An extension of the continual reassessment method using decision theory

The primary goal of a phase I trial is to find the maximally tolerated dose (MTD) of a treatment. The MTD is usually defined in terms of a tolerable probability, q*, of toxicity. Our objective is to find the highest dose with toxicity risk that does not exceed q*, a criterion that is often desired in designing phase I trials. This criterion differs from that of finding the dose with toxicity risk closest to q*, that is used in methods such as the continual reassessment method. We use the theory of decision processes to find optimal sequential designs that maximize the expected number of patients within the trial allocated to the highest dose with toxicity not exceeding q*, among the doses under consideration. The proposed method is very general in the sense that criteria other than the one considered here can be optimized and that optimal dose assignment can be defined in terms of patients within or outside the trial. It includes as an important special case the continual reassessment method. Numerical study indicates the strategy compares favourably with other phase I designs.

Exact calculations of survival probability for diffusion on growing lines, disks, and spheres: The role of dimension

Unlike standard applications of transport theory, the transport of molecules and cells during embryonic development often takes place within growing multidimensional tissues. In this work, we consider a model of diffusion on uniformly growing lines, disks, and spheres. An exact solution of the partial differential equation governing the diffusion of a population of individuals on the growing domain is derived. Using this solution, we study the survival probability, S(t). For the standard nongrowing case with an absorbing boundary, we observe that S(t) decays to zero in the long time limit. In contrast, when the domain grows linearly or exponentially with time, we show that S(t) decays to a constant, positive value, indicating that a proportion of the diffusing substance remains on the growing domain indefinitely. Comparing S(t) for diffusion on lines, disks, and spheres indicates that there are minimal differences in S(t) in the limit of zero growth and minimal differences in S(t) in the limit of fast growth. In contrast, for intermediate growth rates, we observe modest differences in S(t) between different geometries. These differences can be quantified by evaluating the exact expressions derived and presented here.

Improving the estimation of probability of bidder participation in procurement auctions

Anticipating the number and identity of bidders has significant influence in many theoretical results of the auction itself and bidders’ bidding behaviour. This is because when a bidder knows in advance which specific bidders are likely competitors, this knowledge gives a company a head start when setting the bid price. However, despite these competitive implications, most previous studies have focused almost entirely on forecasting the number of bidders and only a few authors have dealt with the identity dimension qualitatively. Using a case study with immediate real-life applications, this paper develops a method for estimating every potential bidder’s probability of participating in a future auction as a function of the tender economic size removing the bias caused by the contract size opportunities distribution. This way, a bidder or auctioner will be able to estimate the likelihood of a specific group of key, previously identified bidders in a future tender.

Achieving a national sample of nursing homes: Balancing probability techniques and practicalities

Sampling design is critical to the quality of quantitative research, yet it does not always receive appropriate attention in nursing research. The current article details how balancing probability techniques with practical considerations produced a representative sample of Australian nursing homes (NHs). Budgetary, logistical, and statistical constraints were managed by excluding some NHs (e.g., those too difficult to access) from the sampling frame; a stratified, random sampling methodology yielded a final sample of 53 NHs from a population of 2,774. In testing the adequacy of representation of the study population, chi-square tests for goodness of fit generated nonsignificant results for distribution by distance from major city and type of organization. A significant result for state/territory was expected and was easily corrected for by the application of weights. The current article provides recommendations for conducting high-quality, probability-based samples and stresses the importance of testing the representativeness of achieved samples.

Reconstructing identity of older people in using day care services in Taiwan: A grounded theory study

Adult day care centers provide a means whereby frail or disabled older people can remain living at home particularly when their family care-givers engage in waged work. In Taiwan, adult day care services appear to meet the cultural needs of both older people and their families for whom filial care is vital. Little research attention has been paid to the use of day care services in Taiwan, the uptake rate of which is low. This grounded theory study explored the ways in which older people and family care-givers construct meanings around the use of day care services in Taiwan. The research methodology drew on the theoretical tenets of symbolic interactionism and methods were informed by the grounded theory. In-depth interviews with 30 participants were undertaken. Reconstructing identity in a shifting world is the core category of the study and reflects a process of reframing whereby older people came to new definitions of social responsibility and independence within the context of the day care center. The implications of the findings is that the older people, rather than seeking to be relieved of social responsibilities, worked very hard to frame and reframe a social role. Rather than letting the institutions undermine or disrupt their identity, the older people worked to actively negotiate and redefine the meaning of self. Thus, although reluctant to come to use the services at the outset, they found a way to manage their lives independently. Social roles and responsibilities as older parents were retained. This study explored the process of meaning construction of day care use and the ways in which this process entailed a reconstruction of the identities of the participants. The evidence from this study underlines the importance of recognizing and acknowledging subjectively conceived identities as work that older people undertake, when in care, to render their lives meaningful.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.

Feminist Disability Theory: Domestic Violence Against Women with a Disability

Women with a disability continue to experience social oppression and domestic violence as a consequence of gender and disability dimensions. Current explanations of domestic violence and disability inadequately explain several features that lead women who have a disability to experience violent situations. This article incorporates both disability and material feminist theory as an alternative explanation to the dominant approaches (psychological and sociological traditions) of conceptualising domestic violence. This paper is informed by a study which was concerned with examining the nature and perceptions of violence against women with a physical impairment. The emerging analytical framework integrating material feminist interpretations and disability theory provided a basis for exploring gender and disability dimensions. Insight was also provided by the women who identified as having a disability in the study and who explained domestic violence in terms of a gendered and disabling experience. The article argues that material feminist interpretations and disability theory, with their emphasis on gender relations, disablism and poverty, should be used as an alternative tool for exploring the nature and consequences of violence against women with a disability.