Models and estimation for systems with recurrent events and usage processes.

This paper considers settings where populations of units may experience recurrent events, termed failures for convenience, and where the units are subject to varying levels of usage. We provide joint models for the recurrent events and usage processes, which facilitate analysis of their relationship as well as prediction of failures. Data on usage are often incomplete and we show how to implement maximum likelihood estimation in such cases. Random effects models with linear usage processes and gamma usage processes are considered in some detail. Data on automobile warranty claims are used to illustrate the proposed models and estimation methodology.

Bayesian analysis of quasi-life tables.

Quasi-life tables, in which the data arise from many concurrent, independent, discrete-time renewal processes, were defined by Baxter (1994, Biometrika 81:567-577), who outlined some methods for estimation. The processes are not observed individually; only the total numbers of renewals at each time point are observed. Crowder and Stephens (2003, Lifetime Data Anal 9:345-355) implemented a formal estimating-equation approach that invokes large-sample theory. However, these asymptotic methods fail to yield sensible estimates for smaller samples. In this paper, we implement a Bayesian analysis based on MCMC computation that works equally well for large and small sample sizes. We give three simulated examples, studying the Bayesian results, the impact of changing prior specification, and empirical properties of the Bayesian estimators of the lifetime distribution parameters. We also study the Baxter (1994, Biometrika 81:567-577) data, and uncover structure that has not been commented upon previously.

Is anoxic depolarisation associated with an ADC threshold? A Markov chain Monte Carlo analysis.

A Bayesian nonlinear hierarchical random coefficients model was used in a reanalysis of a previously published longitudinal study of the extracellular direct current (DC)-potential and apparent diffusion coefficient (ADC) responses to focal ischaemia. The main purpose was to examine the data for evidence of an ADC threshold for anoxic depolarisation. A Markov chain Monte Carlo simulation approach was adopted. The Metropolis algorithm was used to generate three parallel Markov chains and thus obtain a sampled posterior probability distribution for each of the DC-potential and ADC model parameters, together with a number of derived parameters. The latter were used in a subsequent threshold analysis. The analysis provided no evidence indicating a consistent and reproducible ADC threshold for anoxic depolarisation.

Temporal relation between the ADC and DC potential responses to transient focal ischemia in the rat: a Markov chain Monte Carlo simulation analysis.

Markov chain Monte Carlo simulation was used in a reanalysis of the longitudinal data obtained by Harris et al. (J Cereb Blood Flow Metab 20:28-36) in a study of the direct current (DC) potential and apparent diffusion coefficient (ADC) responses to focal ischemia. The main purpose was to provide a formal analysis of the temporal relationship between the ADC and DC responses, to explore the possible involvement of a common latent (driving) process. A Bayesian nonlinear hierarchical random coefficients model was adopted. DC and ADC transition parameter posterior probability distributions were generated using three parallel Markov chains created using the Metropolis algorithm. Particular attention was paid to the within-subject differences between the DC and ADC time course characteristics. The results show that the DC response is biphasic, whereas the ADC exhibits monophasic behavior, and that the two DC components are each distinguishable from the ADC response in their time dependencies. The DC and ADC changes are not, therefore, driven by a common latent process. This work demonstrates a general analytical approach to the multivariate, longitudinal data-processing problem that commonly arises in stroke and other biomedical research.

Influence of supplementary vitamins, minerals and essential fatty acids on the antisocial behaviour of young adult prisoners. Randomised, placebo-controlled trial.

BACKGROUND: There is evidence that offenders consume diets lacking in essential nutrients and this could adversely affect their behaviour. AIMS: To test empirically if physiologically adequate intakes of vitamins, minerals and essential fatty acids cause a reduction in antisocial behaviour. METHOD: Experimental, double-blind, placebo-controlled, randomised trial of nutritional supplements on 231 young adult prisoners, comparing disciplinary offences before and during supplementation. RESULTS: Compared with placebos, those receiving the active capsules committed an average of 26.3% (95% CI 8.3-44.33%) fewer offences (P=0.03, two-tailed). Compared to baseline, the effect on those taking active supplements for a minimum of 2 weeks (n=172) was an average 35.1% (95% CI 16.3-53.9%) reduction of offences (P<0.001, two-tailed), whereas placebos remained within standard error. CONCLUSIONS: Antisocial behaviour in prisons, including violence, are reduced by vitamins, minerals and essential fatty acids with similar implications for those eating poor diets in the community.