Are prescribing doctors sensitive to the price that their patients have to pay in the Spanish National Health System?

[EN] Background This study aims to design an empirical test on the sensitivity of the prescribing doctors to the price afforded for the patient, and to apply it to the population data of primary care dispensations for cardiovascular disease and mental illness in the Spanish National Health System (NHS). Implications for drug policies are discussed. Methods We used population data of 17 therapeutic groups of cardiovascular and mental illness drugs aggregated by health areas to obtain 1424 observations ((8 cardiovascular groups * 70 areas) + (9 psychotropics groups * 96 areas)). All drugs are free for pensioners. For non-pensioner patients 10 of the 17 therapeutic groups have a reduced copayment (RC) status of only 10% of the price with a ceiling of €2.64 per pack, while the remaining 7 groups have a full copayment (FC) rate of 40%. Differences in the average price among dispensations for pensioners and non-pensioners were modelled with multilevel regression models to test the following hypothesis: 1) in FC drugs there is a significant positive difference between the average prices of drugs prescribed to pensioners and non-pensioners; 2) in RC drugs there is no significant price differential between pensioner and non-pensioner patients; 3) the price differential of FC drugs prescribed to pensioners and non-pensioners is greater the higher the price of the drugs. Results The average monthly price of dispensations to pensioners and non-pensioners does not differ for RC drugs, but for FC drugs pensioners get more expensive dispensations than non-pensioners (estimated difference of €9.74 by DDD and month). There is a positive and significant effect of the drug price on the differential price between pensioners and non-pensioners. For FC drugs, each additional euro of the drug price increases the differential by nearly half a euro (0.492). We did not find any significant differences in the intensity of the price effect among FC therapeutic groups. Conclusions Doctors working in the Spanish NHS seem to be sensitive to the price that can be afforded by patients when they fill in prescriptions, although alternative hypothesis could also explain the results found.

Location-price competition with externality: an application to the Tenerife tram

[EN] This paper presents a location–price equilibrium problem on a tree. A sufficient condition for having a Nash equilibrium in a spatial competition model that incorporates price, transport, and externality costs is given. This condition implies both competitors are located at the same point, a vertex that is the unique median of the tree. However, this is not an equilibrium necessary condition. Some examples show that not all medians are equilibria. Finally, an application to the Tenerife tram is presented.

Intrinsic ordering, combinatorial numbers and reliability engineering

[EN]A new algorithm for evaluating the top event probability of large fault trees (FTs) is presented. This algorithm does not require any previous qualitative analysis of the FT. Indeed, its efficiency is independent of the FT logic, and it only depends on the number n of basic system components and on their failure probabilities. Our method provides exact lower and upper bounds on the top event probability by using new properties of the intrinsic order relation between binary strings. The intrinsic order enables one to select binary n-tuples with large occurrence probabilities without necessity to evaluate them. This drastically reduces the complexity of the problem from exponential (2n binary n-tuples) to linear (n Boolean variables)...

Labeling the nodes in the intrinsic order graph with their weights

[EN] This paper deals with the study of some new properties of the intrinsic order graph. The intrinsic order graph is the natural graphical representation of a complex stochastic Boolean system (CSBS). A CSBS is a system depending on an arbitrarily large number n of mutually independent random Boolean variables. The intrinsic order graph displays its 2n vertices (associated to the CSBS) from top to bottom, in decreasing order of their occurrence probabilities. New relations between the intrinsic ordering and the Hamming weight (i.e., the number of 1-bits in a binary n-tuple) are derived. Further, the distribution of the weights of the 2n nodes in the intrinsic order graph is analyzed…

Complex sochastic boolean systems : new properties of the intrinsic order graph

[EN]A complex stochastic Boolean system (CSBS) is a system depending on an arbitrary number n of stochastic Boolean variables. The analysis of CSBSs is mainly based on the intrinsic order: a partial order relation defined on the set f0; 1gn of binary n-tuples. The usual graphical representation for a CSBS is the intrinsic order graph: the Hasse diagram of the intrinsic order. In this paper, some new properties of the intrinsic order graph are studied. Particularly, the set and the number of its edges, the degree and neighbors of each vertex, as well as typical properties, such as the symmetry and fractal structure of this graph, are analyzed…

Intrinsic Order and Hamming Weight

[EN]The intrinsic order is a partial order relation defined on the set {0, 1} n of all binary n-tuples. This ordering enables one to automatically compare binary n-tuple probabilities without computing them, just looking at the relative positions of their 0s & 1s. In this paper, new relations between the intrinsic ordering and the Hamming weight (i.e., the number of 1-bits in a binary n-tuple) are derived. All theoretical results are rigorously proved and illustrated through the intrinsic order graph…