Likelihood-based estimation of the regression model with scrambled responses

A significant problem in the collection of responses to potentially sensitive questions, such as relating to illegal, immoral or embarrassing activities, is non-sampling error due to refusal to respond or false responses. Eichhorn & Hayre (1983) suggested the use of scrambled responses to reduce this form of bias. This paper considers a linear regression model in which the dependent variable is unobserved but for which the sum or product with a scrambling random variable of known distribution, is known. The performance of two likelihood-based estimators is investigated, namely of a Bayesian estimator achieved through a Markov chain Monte Carlo (MCMC) sampling scheme, and a classical maximum-likelihood estimator. These two estimators and an estimator suggested by Singh, Joarder & King (1996) are compared. Monte Carlo results show that the Bayesian estimator outperforms the classical estimators in almost all cases, and the relative performance of the Bayesian estimator improves as the responses become more scrambled.

5-cycle systems of K-v-F with a hole

Recently the problem of the existence of a 5-cycle system of K-v with a hole of size u was completely solved. In this paper we prove necessary and sufficient conditions on v and u for the existence of a 5-cycle system of K-v - F, with a hole of size u.

(m,n)-cycle systems

We describe a method which, in certain circumstances, may be used to prove that the well-known necessary conditions for partitioning the edge set of the complete graph on an odd number of vertices (or the complete graph on an even number of vertices with a 1-factor removed) into cycles of lengths m(1),m(2),...,m(t) are sufficient in the case \{m(1), m(2), ..., m(t)}\=2. The method is used to settle the case where the cycle lengths are 4 and 5. (C) 1998 Elsevier Science B.V. All rights reserved.

A numerical study of large sparse matrix exponentials arising in Markov chains

Krylov subspace techniques have been shown to yield robust methods for the numerical computation of large sparse matrix exponentials and especially the transient solutions of Markov Chains. The attractiveness of these methods results from the fact that they allow us to compute the action of a matrix exponential operator on an operand vector without having to compute, explicitly, the matrix exponential in isolation. In this paper we compare a Krylov-based method with some of the current approaches used for computing transient solutions of Markov chains. After a brief synthesis of the features of the methods used, wide-ranging numerical comparisons are performed on a power challenge array supercomputer on three different models. (C) 1999 Elsevier Science B.V. All rights reserved.AMS Classification: 65F99; 65L05; 65U05.

Relapse and mortality among HIV-infected and uninfected patients with tuberculosis successfully treated with twice weekly directly observed therapy in rural South Africa

Objective: To determine post-treatment relapse and mortality rates among HIV-infected and uninfected patients with tuberculosis treated with a twice-weekly drug regimen under direct observation (DOT). Setting: Hlabisa, South Africa. Patients: A group of 403 patients with tuberculosis (53% HIV infected) cured following treatment with isoniazid (H), rifampicin (R), pyrazinamide (Z) and ethambutol (E) given in hospital (median 17 days), followed by HRZE twice weekly to 2 months and HR twice weekly to 6 months in the community under DOT. Methods: Relapses were identified through hospital readmission and 6-monthly home visits. Relapse (culture for Mycobacterium tuberculosis) and mortality given as rates per 100 person-years observation (PYO) stratified by HIV status and history of previous tuberculosis treatment. Results: Mean (SD) post-treatment follow-up was 1.2 (0.4) years (total PYO = 499); 78 patients (19%) left the area, 58 (14%) died, 248 (62%) remained well and 19 (5%) relapsed. Relapse rates in HIV-infected and uninfected patients were 3.9 [95% confidence interval (CI) 1.5-6.3] and 3.6 (95% CI 1.1-6.1) per 100 PYO (P = 0.7). Probability of relapse at 18 months was estimated as 5% in each group. Mortality was four-fold higher among HIV-infected patients (17.8 and 4.4 deaths per 100 PYO for HIV-infected and uninfected patients, respectively; P < 0.0001). Probability of survival at 24 months was estimated as 59% and 81%, respectively. We observed no increase in relapse or mortality among previously treated patients compared with new patients. A positive smear at 2 months did not predict relapse or mortality. Conclusion: Relapse rates are acceptably low following successful DOT with a twice weekly rifampifin-containing regimen, irrespective of HIV status and previous treatment history. Mortality is substantially increased among HIV-infected patients even following successful DOT and this requires further attention. (C) 1999 Lippincott Williams & Wilkins.

On modifications to the long-term survival mixture model in the presence of competing risks

A mixture model for long-term survivors has been adopted in various fields such as biostatistics and criminology where some individuals may never experience the type of failure under study. It is directly applicable in situations where the only information available from follow-up on individuals who will never experience this type of failure is in the form of censored observations. In this paper, we consider a modification to the model so that it still applies in the case where during the follow-up period it becomes known that an individual will never experience failure from the cause of interest. Unless a model allows for this additional information, a consistent survival analysis will not be obtained. A partial maximum likelihood (ML) approach is proposed that preserves the simplicity of the long-term survival mixture model and provides consistent estimators of the quantities of interest. Some simulation experiments are performed to assess the efficiency of the partial ML approach relative to the full ML approach for survival in the presence of competing risks.

El Nino and arboviral disease prediction

Recent El Nino events have stimulated interest in the development of modeling techniques to forecast extremes of climate and related health events. Previous studies have documented associations between specific climate variables (particularly temperature and rainfall) and outbreaks of arboviral disease. In some countries, such diseases are sensitive to Fl Nino. Here we describe a climate-based model for the prediction of Ross River virus epidemics in Australia. From a literature search and data on case notifications, we determined in which years there were epidemics of Ross River virus in southern Australia between 1928 and 1998. Predictor variables were monthly Southern Oscillation index values for the year of an epidemic or lagged by 1 year. We found that in southeastern states, epidemic years were well predicted by monthly Southern Oscillation index values in January and September in the previous year. The model forecasts that there is a high probability of epidemic Ross River virus in the southern states of Australia in 1999. We conclude that epidemics of arboviral disease can, at least in principle, be predicted on the basis of climate relationships.

Some challenging group presentations

We study some challenging presentations which arise as groups of deficiency zero. In four cases we settle finiteness: we show that two presentations are for finite groups while two are fur infinite groups. Thus we answer three explicit questions in the literature and we provide the first published deficiency zero presentation for a group with derived length seven. The tools we use are coset enumeration and Knuth-Bendix rewriting, which are well-established as methods for proving finiteness or otherwise of a finitely presented group. We briefly comment on their capabilities and compare their performance.

Sausage: protein threading with flexible force fields

Sausage is a protein sequence threading program, but with remarkable run-time flexibility. Using different scripts, it can calculate protein sequence-structure alignments, search structure libraries, swap force fields, create models form alignments, convert file formats and analyse results. There are several different force fields which might be classed as knowledge-based, although they do not rely on Boltzmann statistics. Different force fields are used for alignment calculations and subsequent ranking of calculated models.

Applying the results of a systematic review in general practice

Objective: To assess how general practitioners might interpret and apply the results of a systematic review relevant to general practice. Design: Cross-sectional postal survey of general practitioners in August 1997. Participants: 51 general practitioners in the Southern Division of General Practice in Adelaide and 11 professors or heads of departments of general practice. Main outcome measures:Extent to which comments on the implications for practice and implications for research coincided with the evidence presented in a systematic review of antibiotics for the treatment of acute otitis media in children; and reported probability that respondents would prescribe antibiotics in three brief case scenarios. Results: There was considerable variation in the comments made by general practitioners on the implications of the review for clinical practice. After reading the review, respondents with training in critical appraisal were more likely to state that children with acute otitis media would usually recover spontaneously and reported a lower probability of prescribing antibiotics in two of the three case scenarios. Conclusions: Providing systematic reviews is not sufficient for the results of such evidence to be translated:into clinical practice. There is an association between critical appraisal skills and the application of evidence-based practice.

Percolative fragmentation of char particles during gasification

Percolative fragmentation was confirmed to occur during gasification of three microporous coal chars. Indirect evidence obtained by the variation of electrical resistivity (ER) with conversion was supported by direct observation of numerous fragments during gasification. The resistivity increases slowly at low conversions and then sharply after a certain conversion value, which is a typical percolation phenomenon suggesting the occurrence of internal fragmentation at high conversion. Two percolation models are applied to interpret the experimental data and determine the percolation threshold. A percolation threshold of 0.02-0.07 was found, corresponding to a critical conversion of 92-96% for fragmentation. The electrical resistivity variation at high conversions is found to be very sensitive to diffusional effects during gasification. Partially burnt samples with a narrow initial particle size range were also observed microscopically, and found to yield a large number of small fragments even when the particles showed no disintegration and chemical control prevailed. It is proposed that this is due to the separation of isolated clusters from the particle surface. The particle size distribution of the fragments was essentially independent of the reaction conditions and the char type, and supported the prediction by percolation theory that the number fraction distribution varies linearly with mass in a log-log plot. The results imply that perimeter fragmentation would occur in practical combustion systems in which the reactions are strongly diffusion affected.

Optimal release strategies for biological control agents: an application of stochastic dynamic programming to population management

1. Establishing biological control agents in the field is a major step in any classical biocontrol programme, yet there are few general guidelines to help the practitioner decide what factors might enhance the establishment of such agents. 2. A stochastic dynamic programming (SDP) approach, linked to a metapopulation model, was used to find optimal release strategies (number and size of releases), given constraints on time and the number of biocontrol agents available. By modelling within a decision-making framework we derived rules of thumb that will enable biocontrol workers to choose between management options, depending on the current state of the system. 3. When there are few well-established sites, making a few large releases is the optimal strategy. For other states of the system, the optimal strategy ranges from a few large releases, through a mixed strategy (a variety of release sizes), to many small releases, as the probability of establishment of smaller inocula increases. 4. Given that the probability of establishment is rarely a known entity, we also strongly recommend a mixed strategy in the early stages of a release programme, to accelerate learning and improve the chances of finding the optimal approach.

Inhibition of transmitter release and long-term depression in the avian hippocampus

Long-term depression has recently been shown to occur at glutamatergic synapses in the avian hippocampus and requires activation of calcium/calmodulin-dependent protein kinase II in the nerve terminal. Here using whole cell and intracellular recordings from brain slices, we show that the N-type calcium channel contributes significantly to glutamate release in the avian hippocampus. Activation of the metabotrobic gamma-aminobutyric acid (GABA)(B) receptor by the specific agonist baclofen blocks synaptic transmission. The action of baclofen was associated with a change in paired pulse facilitation indicating that it resulted from a reduction in the probability of transmitter release, In contrast, no change in paired pulse facilitation was observed following the induction of long-term depression. These results show that activation of GABA(B) receptors and long-term depression reduce transmitter release by distinct mechanisms. (C) 2000 Elsevier Science Ireland Ltd. All rights reserved.

Further results on the relationship between mu-invariant measures and quasi-stationary distributions for absorbing continuous-time Markov chains

This note considers continuous-time Markov chains whose state space consists of an irreducible class, C, and an absorbing state which is accessible from C. The purpose is to provide results on mu-invariant and mu-subinvariant measures where absorption occurs with probability less than one. In particular, the well-known premise that the mu-invariant measure, m, for the transition rates be finite is replaced by the more natural premise that m be finite with respect to the absorption probabilities. The relationship between mu-invariant measures and quasi-stationary distributions is discussed. (C) 2000 Elsevier Science Ltd. All rights reserved.

Perceived need for mental health care, findings from the Australian National Survey of Mental Health and Well-being

Background. The Australian National Survey of Mental Health and Well-being was designed to detect and describe psychiatric morbidity, associated disability, service use and perceived need for care. The survey employed a single-phase interview methodology, delivering a field questionnaire to a clustered probability sample of 10641 Australians. Perceived need was sampled with an instrument designed for this survey, the Perceived Need for Care Questionnaire (PNCQ). This questionnaire gathers information about five categories of perceived need, assigning each to one of four levels of perceived need. Reliability and validity studies showed satisfactory performance of the instrument. Methods. Perceived need for mental health care in the Australian population has been analysed using PNCQ data, relating this to diagnostic and service utilization data from the above survey. Results. The survey findings indicate that an estimated 13.8 % of the Australian population have perceived need for mental health care. Those who met interview criteria for a psychiatric diagnosis and also expressed perceived need make up 9.9 % of the population. An estimated 11.0% of the population are cases of untreated prevalence, a minority (3.6% of the population) of whom expressed perceived need for mental health care. Among persons using services, those without a psychiatric diagnosis based on interview criteria (4.4% of the population), showed high levels of perceived met need. Conclusions. The overall rate of perceived need found by this methodology lies between those found in the USA and Canada. The findings suggest that service use in the absence of diagnosis elicited by survey questionnaires may often represent successful intervention. In the survey, untreated prevalence was commonly not accompanied by perceived need for mental health care.