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.

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.

Large numbers of explanatory variables: a probabilistic assessment.

Recently, Cox and Battey (2017 Proc. Natl Acad. Sci. USA114, 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.

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.

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.

Statistical thinking for 21st century scientists.

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.

Direction of association between bite wounds and Mycobacterium bovis infection in badgers: implications for transmission.

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.

Herd-level risk factors of bovine tuberculosis in England and Wales after the 2001 foot-and-mouth disease epidemic.

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.

Lung transplantation for cystic fibrosis.

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.

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.

The prevalence, distribution and severity of detectable pathological lesions in badgers naturally infected with Mycobacterium bovis.

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.

Impacts of widespread badger culling on cattle tuberculosis: concluding analyses from a large-scale field trial.

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