Parameter Identifiability and Redundancy in a General Class of Stochastic Carcinogenesis Models

Background Heidenreich et al. (Risk Anal 1997 17 391–399) considered parameter identifiability in the context of the two-mutation cancer model and demonstrated that combinations of all but two of the model parameters are identifiable. We consider the problem of identifiability in the recently developed carcinogenesis models of Little and Wright (Math Biosci 2003 183 111–134) and Little et al. (J Theoret Biol 2008 254 229–238). These models, which incorporate genomic instability, generalize a large number of other quasi-biological cancer models, in particular those of Armitage and Doll (Br J Cancer 1954 8 1–12), the two-mutation model (Moolgavkar et al. Math Biosci 1979 47 55–77), the generalized multistage model of Little (Biometrics 1995 51 1278–1291), and a recently developed cancer model of Nowak et al. (PNAS 2002 99 16226–16231). Methodology/Principal Findings We show that in the simpler model proposed by Little and Wright (Math Biosci 2003 183 111–134) the number of identifiable combinations of parameters is at most two less than the number of biological parameters, thereby generalizing previous results of Heidenreich et al. (Risk Anal 1997 17 391–399) for the two-mutation model. For the more general model of Little et al. (J Theoret Biol 2008 254 229–238) the number of identifiable combinations of parameters is at most less than the number of biological parameters, where is the number of destabilization types, thereby also generalizing all these results. Numerical evaluations suggest that these bounds are sharp. We also identify particular combinations of identifiable parameters. Conclusions/Significance We have shown that the previous results on parameter identifiability can be generalized to much larger classes of quasi-biological carcinogenesis model, and also identify particular combinations of identifiable parameters. These results are of theoretical interest, but also of practical significance to anyone attempting to estimate parameters for this large class of cancer models

The ecology of outdoor rape: The case of Stockholm, Sweden

The objective of this article is to report the results of an ecological study into the geography of rape in Stockholm, Sweden, using small area data. In order to test the importance of factors indicating opportunity, accessibility and anonymity to the understanding of the geography of rape, a two-stage modelling approach is implemented. First, the overall risk factors associated with the occurrence of rape are identified using a standard Poisson regression, then a local analysis using profile regression is performed. Findings from the whole-map analysis show that accessibility, opportunity and anonymity are all, to different degrees, important in explaining the overall geography of rape - examples of these risk factors are the presence of subway stations or whether a basområde is close to the city centre. The local analysis reveals two groupings of high risk of rape areas associated with a variety of risk factors: city centre areas with a concentration of alcohol outlets, high residential population turnover and high counts of robbery; and poor suburban areas with schools and large female residential populations where subway stations are located and where people express a high fear of crime. The article concludes by reflecting upon the importance of these results for future research as well as indicating the implications of these results for policy

Parameter identifiability and redundancy: theoretical considerations

Abstract In this paper we outline general considerations on parameter identifiability, and introduce the notion of weak local identifiability and gradient weak local identifiability. These are based on local properties of the likelihood, in particular the rank of the Hessian matrix. We relate these to the notions of parameter identifiability and redundancy previously introduced by Rothenberg (Econometrica 39 (1971) 577-591) and Catchpole and Morgan (Biometrika 84 (1997) 187-196). Within certain special classes of exponential family models, gradient weak local identifiability is shown to be equivalent to lack of parameter redundancy. We consider applications to a recently developed class of cancer models of Littl

A λ-cut approximate algorithm for goal-based bilevel risk management systems

Bilevel programming techniques a re developed for decentralised decision problems with decision makers located in two levels. Both upper and lower decision makers, termed as leader and follower, try to optimize their own objectives in solution procedure but are affected by those of the other levels. When a bilevel decision model is built with fuzzy codlicients and the leader and/or follower have goals for their objectives, we call it fuzzy goal bilevel (FGBL) decision problem. This paper first proposes a A-cut set based FGBL model. A programmable A-CUt approximate algorithm is then presented in detail. Based on this algorithm, a FCBL software system is developed to reach solutions for FGBL decision problems. Finally, two examples are given to illustrate the application of the proposed algorithm