Variational formulas and cocycle solutions for directed polymer and percolation models

We discuss variational formulas for the law of large numbers limits of certain models of motion in a random medium: namely, the limiting time constant for last-passage percolation and the limiting free energy for directed polymers. The results are valid for models in arbitrary dimension, steps of the admissible paths can be general, the environment process is ergodic under spatial translations, and the potential accumulated along a path can depend on the environment and the next step of the path. The variational formulas come in two types: one minimizes over gradient-like cocycles, and another one maximizes over invariant measures on the space of environments and paths. Minimizing cocycles can be obtained from Busemann functions when these can be proved to exist. The results are illustrated through 1+1 dimensional exactly solvable examples, periodic examples, and polymers in weak disorder

Enhanced infection prophylaxis reduces mortality in severely immunosuppressed HIV-infected adults and older children initiating antiretroviral therapy in Kenya, Malawi, Uganda and Zimbabwe: the REALITY trial

Meeting abstract FRAB0101LB from 21st International AIDS Conference 18–22 July 2016, Durban, South Africa. Introduction: Mortality from infections is high in the first 6 months of antiretroviral therapy (ART) among HIV‐infected adults and children with advanced disease in sub‐Saharan Africa. Whether an enhanced package of infection prophylaxis at ART initiation would reduce mortality is unknown. Methods: The REALITY 2×2×2 factorial open‐label trial (ISRCTN43622374) randomized ART‐naïve HIV‐infected adults and children >5 years with CD4 <100 cells/mm3. This randomization compared initiating ART with enhanced prophylaxis (continuous cotrimoxazole plus 12 weeks isoniazid/pyridoxine (anti‐tuberculosis) and fluconazole (anti‐cryptococcal/candida), 5 days azithromycin (anti‐bacterial/protozoal) and single‐dose albendazole (anti‐helminth)), versus standard‐of‐care cotrimoxazole. Isoniazid/pyridoxine/cotrimoxazole was formulated as a scored fixed‐dose combination. Two other randomizations investigated 12‐week adjunctive raltegravir or supplementary food. The primary endpoint was 24‐week mortality. Results: 1805 eligible adults (n = 1733; 96.0%) and children/adolescents (n = 72; 4.0%) (median 36 years; 53.2% male) were randomized to enhanced (n = 906) or standard prophylaxis (n = 899) and followed for 48 weeks (3.8% loss‐to‐follow‐up). Median baseline CD4 was 36 cells/mm3 (IQR: 16–62) but 47.3% were WHO Stage 1/2. 80 (8.9%) enhanced versus 108(12.2%) standard prophylaxis died before 24 weeks (adjusted hazard ratio (aHR) = 0.73 (95% CI: 0.54–0.97) p = 0.03; Figure 1) and 98(11.0%) versus 127(14.4%) respectively died before 48 weeks (aHR = 0.75 (0.58–0.98) p = 0.04), with no evidence of interaction with the two other randomizations (p > 0.8). Enhanced prophylaxis significantly reduced incidence of tuberculosis (p = 0.02), cryptococcal disease (p = 0.01), oral/oesophageal candidiasis (p = 0.02), deaths of unknown cause (p = 0.02) and (marginally) hospitalisations (p = 0.06) but not presumed severe bacterial infections (p = 0.38). Serious and grade 4 adverse events were marginally less common with enhanced prophylaxis (p = 0.06). CD4 increases and VL suppression were similar between groups (p > 0.2). Conclusions: Enhanced infection prophylaxis at ART initiation reduces early mortality by 25% among HIV‐infected adults and children with advanced disease. The pill burden did not adversely affect VL suppression. Policy makers should consider adopting and implementing this low‐cost broad infection prevention package which could save 3.3 lives for every 100 individuals treated