Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

Assessment of statistical change criteria used to define significant change in neuropsychological test performance following cardiac surgery

Objective: This paper compares four techniques used to assess change in neuropsychological test scores before and after coronary artery bypass graft surgery (CABG), and includes a rationale for the classification of a patient as overall impaired. Methods: A total of 55 patients were tested before and after surgery on the MicroCog neuropsychological test battery. A matched control group underwent the same testing regime to generate test–retest reliabilities and practice effects. Two techniques designed to assess statistical change were used: the Reliable Change Index (RCI), modified for practice, and the Standardised Regression-based (SRB) technique. These were compared against two fixed cutoff techniques (standard deviation and 20% change methods). Results: The incidence of decline across test scores varied markedly depending on which technique was used to describe change. The SRB method identified more patients as declined on most measures. In comparison, the two fixed cutoff techniques displayed relatively reduced sensitivity in the detection of change. Conclusions: Overall change in an individual can be described provided the investigators choose a rational cutoff based on likely spread of scores due to chance. A cutoff value of ≥20% of test scores used provided acceptable probability based on the number of tests commonly encountered. Investigators must also choose a test battery that minimises shared variance among test scores.

Criteria for quantum coherent transfer of excitations between chromophores in a polar solvent

We show that the quantum decoherence of Forster resonant energy transfer between two optically active molecules can be described by a spin-boson model. This allows us to give quantitative criteria that are necessary for coherent quantum oscillations of excitations between the chromophores. Experimental tests of our results should be possible with flourescent resonant energy transfer (FRET) spectroscopy. Although we focus on the case of protein-pigment complexes our results are also relevant to quantum dots and organic molecules in a dielectric medium. (c) 2006 Elsevier B.V. All rights reserved.

Comparison of ASAS improvement criteria for ankylosing spondylitis with clinically relevant improvement according to an expert panel

Objective: To investigate whether the recently developed (statistically derived) "ASsessment in Ankylosing Spondylitis Working Group" improvement criteria (ASAS-IC) for ankylosing spondylitis (AS) reflect clinically relevant improvement according to the opinion of an expert panel. Methods: The ASAS-IC consist of four domains: physical function, spinal pain, patient global assessment, and inflammation. Scores on these four domains of 55 patients with AS, who had participated in a non-steroidal anti-inflammatory drug efficacy trial, were presented to an international expert panel (consisting of patients with AS and members of the ASAS Working Group) in a three round Delphi exercise. The number of (non-) responders according to the ASAS-IC was compared with the final-consensus of the experts. The most important domains in the opinion of the experts were identified, and also selected with discriminant analysis. A number of provisional criteria sets that best represented the consensus of the experts were defined. Using other datasets, these clinically derived criteria sets as well as the statistically derived ASAS-IC were then tested for discriminative properties and for agreement with the end of trial efficacy by patient and doctor. Results: Forty experts completed the three Delphi rounds. The experts considered twice as many patients to be responders than the ASAS-IC (42 v 21). Overall agreement between experts and ASAS-IC was 62%. Spinal pain was considered the most important domain by most experts and was also selected as such by discriminant analysis. Provisional criteria sets with an agreement of greater than or equal to 80% compared with the consensus of the experts showed high placebo response rates (27-42%), in contrast with the ASAS-IC with a predefined placebo response rate of 25%. All criteria sets and the ASAS-IC discriminated well between active and placebo treatment (chi(2) = 36-45; p < 0.001). Compared with the end of trial efficacy assessment, the provisional criteria sets showed an agreement of 71-82%, sensitivity of 67-83%, and specificity of 81-88%. The ASAS-IC showed an agreement of 70%, sensitivity of 62%, and specificity of 89%. Conclusion: The ASAS-IC are strict in defining response, are highly specific, and consequently show lower sensitivity than the clinically derived criteria sets. However, those patients who are considered as responders by applying the ASAS-IC are acknowledged as such by the expert panel as well as by. patients' and doctors' judgments, and are therefore likely to be true responders.