Effectiveness of behavioural graded activity compared with physiotherapy treatment in chronic neck pain: design of a randomised clinical trial [ISRCTN88733332]

BACKGROUND: Chronic neck pain is a common complaint in the Netherlands with a point prevalence of 14.3%. Patients with chronic neck pain are often referred to a physiotherapist and, although many treatments are available, it remains unclear which type of treatment is to be preferred. The objective of this article is to present the design of a randomised clinical trial, Ephysion, which examines the clinical and cost effectiveness of behavioural graded activity compared with a physiotherapy treatment for patients with chronic non-specific neck pain. METHODS: Eligible patients with non-specific neck pain persisting longer than 3 months will be randomly allocated to either the behavioural graded activity programme or to the physiotherapy treatment. The graded activity programme is based on an operant approach, which uses a time-contingent method to increase the patient's activity level. This treatment is compared with physiotherapy treatment using a pain-contingent method. Primary treatment outcome is the patient's global perceived effect concerning recovery from the complaint. Global perceived effect on daily functioning is also explored as primary outcome to establish the impact of treatment on daily activity. Direct and indirect costs will also be assessed. Secondary outcomes include the patient's main complaints, pain intensity, medical consumption, functional status, quality of life, and psychological variables. Recruitment of patients will take place up to the end of the year 2004 and follow-up measurement will continue until end 2005

A strong approximation of the shortt process

A shortt of a one-dimensional probability distribution is defined to be an interval which has at least probability t and minimal length. The length of a shortt, U(t), and its obvious estimator, Un (t), are significant measures of scale of a probability distribu tion and the corresponding random sample, respectively. The shortt process is defined to be y'n(Un(t) - U(t))/U'(t), similarly to the definition of the quantile process. It is known that this process converges weakly, under natural regularity conditions, to a Brownian bridge. In this note a strong approximation of the shortt process by a Kiefer process is established, which yields the weak convergence as a corollary. Applications of the result to the global and local strong limiting behaviour of the shortt process are also presented

A Probabilistic Real-Time Calculus for Performance Evaluation

In this paper we develop a probabilistic real-time calculus for performance evaluation. The calculus applies a simple generative model of probabilities. Next to probabilistic action transitions, probabilistic time transitions are supported. An operational characterization is given in terms of a labelled transition system. The operational rules for the real-time part of the calculus are constructed in such a way, that the transition system can be interpreted as a discrete-time Markov chain. They further yield a constructive approach towards the efficient execution of processes and generation of transition graphs. On top of the operational rules, bisimulation equivalence is defined and proven to be a congruence for all operators. We define three different performance characteristics in terms of reward functions and prove that equivalent processes have an identical performance. Using an ergodic theorem of Markov chains, we further show how these performance figures can be computed in practice. We introduce an experimental software tool and we show how it can be applied to calculate the performance of a nontrivial real-time data communication protocol.