When trying to learn a model for the prediction of an outcome given a set of covariates, a statistician has many estimation procedures in their toolbox. A few examples of these candidate learners are: least squares, least angle regression, random forests, and spline regression. Previous articles (van der Laan and Dudoit (2003); van der Laan et al. (2006); Sinisi et al. (2007)) theoretically validated the use of cross validation to select an optimal learner among many candidate learners. Motivated by this use of cross validation, we propose a new prediction method for creating a weighted combination of many candidate learners to build the super learner. This article proposes a fast algorithm for constructing a super learner in prediction which uses V-fold cross-validation to select weights to combine an initial set of candidate learners. In addition, this paper contains a practical demonstration of the adaptivity of this so called super learner to various true data generating distributions. This approach for construction of a super learner generalizes to any parameter which can be defined as a minimizer of a loss function.

Certain respiratory tract infections are transmitted through air. Coughing and sneezing by an infected person can emit pathogen-containing particles with diameters less than 10 microm that can reach the alveolar region. Based on our analysis of the sparse literature on respiratory aerosols, we estimated that emitted particles quickly decrease in diameter due to water loss to one-half the initial values, and that in one cough the volume in particles with initial diameters less than 20 microm is 60 x 10(-8) mL. The pathogen emission rate from a source case depends on the frequency of expiratory events, the respirable particle volume, and the pathogen concentration in respiratory fluid. Viable airborne pathogens are removed by exhaust ventilation, particle settling, die-off, and air disinfection methods; each removal mechanism can be assigned a first-order rate constant. The pathogen concentration in well-mixed room air depends on the emission rate, the size distribution of respirable particles carrying pathogens, and the removal rate constants. The particle settling rate and the alveolar deposition fraction depend on particle size. Given these inputs plus a susceptible person's breathing rate and exposure duration to room air, an expected alveolar dosemicrois estimated. If the infectious dose is one organism, as appears to be true for tuberculosis, infection risk is estimated by the expression: R = 1-exp(-micro). Using published tuberculosis data concerning cough frequency, bacilli concentration in respiratory fluid, and die-off rate, we illustrate the model via a plausible scenario for a person visiting the room of a pulmonary tuberculosis case. We suggest that patients termed "superspreaders" or "dangerous disseminators" are those infrequently encountered persons with high values of cough and/or sneeze frequency, elevated pathogen concentration in respiratory fluid, and/or increased respirable aerosol volume per expiratory event such that their pathogen emission rate is much higher than average.

SummaryBackgroundDiarrhoea and growth faltering in early childhood are associated with subsequent adverse outcomes. We aimed to assess whether water quality, sanitation, and handwashing interventions alone or combined with nutrition interventions reduced diarrhoea or growth faltering.MethodsThe WASH Benefits Bangladesh cluster-randomised trial enrolled pregnant women from villages in rural Bangladesh and evaluated outcomes at 1-year and 2-years' follow-up. Pregnant women in geographically adjacent clusters were block-randomised to one of seven clusters: chlorinated drinking water (water); upgraded sanitation (sanitation); promotion of handwashing with soap (handwashing); combined water, sanitation, and handwashing; counselling on appropriate child nutrition plus lipid-based nutrient supplements (nutrition); combined water, sanitation, handwashing, and nutrition; and control (data collection only). Primary outcomes were caregiver-reported diarrhoea in the past 7 days among children who were in utero or younger than 3 years at enrolment and length-for-age Z score among children born to enrolled pregnant women. Masking was not possible for data collection, but analyses were masked. Analysis was by intention to treat. This trial is registered at ClinicalTrials.gov, number NCC01590095.FindingsBetween May 31, 2012, and July 7, 2013, 5551 pregnant women in 720 clusters were randomly allocated to one of seven groups. 1382 women were assigned to the control group; 698 to water; 696 to sanitation; 688 to handwashing; 702 to water, sanitation, and handwashing; 699 to nutrition; and 686 to water, sanitation, handwashing, and nutrition. 331 (6%) women were lost to follow-up. Data on diarrhoea at year 1 or year 2 (combined) were available for 14 425 children (7331 in year 1, 7094 in year 2) and data on length-for-age Z score in year 2 were available for 4584 children (92% of living children were measured at year 2). All interventions had high adherence. Compared with a prevalence of 5·7% (200 of 3517 child weeks) in the control group, 7-day diarrhoea prevalence was lower among index children and children under 3 years at enrolment who received sanitation (61 [3·5%] of 1760; prevalence ratio 0·61, 95% CI 0·46–0·81), handwashing (62 [3·5%] of 1795; 0·60, 0·45–0·80), combined water, sanitation, and handwashing (74 [3·9%] of 1902; 0·69, 0·53–0·90), nutrition (62 [3·5%] of 1766; 0·64, 0·49–0·85), and combined water, sanitation, handwashing, and nutrition (66 [3·5%] of 1861; 0·62, 0·47–0·81); diarrhoea prevalence was not significantly lower in children receiving water treatment (90 [4·9%] of 1824; 0·89, 0·70–1·13). Compared with control (mean length-for-age Z score −1·79), children were taller by year 2 in the nutrition group (mean difference 0·25 [95% CI 0·15–0·36]) and in the combined water, sanitation, handwashing, and nutrition group (0·13 [0·02–0·24]). The individual water, sanitation, and handwashing groups, and combined water, sanitation, and handwashing group had no effect on linear growth.InterpretationNutrient supplementat...