The Two-Interval Line-Segment Problem

In this paper, the NPMLE in the one-dimensional line segment problem is defined and studied, where line segments on the real line through two non-overlapping intervals are observed. The self-consistency equations for the NPMLE are defined and a quick algorithm for solving them is provided. Supnorm weak convergence to a Gaussian process and efficiency of the NPMLE is proved. The problem has a strong geological application in the study of the lifespan of species.

Design of mixed-longitudinal studies

Cross-sectional designs, longitudinal designs in which a single cohort is followed over time, and mixed-longitudinal designs in which several cohorts are followed for a shorter period are compared by their precision, potential for bias due to age, time and cohort effects, and feasibility. Mixed longitudinal studies have two advantages over longitudinal studies: isolation of time and age effects and shorter completion time. Though the advantages of mixed-longitudinal studies are clear, choosing an optimal design is difficult, especially given the number of possible combinations of the number of cohorts and number of overlapping intervals between cohorts. The purpose of this paper is to determine the optimal design for detecting differences in group growth rates.^ The type of mixed-longitudinal study appropriate for modeling both individual and group growth rates is called a "multiple-longitudinal" design. A multiple-longitudinal study typically requires uniform or simultaneous entry of subjects, who are each observed till the end of the study.^ While recommendations for designing pure-longitudinal studies have been made by Schlesselman (1973b), Lefant (1990) and Helms (1991), design recommendations for multiple-longitudinal studies have never been published. It is shown that by using power analyses to determine the minimum number of occasions per cohort and minimum number of overlapping occasions between cohorts, in conjunction with a cost model, an optimal multiple-longitudinal design can be determined. An example of systolic blood pressure values for cohorts of males and cohorts of females, ages 8 to 18 years, is given. ^

Bootstrap approaches for estimation and confidence intervals of long term memory processes

In this work, we investigate an alternative bootstrap approach based on a result of Ramsey [F.L. Ramsey, Characterization of the partial autocorrelation function, Ann. Statist. 2 (1974), pp. 1296-1301] and on the Durbin-Levinson algorithm to obtain a surrogate series from linear Gaussian processes with long range dependence. We compare this bootstrap method with other existing procedures in a wide Monte Carlo experiment by estimating, parametrically and semi-parametrically, the memory parameter d. We consider Gaussian and non-Gaussian processes to prove the robustness of the method to deviations from normality. The approach is also useful to estimate confidence intervals for the memory parameter d by improving the coverage level of the interval.

Overlapping medical alarms are almost indiscriminable

Objective: We explore how accurately and quickly nurses can identify melodic medical equipment alarms when no mnemonics are used, when alarms may overlap, and when concurrent tasks are performed. Background: The international standard IEC 60601-1-8 (International Electrotechnical Commission, 2005) has proposed simple melodies to distinguish seven alarm sources. Previous studies with nonmedical participants reveal poor learning of melodic alarms and persistent confusions between some of them. The effects of domain expertise, concurrent tasks, and alarm overlaps are unknown. Method: Fourteen intensive care and general medical unit nurses learned the melodic alarms without mnemonics in two sessions on separate days. In the second half of Day 2 the nurses identified single alarms or pairs of alarms played in sequential, partially overlapping, or nearly completely overlapping configurations. For half the experimental blocks nurses performed a concurrent mental arithmetic task. Results: Nurses' learning was poor and was no better than the learning of nonnurses in a previous study. Nurses showed the previously noted confusions between alarms. Overlapping alarms were exceptionally difficult to identify. The concurrent task affected response time but not accuracy. Conclusion: Because of a failure of auditory stream segregation, the melodic alarms cannot be discriminated when they overlap. Directives to sequence the sounding of alarms in medical electrical equipment must be strictly adhered to, or the alarms must redesigned to support better auditory streaming. Application: Actual or potential uses of this research include the implementation of IEC 60601-1-8 alarms in medical electrical equipment.

Maintenance optimisation of a multi-state series-parallel system considering economic dependence and state-dependent inspection intervals

This paper presents a maintenance optimisation method for a multi-state series-parallel system considering economic dependence and state-dependent inspection intervals. The objective function considered in the paper is the average revenue per unit time calculated based on the semi-regenerative theory and the universal generating function (UGF). A new algorithm using the stochastic ordering is also developed in this paper to reduce the search space of maintenance strategies and to enhance the efficiency of optimisation algorithms. A numerical simulation is presented in the study to evaluate the efficiency of the proposed maintenance strategy and optimisation algorithms. The simulation result reveals that maintenance strategies with opportunistic maintenance and state-dependent inspection intervals are more cost-effective when the influence of economic dependence and inspection cost is significant. The study further demonstrates that the optimisation algorithm proposed in this paper has higher computational efficiency than the commonly employed heuristic algorithms.

Critical timescales and time intervals for coupled linear processes

In 1991, McNabb introduced the concept of mean action time (MAT) as a finite measure of the time required for a diffusive process to effectively reach steady state. Although this concept was initially adopted by others within the Australian and New Zealand applied mathematics community, it appears to have had little use outside this region until very recently, when in 2010 Berezhkovskii and coworkers rediscovered the concept of MAT in their study of morphogen gradient formation. All previous work in this area has been limited to studying single–species differential equations, such as the linear advection–diffusion–reaction equation. Here we generalise the concept of MAT by showing how the theory can be applied to coupled linear processes. We begin by studying coupled ordinary differential equations and extend our approach to coupled partial differential equations. Our new results have broad applications including the analysis of models describing coupled chemical decay and cell differentiation processes, amongst others.

Beyond point forecasting : evaluation of alternative prediction intervals for tourist arrivals

This paper evaluates the performances of prediction intervals generated from alternative time series models, in the context of tourism forecasting. The forecasting methods considered include the autoregressive (AR) model, the AR model using the bias-corrected bootstrap, seasonal ARIMA models, innovations state space models for exponential smoothing, and Harvey’s structural time series models. We use thirteen monthly time series for the number of tourist arrivals to Hong Kong and Australia. The mean coverage rates and widths of the alternative prediction intervals are evaluated in an empirical setting. It is found that all models produce satisfactory prediction intervals, except for the autoregressive model. In particular, those based on the biascorrected bootstrap perform best in general, providing tight intervals with accurate coverage rates, especially when the forecast horizon is long.

Socio-demographic vulnerability to heatwave impacts in Brisbane, Australia : a time series analysis

Objective: Examining the association between socioeconomic disadvantage and heat-related emergency department (ED) visits during heatwave periods in Brisbane, 2000–2008. Methods: Data from 10 public EDs were analysed using a generalised additive model for disease categories, age groups and gender. Results: Cumulative relative risks (RR) for non-external causes other than cardiovascular and respiratory diseases were 1.11 and 1.05 in most and least disadvantaged areas, respectively. The pattern persisted on lags 0–2. Elevated risks were observed for all age groups above 15 years in all areas. However, with RRs of 1.19–1.28, the 65–74 years age group in more disadvantaged areas stood out, compared with RR=1.08 in less disadvantaged areas. This pattern was observed on lag 0 but did not persist. The RRs for male presentations were 1.10 and 1.04 in most and less disadvantaged areas; for females, RR was 1.04 in less disadvantaged areas. This pattern persisted across lags 0–2. Conclusions: Heat-related ED visits increased during heatwaves. However, due to overlapping confidence intervals, variations across socioeconomic areas should be interpreted cautiously. Implications: ED data may be utilised for monitoring heat-related health impacts, particularly on the first day of heatwaves, to facilitate prompt interventions and targeted resource allocation.

Exact parametric confidence intervals for Bland-Altman limits of agreement

Purpose The previous literature on Bland-Altman analysis only describes approximate methods for calculating confidence intervals for 95% Limits of Agreement (LoAs). This paper describes exact methods for calculating such confidence intervals, based on the assumption that differences in measurement pairs are normally distributed. Methods Two basic situations are considered for calculating LoA confidence intervals: the first where LoAs are considered individually (i.e. using one-sided tolerance factors for a normal distribution); and the second, where LoAs are considered as a pair (i.e. using two-sided tolerance factors for a normal distribution). Equations underlying the calculation of exact confidence limits are briefly outlined. Results To assist in determining confidence intervals for LoAs (considered individually and as a pair) tables of coefficients have been included for degrees of freedom between 1 and 1000. Numerical examples, showing the use of the tables for calculating confidence limits for Bland-Altman LoAs, have been provided. Conclusions Exact confidence intervals for LoAs can differ considerably from Bland and Altman’s approximate method, especially for sample sizes that are not large. There are better, more precise methods for calculating confidence intervals for LoAs than Bland and Altman’s approximate method, although even an approximate calculation of confidence intervals for LoAs is likely to be better than none at all. Reporting confidence limits for LoAs considered as a pair is appropriate for most situations, however there may be circumstances where it is appropriate to report confidence limits for LoAs considered individually.

Depression in Working Adults: Comparing the Costs and Health Outcomes of Working When Ill

Objective Working through a depressive illness can improve mental health but also carries risks and costs from reduced concentration, fatigue, and poor on-the-job performance. However, evidence-based recommendations for managing work attendance decisions, which benefit individuals and employers, are lacking. Therefore, this study has compared the costs and health outcomes of short-term absenteeism versus working while ill (“presenteeism”) amongst employed Australians reporting lifetime major depression. Methods Cohort simulation using state-transition Markov models simulated movement of a hypothetical cohort of workers, reporting lifetime major depression, between health states over one- and five-years according to probabilities derived from a quality epidemiological data source and existing clinical literature. Model outcomes were health service and employment-related costs, and quality-adjusted-life-years (QALYs), captured for absenteeism relative to presenteeism, and stratified by occupation (blue versus white-collar). Results Per employee with depression, absenteeism produced higher mean costs than presenteeism over one- and five-years ($42,573/5-years for absenteeism, $37,791/5-years for presenteeism). However, overlapping confidence intervals rendered differences non-significant. Employment-related costs (lost productive time, job turnover), and antidepressant medication and service use costs of absenteeism and presenteeism were significantly higher for white-collar workers. Health outcomes differed for absenteeism versus presenteeism amongst white-collar workers only. Conclusions Costs and health outcomes for absenteeism and presenteeism were not significantly different; service use costs excepted. Significant variation by occupation type was identified. These findings provide the first occupation-specific cost evidence which can be used by clinicians, employees, and employers to review their management of depression-related work attendance, and may suggest encouraging employees to continue working is warranted.

Methods for constructing uncertainty intervals for queries of Bayesian nets

In this paper the issue of finding uncertainty intervals for queries in a Bayesian Network is reconsidered. The investigation focuses on Bayesian Nets with discrete nodes and finite populations. An earlier asymptotic approach is compared with a simulation-based approach, together with further alternatives, one based on a single sample of the Bayesian Net of a particular finite population size, and another which uses expected population sizes together with exact probabilities. We conclude that a query of a Bayesian Net should be expressed as a probability embedded in an uncertainty interval. Based on an investigation of two Bayesian Net structures, the preferred method is the simulation method. However, both the single sample method and the expected sample size methods may be useful and are simpler to compute. Any method at all is more useful than none, when assessing a Bayesian Net under development, or when drawing conclusions from an ‘expert’ system.