A NOTE ON EVANESCENT PROCESSES

This note examines the connection between μ-invariant measures for the transition function of a continuous-time Markov chain and those of its q-matrix, Q. The major result establishes a necessary and aufficient condition for a convergent μ-invariant measure for Q to be μ-inhant for the minimal transition function, P, under the assumption that P is honest. This corrects Theorem 6 of Vere-Jones (1969) and the first part of Corollary 1 of Pollett (1986), both of which assert that the above conclusion holds in the absence of this condition. The error was pointed out by E.A. van Doom (1991) and the counterexample which be presented provides the basis for the present arguments. In determining where the error occurred in the original proof, we are able to identify a simple sufficient condition for μ-invariance.     

A role-reversal in the mother-daughter relationship

Psychoanalytic theorists have noted a particular dynamic in the mother-infant relationship in which the emotional needs of the mother predominate. When this situation occurs, the emotional needs of the infant may go unmet, resulting in impaired self-development. Through an integration of the ideas of mainstream psychoanalytic theorists and feminist psychoanalytic thinkers, this paper proposes the idea that, because of the intensity of the mother-daughter relationship, this dynamic may be more prevalent between mothers and daughters than between mothers and sons. A mother-daughter relationship is described in which the mother comes to depend on her daughter for emotional attunement and response, and the mother's selfobject needs predominate. As a consequence, the daughter is unable to develop a cohesive sense of self and experiences difficulty in achieving separation. Two clinical reports are presented to illustrate the way in which this mother-daughter dynamic manifests itself in the patient's life and in the therapeutic relationship. A negative transference dynamic is described resulting from these patient's fear of duplicating their relationship with their mothers in the therapeutic relationship by having to meet the selfobject needs of the therapist.     

BIAS IN LIST-ASSISTED TELEPHONE SAMPLES

A number of researchers have suggested list-assisted samplingfor the selection of telephone households to overcome some ofthe operational difficulties associated with the Mitofsky-Waksbergmethods of random digit dialing (RDD). An advantage of a list-assistedmethod of RDD is that an equal probability systematic sampleof telephone numbers can be selected and the variances of estimatesfrom such a sample are usually lower than from a clustered designlike the Mitofsky-Waksberg method. The main disadvantage ofthe list-assisted method is that it excludes some householdsfrom the sample, thus creating a coverage bias in the estimates.This article describes research on the coverage bias for a particularmethod of list-assisted sampling. The two key determinants ofcoverage bias are the proportion of households that are noteligible for the sample and the differences in the characteristicsof the covered and not covered populations. The results showthat about 4 percent of all households are excluded in nationalsamples using this method of sampling. Furthermore, they showthat the differences between the covered and uncovered populationsare generally not large. The coverage bias resulting from theseconditions may often be small.     

Ethnicity, migration and health: A population-based study of 338 refugees from Latin America, 396 nonrefugee immigrants from Finland and 161 from southern Europe and 996 age-, sex- and education-matched controls from Sweden

This article shows the influence of being a refugee from Latin America or a nonrefugee immigrant from southern Europe or Finland on self-reported illness, controlling for social factors and lifestyle. The study population consisted of 338 Latin American refugees, a random sample of 396 Finnish and 161 southern European immigrants and 996 age-, sex- and education-matched Swedish controls. The data were analysed unmatched with logistic regression (multivariate analysis) in main effect models. The strongest independent risk indicator for long-term illness was being a Latin American refugee (estimated odds ratio (OR)=2.96, 95% confidence interval (CI)=2.19–3.82). There was a significant association between being a Latin American refugee and period prevalence, ill health and unsatisfied need for care. Being a southern European or Finnish immigrant was a risk indicator of ill health but was not associated with the other dependent factors. Not feeling secure in daily life was a strong risk indicator for long-term illness and ill health (estimated OR=1.89, 95% CI=1.26–2.76 and OR=3.04, 95% CI= 1.97–4.48) respectively). Being a Latin American refugee was equal in importance to traditional risk factors such as overweight and not taking regular exercise for long-term illness and ill health.     

Multiparameter evidence synthesis in epidemiology and medical decision-making: current approaches

Summary.  Alongside the development of meta-analysis as a tool for summarizing research literature, there is renewed interest in broader forms of quantitative synthesis that are aimed at combining evidence from different study designs or evidence on multiple parameters. These have been proposed under various headings: the confidence profile method, cross-design synthesis, hierarchical models and generalized evidence synthesis. Models that are used in health technology assessment are also referred to as representing a synthesis of evidence in a mathematical structure. Here we review alternative approaches to statistical evidence synthesis, and their implications for epidemiology and medical decision-making. The methods include hierarchical models, models informed by evidence on different functions of several parameters and models incorporating both of these features. The need to check for consistency of evidence when using these powerful methods is emphasized. We develop a rationale for evidence synthesis that is based on Bayesian decision modelling and expected value of information theory, which stresses not only the need for a lack of bias in estimates of treatment effects but also a lack of bias in assessments of uncertainty. The increasing reliance of governmental bodies like the UK National Institute for Clinical Excellence on complex evidence synthesis in decision modelling is discussed.     

A continuous sampling plan using CUSUMs

A Continuous Sampling Plan, CSP-CUSUM, is proposed based on the use of Cumulative Sums (CUSUMs) for deciding when to switch between the phases of sampling inspection and 100% inspection. The Geometric CUSUM, also termed the Run-length CUSUM, is chosen for this purpose, and two separate CUSUMs are to be operated, one for each inspection phase. The conventional measures of performance for CSPs such as average outgoing quality, average fraction inspected, and average proportion passed under sampling inspection are evaluated for CSP-CUSUM, and comparisons with some standard CSPs are presented. An additional performance-measure, Average Cycle Length, is proposed. A table is provided to aid the choice of parameters for the operation of CSP-CUSUM. It is recommended that a Geometric CUSUM control chart be maintained in parallel with CSP-CUSUM to detect significant upward shifts in the incoming fraction defective.     

Computing maximum likelihood estimates from type II doubly censored exponential data

It is well-known that, under Type II double censoring, the maximum likelihood (ML) estimators of the location and scale parameters, θ and δ, of a twoparameter exponential distribution are linear functions of the order statistics. In contrast, when θ is known, theML estimator of δ does not admit a closed form expression. It is shown, however, that theML estimator of the scale parameter exists and is unique. Moreover, it has good large-sample properties. In addition, sharp lower and upper bounds for this estimator are provided, which can serve as starting points for iterative interpolation methods such as regula falsi. Explicit expressions for the expected Fisher information and Cramér-Rao lower bound are also derived. In the Bayesian context, assuming an inverted gamma prior on δ, the uniqueness, boundedness and asymptotics of the highest posterior density estimator of δ can be deduced in a similar way. Finally, an illustrative example is included.