The consequences of delaying insulin initiation in UK type 2 diabetes patients failing oral hyperglycaemic agents: a modelling study

<p>Abstract</p> <p>Background</p> <p>Recent data have shown that type 2 diabetes patients in the UK delay initiating insulin on average for over 11 years after first being prescribed an oral medication. Using a published computer simulation model of diabetes we used UK-specific data to estimate the clinical consequences of immediately initiating insulin versus delaying initiation for periods in line with published estimates.</p> <p>Methods</p> <p>In the base case scenario simulated patients, with characteristics based on published UK data, were modelled as either initiating insulin immediately or delaying for 8 years. Clinical outcomes in terms of both life expectancy and quality-adjusted life expectancy and also diabetes-related complications (cumulative incidence and time to onset) were projected over a 35 year time horizon. Treatment effects associated with insulin use were taken from published studies and sensitivity analyses were performed around time to initiation of insulin, insulin efficacies and hypoglycaemia utilities.</p> <p>Results</p> <p>For patients immediately initiating insulin there were increases in (undiscounted) life expectancy of 0.61 years and quality-adjusted life expectancy of 0.34 quality-adjusted life years versus delaying initiation for 8 years. There were also substantial reductions in cumulative incidence and time to onset of all diabetes-related complications with immediate versus delayed insulin initiation. Sensitivity analyses showed that a reduced delay in insulin initiation or change in insulin efficacy still demonstrated clinical benefits for immediate versus delayed initiation.</p> <p>Conclusion</p> <p>UK type 2 diabetes patients are at increased risk of a large number of diabetes-related complications due to an unnecessary delay in insulin initiation. Despite clear guidelines recommending tight glycaemic control this failure to begin insulin therapy promptly is likely to result in needlessly reduced life expectancy and compromised quality of life.</p

Covering radius in the Hamming permutation space

© 2019 Elsevier LtdLet Sn denote the set of permutations of {1,2,…,n}. The function f(n,s) is defined to be the minimum size of a subset S⊆Sn with the property that for any ρ∈Sn there exists some σ∈S such that the Hamming distance between ρ and σ is at most n−s. The value of f(n,2) is the subject of a conjecture by Kézdy and Snevily, which implies several famous conjectures about Latin squares. We prove that the odd n case of the Kézdy–Snevily Conjecture implies the whole conjecture. We also show that f(n,2)>3n∕4 for all n, that s! [Formula presented] [Formula presented] if s⩾311Nsciescopu

Counting and enumerating partial Latin rectangles by means of computer algebra systems and CSP solvers

This paper provides an in-depth analysis of how computer algebra systems and CSP solvers can be used to deal with the problem of enumerating and distributing the set of $r\times s$ partial Latin rectangles based on $n$ symbols according to their weight, shape, type or structure. The computation of Hilbert functions and triangular systems of radical ideals enables us to solve this problem for all $r,s,n\leq 6$. As a by-product, explicit formulas are determined for the number of partial Latin rectangles of weight up to six. Further, in order to illustrate the effectiveness of the computational method, we focus on the enumeration of three subsets: (a) non-compressible and regular, (b) totally symmetric, and (c) totally conjugate orthogonal partial Latin squares. In particular, the former enables us to enumerate the set of seminets of point rank up to eight and to prove the existence of two new configurations of point rank eight. Finally, as an illustrative application, it is also exposed a method to construct totally symmetric partial Latin squares that gives rise, under certain conditions, to new families of Lie partial quasigroup rings