A frequentist framework of inductive reasoning

Reacting against the limitation of statistics to decision procedures, R. A. Fisher proposed for inductive reasoning the use of the fiducial distribution, a parameter-space distribution of epistemological probability transferred directly from limiting relative frequencies rather than computed according to the Bayes update rule. The proposal is developed as follows using the confidence measure of a scalar parameter of interest. (With the restriction to one-dimensional parameter space, a confidence measure is essentially a fiducial probability distribution free of complications involving ancillary statistics.) A betting game establishes a sense in which confidence measures are the only reliable inferential probability distributions. The equality between the probabilities encoded in a confidence measure and the coverage rates of the corresponding confidence intervals ensures that the measure's rule for assigning confidence levels to hypotheses is uniquely minimax in the game. Although a confidence measure can be computed without any prior distribution, previous knowledge can be incorporated into confidence-based reasoning. To adjust a p-value or confidence interval for prior information, the confidence measure from the observed data can be combined with one or more independent confidence measures representing previous agent opinion. (The former confidence measure may correspond to a posterior distribution with frequentist matching of coverage probabilities.) The representation of subjective knowledge in terms of confidence measures rather than prior probability distributions preserves approximate frequentist validity.Comment: major revisio

Greigite formation in aqueous solutions: critical constraints into the role of iron and sulphur ratios, pH and Eh, and temperature using reaction pathway modelling

Greigite forms as an intermediate phase along the pyrite reaction pathway. Despite being considered metastable, it is observed in numerous shallow natural systems, suggesting it could be a unique proxy for diagenetic and environmental conditions. We use thermodynamic reaction pathway modelling in PHREEQC software, to understand the role of iron and sulphur ratios, pH and Eh, and temperature on the formation and retention of greigite in aqueous solutions. With newly available experimental thermodynamic properties, this work identifies the chemical boundary conditions for greigite formation in aqueous solutions. Greigite precipitation is likely favourable in anoxic and alkaline aqueous solutions at or below 25 °C. Our numerical experiments show that greigite is closer to saturation in iron-rich solutions with minor sulphur input. Greigite precipitation in strongly alkaline solutions suggest polysulfides and ferric iron-bearing minerals may be favourable reactants for its formation. Greigite precipitates at iron and sulphur concentrations that are over two orders of magnitude greater than iron sulphide-hosted natural porewaters. This disparity between model and field observations suggest microenvironments within bulk solutions may be important for greigite formation and retention. These constraints suggest greigite is more likely to form alongside pyrite in shallow, non-steady state aqueous solutions

Struggles over access to the Muslim public sphere: Multiple publics and discourses on agency, belonging and citizenship (Introduction to the Themed Section)

Abstract This introductory essay provides the context for the articles in this Themed Section. Despite the diversity in locations, historical backgrounds and contemporary processes of change, all contributors to this Themed Section focus on the struggle of Muslim groups over access to an emergent Muslim public sphere. They highlight the contestations of and shifts in the notions of agency, belonging, and citizenship in nation-states with Muslim communities within its borders. The introduction consists of two parts. The first part reviews the notion of the public sphere as conceptualized by Habermas and critiqued by scholars of a diversity of backgrounds. In relation to the concept of the Muslim public sphere, three aspects of critique are given closer c

Recombination rate and selection strength in HIV intra-patient evolution

The evolutionary dynamics of HIV during the chronic phase of infection is driven by the host immune response and by selective pressures exerted through drug treatment. To understand and model the evolution of HIV quantitatively, the parameters governing genetic diversification and the strength of selection need to be known. While mutation rates can be measured in single replication cycles, the relevant effective recombination rate depends on the probability of coinfection of a cell with more than one virus and can only be inferred from population data. However, most population genetic estimators for recombination rates assume absence of selection and are hence of limited applicability to HIV, since positive and purifying selection are important in HIV evolution. Here, we estimate the rate of recombination and the distribution of selection coefficients from time-resolved sequence data tracking the evolution of HIV within single patients. By examining temporal changes in the genetic composition of the population, we estimate the effective recombination to be r=1.4e-5 recombinations per site and generation. Furthermore, we provide evidence that selection coefficients of at least 15% of the observed non-synonymous polymorphisms exceed 0.8% per generation. These results provide a basis for a more detailed understanding of the evolution of HIV. A particularly interesting case is evolution in response to drug treatment, where recombination can facilitate the rapid acquisition of multiple resistance mutations. With the methods developed here, more precise and more detailed studies will be possible, as soon as data with higher time resolution and greater sample sizes is available.Comment: to appear in PLoS Computational Biolog

Eradication of chronic myeloid leukemia stem cells: a novel mathematical model predicts no therapeutic benefit of adding G-CSF to imatinib

Imatinib mesylate induces complete cytogenetic responses in patients with chronic myeloid leukemia (CML), yet many patients have detectable BCR-ABL transcripts in peripheral blood even after prolonged therapy. Bone marrow studies have shown that this residual disease resides within the stem cell compartment. Quiescence of leukemic stem cells has been suggested as a mechanism conferring insensitivity to imatinib, and exposure to the Granulocyte-Colony Stimulating Factor (G-CSF), together with imatinib, has led to a significant reduction in leukemic stem cells in vitro. In this paper, we design a novel mathematical model of stem cell quiescence to investigate the treatment response to imatinib and G-CSF. We find that the addition of G-CSF to an imatinib treatment protocol leads to observable effects only if the majority of leukemic stem cells are quiescent; otherwise it does not modulate the leukemic cell burden. The latter scenario is in agreement with clinical findings in a pilot study administering imatinib continuously or intermittently, with or without G-CSF (GIMI trial). Furthermore, our model predicts that the addition of G-CSF leads to a higher risk of resistance since it increases the production of cycling leukemic stem cells. Although the pilot study did not include enough patients to draw any conclusion with statistical significance, there were more cases of progression in the experimental arms as compared to continuous imatinib. Our results suggest that the additional use of G-CSF may be detrimental to patients in the clinic

An empirical approach towards the efficient and optimal production of influenza-neutralizing ovine polyclonal antibodies demonstrates that the novel adjuvant CoVaccine HT(TM) is functionally superior to Freund's adjuvant

Passive immunotherapies utilising polyclonal antibodies could have a valuable role in preventing and treating infectious diseases such as influenza, particularly in pandemic situations but also in immunocompromised populations such as the elderly, the chronically immunosuppressed, pregnant women, infants and those with chronic diseases. The aim of this study was to optimise current methods used to generate ovine polyclonal antibodies. Polyclonal antibodies to baculovirus-expressed recombinant influenza haemagglutinin from A/Puerto Rico/8/1934 H1N1 (PR8) were elicited in sheep using various immunisation regimens designed to investigate the priming immunisation route, adjuvant formulation, sheep age, and antigen dose, and to empirically ascertain which combination maximised antibody output. The novel adjuvant CoVaccine HT™ was compared to Freund’s adjuvant which is currently the adjuvant of choice for commercial production of ovine polyclonal Fab therapies. CoVaccine HT™ induced significantly higher titres of functional ovine anti-haemagglutinin IgG than Freund’s adjuvant but with fewer side effects, including reduced site reactions. Polyclonal hyperimmune sheep sera effectively neutralised influenza virus in vitro and, when given before or after influenza virus challenge, prevented the death of infected mice. Neither the age of the sheep nor the route of antigen administration appeared to influence antibody titre. Moreover, reducing the administrated dose of haemagglutinin antigen minimally affected antibody titre. Together, these results suggest a cost effective way of producing high and sustained yields of functional ovine polyclonal antibodies specifically for the prevention and treatment of globally significant diseases.Natalie E. Stevens, Cara K. Fraser, Mohammed Alsharifi, Michael P. Brown, Kerrilyn R. Diener, John D. Haybal

Challenges of Loss to Follow-up in Tuberculosis Research.

In studies evaluating methods for diagnosing tuberculosis (TB), follow-up to verify the presence or absence of active TB is crucial and high dropout rates may significantly affect the validity of the results. In a study assessing the diagnostic performance of the QuantiFERON®-TB Gold In-Tube test in TB suspect children in Tanzania, factors influencing patient adherence to attend follow-up examinations and reasons for not attending were examined. In 160 children who attended and 102 children who did not attend scheduled 2-month follow-up baseline health characteristics, demographic data and risk factors for not attending follow-up were determined. Qualitative interviews were used to understand patient and caretakers reasons for not returning for scheduled follow-up. Being treated for active tb in the dots program (OR: 4.14; 95% CI:1.99-8.62;p-value<0.001) and receiving money for the bus fare (OR:129; 95% CI 16->100;P-value<0.001) were positive predictors for attending follow-up at 2 months, and 21/85(25%) of children not attending scheduled follow-up had died. Interviews revealed that limited financial resources, i.e. lack of money for transportation and poor communication, were related to non-adherence. Patients lost to follow-up is a potential problem for TB research. Receiving money for transportation to the hospital and communication is crucial for adherence to follow-up conducted at a study facility. Strategies to ensure follow-up should be part of any study protocol