Economic consequences of near-patient test results - the case of tests for the Helicobacter Pylori bacterium in dyspepsia

Abstract Diagnostic tests and in particular laboratory tests are often important in diagnostic work-up and monitoring of patients. Therefore the economic consequences of medical actions based on test results may amount to a substantial proportion of health service costs. Thus, it is of public interest to study the consequences and costs of using laboratory tests. We develop a model for economic evaluation related to the diagnostic accuracy (sensitivity and specificity) of near patient tests. Blood sample based tests to detect the bacterium Helicobacter Pylori (HP) are useful in diagnosing peptic ulcer and suitable to illustrate the model. First, general practitioners’ initial management plans for a dyspeptic patient are elucidated using a paper vignette survey. Based on survey results, and medical literature, a decision tree is constructed to visualize expected costs and outcomes resulting from using three different HP tests in the clinical situation described in the vignette. Tests included are two rapid tests for use in general practice, and one hospital laboratory test for comparison. The tests had different sensitivities and specificities. Then a costeffectiveness analysis is undertaken from a societal perspective. Finally we use sensitivity analyses to model the decision uncertainty. Estimating for a follow-up period of 120 days, the rapid test with lower sensitivity and specificity than the hospital HP test is cost-effective because the laboratory result is available immediately. Further, in general practice, the rapid test with the highest sensitivity is significantly cost effective compared to the test with the highest specificity when the willingness to pay for each dyspepsia-free day exceeds €42.6. When deciding whether a laboratory analysis should be analysed in the office laboratory or not, it is important to consider both the diagnostic accuracy of the tests and the waiting time for the alternative, i.e. a hospital laboratory result.cost-effectiveness; laboratory tests; general practice; probabilistic sensitivity; analysis

Decision-making in General Practice: The importance of laboratory analyses when choosing medical actions

The focus of this study is the effect of a laboratory analysis and socioeconomic variables on choosing medical actions in a specific situation (a clinical vignette - a young woman, Mrs Hansen, with dyspepsia - presented to GPs). We assume that the GP’s decision depends on what he or she thinks is best for the patients, based on the best clinical evidence available. Significant variables associated with the choice of medical actions are: the result of the Helicobacter pylori (HP) test, the GP’s stated importance of HPRT, the location of the general practice, the GP recommending sick leave, the GP’s stated probability that Mrs Hansen’s symptoms are due to a H.pylori infection after the HP-result is known, and how the GP follows up the patient. Our results show that the HP-analysis has a significant and major influence on the GPs choice of medical actions. Therefore the quality of the analysis is likely to affect the patients’ health and social costs. Hence institutions for quality monitoring and improvement are important elements of health care reforms. Such institutions should balance cost and benefits of quality improving measures, and will be the focus of closer studies in our future research.Discrete choice models; Decision-making; Primary Health Care

Vertex coloring of plane graphs with nonrepetitive boundary paths

A sequence $s_1,s_2,...,s_k,s_1,s_2,...,s_k$ is a repetition. A sequence $S$ is nonrepetitive, if no subsequence of consecutive terms of $S$ form a repetition. Let $G$ be a vertex colored graph. A path of $G$ is nonrepetitive, if the sequence of colors on its vertices is nonrepetitive. If $G$ is a plane graph, then a facial nonrepetitive vertex coloring of $G$ is a vertex coloring such that any facial path is nonrepetitive. Let $\pi_f(G)$ denote the minimum number of colors of a facial nonrepetitive vertex coloring of $G$. Jendro\vl and Harant posed a conjecture that $\pi_f(G)$ can be bounded from above by a constant. We prove that $\pi_f(G)\le 24$ for any plane graph $G$

On the intersections of Fibonacci, Pell, and Lucas numbers

We describe how to compute the intersection of two Lucas sequences of the forms $\{U_n(P,\pm 1) \}_{n=0}^{\infty}$ or $\{V_n(P,\pm 1) \}_{n=0}^{\infty}$ with $P\in\mathbb{Z}$ that includes sequences of Fibonacci, Pell, Lucas, and Lucas-Pell numbers. We prove that such an intersection is finite except for the case $U_n(1,-1)$ and $U_n(3,1)$ and the case of two $V$-sequences when the product of their discriminants is a perfect square. Moreover, the intersection in these cases also forms a Lucas sequence. Our approach relies on solving homogeneous quadratic Diophantine equations and Thue equations. In particular, we prove that 0, 1, 2, and 5 are the only numbers that are both Fibonacci and Pell, and list similar results for many other pairs of Lucas sequences. We further extend our results to Lucas sequences with arbitrary initial terms

The Entropy of Square-Free Words

Finite alphabets of at least three letters permit the construction of square-free words of infinite length. We show that the entropy density is strictly positive and derive reasonable lower and upper bounds. Finally, we present an approximate formula which is asymptotically exact with rapid convergence in the number of letters.Comment: 18 page

On the facial Thue choice index via entropy compression

A sequence is nonrepetitive if it contains no identical consecutive subsequences. An edge colouring of a path is nonrepetitive if the sequence of colours of its consecutive edges is nonrepetitive. By the celebrated construction of Thue, it is possible to generate nonrepetitive edge colourings for arbitrarily long paths using only three colours. A recent generalization of this concept implies that we may obtain such colourings even if we are forced to choose edge colours from any sequence of lists of size 4 (while sufficiency of lists of size 3 remains an open problem). As an extension of these basic ideas, Havet, Jendrol', Sot\'ak and \v{S}krabul'\'akov\'a proved that for each plane graph, 8 colours are sufficient to provide an edge colouring so that every facial path is nonrepetitively coloured. In this paper we prove that the same is possible from lists, provided that these have size at least 12. We thus improve the previous bound of 291 (proved by means of the Lov\'asz Local Lemma). Our approach is based on the Moser-Tardos entropy-compression method and its recent extensions by Grytczuk, Kozik and Micek, and by Dujmovi\'c, Joret, Kozik and Wood

Dense Packings of Congruent Circles in Rectangles with a Variable Aspect Ratio

We use computational experiments to find the rectangles of minimum area into which a given number n of non-overlapping congruent circles can be packed. No assumption is made on the shape of the rectangles. Most of the packings found have the usual regular square or hexagonal pattern. However, for 1495 values of n in the tested range n =< 5000, specifically, for n = 49, 61, 79, 97, 107,... 4999, we prove that the optimum cannot possibly be achieved by such regular arrangements. The evidence suggests that the limiting height-to-width ratio of rectangles containing an optimal hexagonal packing of circles tends to 2-sqrt(3) as n tends to infinity, if the limit exists.Comment: 21 pages, 13 figure

Avoidability of formulas with two variables

In combinatorics on words, a word $w$ over an alphabet $\Sigma$ is said to avoid a pattern $p$ over an alphabet $\Delta$ of variables if there is no factor $f$ of $w$ such that $f=h(p)$ where $h:\Delta^*\to\Sigma^*$ is a non-erasing morphism. A pattern $p$ is said to be $k$-avoidable if there exists an infinite word over a $k$-letter alphabet that avoids $p$. We consider the patterns such that at most two variables appear at least twice, or equivalently, the formulas with at most two variables. For each such formula, we determine whether it is $2$-avoidable, and if it is $2$-avoidable, we determine whether it is avoided by exponentially many binary words