is characterized by developmental abnormalities and by the postnatal occurrence of cancers, especially basal cell carcinomas (BCCs), the most common human cancer. Heritable mutations in BCNS patients and a somatic mutation in a sporadic BCC were identified in a human homolog of the Drosophila patched (ptc) gene. The ptc gene encodes a transmembrane protein that in Drosophila acts in opposition to the Hedgehog signaling protein, controlling cell fates, patterning, and growth in numerous tissues. The human PTC gene appears to be crucial for proper embryonic development and for tumor suppression.

Mutations in the gene encoding cystatin B in progressive myoclonus epilepsy (EPM1)

Progressive myoclonus epilepsy of the Unverricht-Lundborg type (EPM1) is an autosomal recessive inherited form of epilepsy, previously linked to human chromosome 21q22.3. The gene encoding cystatin B was shown to be localized to this region, and levels of messenger RNA encoded by this gene were found to be decreased in cells from affected individuals. Two mutations, a 3' splice site mutation and a stop codon mutation, were identified in the gene encoding cystatin B in EPM1 patients but were not present in unaffected individuals. These results provide evidence that mutations in the gene encoding cystatin B are responsible for the primary defect in patients with EPM1.

Blocks of limited haplotype diversity revealed by high-resolution scanning of human chromosome 21.

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.

Social group size affects Mycobacterium bovis infection in European badgers (Meles meles).

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 in cattle and badgers in localized culling areas.

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.

On the linear in probability model for binary data.

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.

Functional effects of the mouse weaver mutation on G protein-gated inwardly rectifying K+ channels.

The weaver mutation corresponds to a substitution of glycine to serine in the H5 region of a G protein-gated inwardly rectifying K+ channel gene (GIRK2). By studying mutant GIRK2 weaver homomultimeric channels and heteromultimeric channels comprised of GIRK2 weaver and GIRK1 in Xenopus oocytes, we found that GIRK2 weaver homomultimeric channels lose their selectivity for K+ ions, giving rise to inappropriate receptor-activated and basally active Na+ currents, whereas heteromultimers of GIRK2 weaver and GIRK1 appeared to have reduced current. Immunohistochemical localization indicates that GIRK2 and GIRK1 proteins are expressed in the cerebellar neurons of mice at postnatal day 4, at a time when these neurons normally undergo differentiation. Thus, the aberrant behavior of mutant GIRK2 weaver channels could affect the development of weaver mice in at least two distinct ways.

Human GAP-43: its deduced amino acid sequence and chromosomal localization in mouse and human.

The growth-associated protein (GAP-43) is considered a crucial component of an effective regenerative response in the nervous system. Its phosphorylation by protein kinase C correlates with long-term potentiation. Sequence analysis of human cDNAs coding for this protein shows that the human GAP-43 gene is highly homologous to the rat gene; this homology extends into the 3'-untranslated region. However, the human protein contains a 10 amino acid insert. Somatic cell hybrids demonstrate localization of the GAP-43 gene to human chromosome 3 and to mouse chromosome 16.