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This document was prepared for the CD2/3 Review on June 25 – 26, 2015.

We construct the universal type structure for conditional probability systems without any topological assumption, namely a type structure that is terminal, belief-complete, and non-redundant. In particular, in order to obtain the belief-completeness in a constructive way, we extend the work of Meier [An Infinitary Probability Logic for Type Spaces. Israel Journal of Mathematics, 192, 1-58] by proving strong soundness and strong completeness of an infinitary conditional probability logic with truthful and non-epistemic conditioning events., Comment: In Proceedings TARK 2017, arXiv:1707.08250

Background Recurrent vascular events remain a major source of morbidity and mortality after stroke or transient ischemic attack (TIA). The IRIS Trial is evaluating an approach to secondary prevention based on the established association between insulin resistance and increased risk for ischemic vascular events. Specifically, IRIS will test the effectiveness of pioglitazone, an insulin-sensitizing drug of the thiazolidinedione class, for reducing the risk for stroke and myocardial infarction (MI) among insulin resistant, nondiabetic patients with a recent ischemic stroke or TIA. Design Eligible patients for IRIS must have had insulin resistance defined by a Homeostasis Model Assessment–Insulin Resistance >3.0 without meeting criteria for diabetes. Within 6 months of the index stroke or TIA, patients were randomly assigned to pioglitazone (titrated from 15 to 45 mg/d) or matching placebo and followed for up to 5 years. The primary outcome is time to stroke or MI. Secondary outcomes include time to stroke alone, acute coronary syndrome, diabetes, cognitive decline, and all-cause mortality. Enrollment of 3,876 participants from 179 sites in 7 countries was completed in January 2013. Participant follow-up will continue until July 2015. Summary The IRIS Trial will determine whether treatment with pioglitazone improves cardiovascular outcomes of nondiabetic, insulin-resistant patients with stroke or TIA. Results are expected in early 2016.

Summary Background Some countries fortify flour with folic acid to prevent neural tube defects but others do not, partly because of concerns about possible cancer risks. We aimed to assess any effects on site-specific cancer rates in the randomised trials of folic acid supplementation, at doses higher than those from fortification. Methods In these meta-analyses, we sought all trials completed before 2011 that compared folic acid versus placebo, had scheduled treatment duration at least 1 year, included at least 500 participants, and recorded data on cancer incidence. We obtained individual participant datasets that included 49 621 participants in all 13 such trials (ten trials of folic acid for prevention of cardiovascular disease [n=46 969] and three trials in patients with colorectal adenoma [n=2652]). All these trials were evenly randomised. The main outcome was incident cancer (ignoring non-melanoma skin cancer) during the scheduled treatment period (among participants who were still free of cancer). We compared those allocated folic acid with those allocated placebo, and used log-rank analyses to calculate the cancer incidence rate ratio (RR). Findings During a weighted average scheduled treatment duration of 5·2 years, allocation to folic acid quadrupled plasma concentrations of folic acid (57·3 nmol/L for the folic acid groups vs 13·5 nmol/L for the placebo groups), but had no significant effect on overall cancer incidence (1904 cancers in the folic acid groups vs 1809 cancers in the placebo groups, RR 1·06, 95% CI 0·99–1·13, p=0·10). There was no trend towards greater effect with longer treatment. There was no significant heterogeneity between the results of the 13 individual trials (p=0·23), or between the two overall results in the cadiovascular prevention trials and the adenoma trials (p=0·13). Moreover, there was no significant effect of folic acid supplementation on the incidence of cancer of the large intestine, prostate, lung, breast, or any other specific site. Interpretation Folic acid supplementation does not substantially increase or decrease incidence of site-specific cancer during the first 5 years of treatment. Fortification of flour and other cereal products involves doses of folic acid that are, on average, an order of magnitude smaller than the doses used in these trials. Funding British Heart Foundation, Medical Research Council, Cancer Research UK, Food Standards Agency.