Wait-and-switch stochastic model of the non-Debye relaxation. Derivation of the Burr survival probability

Stochastic mechanism of relaxation, in which a dipole waits until a favourable condition for reorientation exists, is discussed. Assuming that an imposed direction of a dipole moment may be changed when a migrating defect reaches the dipole, we present a mathematically rigorous scheme relating the local random characteristics of a macroscopic system to its effective relaxation behaviour. We derive a relaxation function (the Burr survival probability) that is characterized by the stretched exponential or the power-law behaviour.     

Duration of long-term care: Socio-economic factors,type of care interactions and evolution

The time spent in dependence and the type of care an elderly receives are the two main cost drivers of long-term care (LTC). We aim to provide a better understanding of the duration of care by using a comprehensive social insurance dataset covering the LTC needs in Switzerland over a 20-years-period and including 230 000 observations on dependent elderly. First, using the framework of survival analysis, we calculate Kaplan–Meier estimates for the care duration and derive the main explaining factors through econometric models when care is received at home and in an institution. Retaining only significant covariates, the final accelerated failure time models allow us to predict the duration for different profiles of elderly along their age, gender, region of residence, type of household composition, acuity level and pre-retirement income. Second, we study the interaction of care durations when care is provided at home and in an institution. While our data supports that for short at-home care durations the time spent in institutional care is reduced, we find that both types of care are non-substitutes when the time spent at home has been longer. Under the latter regime, the time spent in institutional care remains at a constant level. Finally, given the longevity improvements over the period of observation, we analyze the impact of living longer on the time spent in dependence. Our results show that while the mean age at entry in dependence grows, the overall care duration does not significantly change. Given the expected increasing number of elderly in most developed countries, our study is relevant for government planning, budgeting social insurance schemes, estimating personal savings needs and calculating private insurance premiums.     

The survival probability of critical and subcritical branching processes in finite state space Markovian environment

Let ${\left(Z_n\right)}_{n\ge 0}$ be a branching process in a random environment defined by a Markov chain ${\left(X_n\right)}_{n\ge 0}$ with values in a finite state space $\mathbb{X}$. Let ${\mathbb{P}}_i$ be the probability law generated by the trajectories of ${\left(X_n\right)}_{n\ge 0}$ starting at $X_0=i\in \mathbb{X}.$ We study the asymptotic behaviour of the joint survival probability ${\mathbb{P}}_i\left(Z_n>0,X_n=j\right)$, $j\in \mathbb{X}$ as $n\to +\infty$ in the critical and strongly, intermediate and weakly subcritical cases.     

Persistence of sums of correlated increments and clustering in cellular automata

Let $T$ be the first return time to $(?\infty ,0]$ of sums of increments given by a functional of a stationary Markov chain. We determine the asymptotic behavior of the survival probability, $\mathbb{P}(T\ge t)～C{t}^{?1∕2}$ for an explicit constant $C$. Our analysis is based on a connection between the survival probability and the running maximum of the time-reversed process, and relies on a functional central limit theorem for Markov chains. As applications, we recover known clustering results for the 3-color cyclic cellular automaton and the Greenberg–Hastings model, and we prove a new clustering result for the 3-color firefly cellular automaton.     

A Markov model for analyzing the evolution of bladder carcinoma

A Markovian approach to analyze different states of the superficial vesical carcinoma is considered, taking into account up to two recurrences and the possibility of progression. So, three transient states are considered: free of disease, first, and second recurrence; and an absorbent state, the progression. A methodology based in phase-type distributions is also used, that allows the usual quantities of interest in survival studies to be expressed in a well-structured form. This type of distribution has shown its utility in queue theory, and has the advantage that mathematical expressions can be presented in a closed form that allows algebraic treatment.     

Extension of Mood’s median test for survival data

Mood’s median test for testing the equality of medians is a nonparametric approach, which has been widely used for uncensored data in practice. For survival data, many nonparametric methods have been proposed to test for the equality of survival curves. However, if the survival medians, rather than the curves, are compared, those methods are not applicable. Some approaches have been developed to fill this gap. Unfortunately, in general those tests have inflated type I error rates, which make them inapplicable to survival data with small sample sizes. In this paper, Mood’s median test for uncensored data is extended for survival data. The results from a comprehensive simulation study show that the proposed test outperforms existing methods in terms of controlling type I error rate and detecting power.     

Random effects Weibull regression model for occupational lifetime

With great interest we read the recent publication of Sohn et al. [Sohn, S.Y., Chang, I.S., Moon, T.H., 2007. Random effects Weibull regression model for occupational lifetime. European Journal of Operational Research 179, 124–131] on a Weibull regression model with random effects for modelling occupational lifetime. We congratulate Sohn and colleagues on their comprehensive and clearly written paper. Nevertheless, we would like to comment on two points, the first regarding the moments of the underlying Weibull distribution, the second regarding the relations of Sohn’s model to the class of frailty models.     

Ruin probabilities for a risk process with stochastic return on investments

In this paper, we consider a risk process with stochastic return on investments. The basic risk process is the classical risk process while the return on the investment generating process is a compound Poisson process plus a Brownian motion with positive drift. We obtain an integral equation for the ultimate ruin probability which is twice continuously differentiable under certain conditions. We then derive explicit expressions for the lower bound for the ruin probability. We also study a joint distribution related to exponential functionals of Brownian motion which is required in the derivations of the explicit expressions for the lower bound.     

Network regularised Cox regression and multiplex network models to predict disease comorbidities and survival of cancer

In cancer genomics, gene expression levels provide important molecular signatures for all types of cancer, and this could be very useful for predicting the survival of cancer patients. However, the main challenge of gene expression data analysis is high dimensionality, and microarray is characterised by few number of samples with large number of genes. To overcome this problem, a variety of penalised Cox proportional hazard models have been proposed. We introduce a novel network regularised Cox proportional hazard model and a novel multiplex network model to measure the disease comorbidities and to predict survival of the cancer patient. Our methods are applied to analyse seven microarray cancer gene expression datasets: breast cancer, ovarian cancer, lung cancer, liver cancer, renal cancer and osteosarcoma. Firstly, we applied a principal component analysis to reduce the dimensionality of original gene expression data. Secondly, we applied a network regularised Cox regression model on the reduced gene expression datasets. By using normalised mutual information method and multiplex network model, we predict the comorbidities for the liver cancer based on the integration of diverse set of omics and clinical data, and we find the diseasome associations (disease–gene association) among different cancers based on the identified common significant genes. Finally, we evaluated the precision of the approach with respect to the accuracy of survival prediction using ROC curves. We report that colon cancer, liver cancer and renal cancer share the CXCL5 gene, and breast cancer, ovarian cancer and renal cancer share the CCND2 gene. Our methods are useful to predict survival of the patient and disease comorbidities more accurately and helpful for improvement of the care of patients with comorbidity. Software in Matlab and R is available on our GitHub page: https://github.com/ssnhcom/NetworkRegularisedCox.git.     

Bipartite network analysis reveals metabolic gene expression profiles that are highly associated with the clinical outcomes of acute myeloid leukemia

Dysregulated and reprogrammed metabolism are one of the most important characteristics of cancer, and exploiting cancer cell metabolism can aid in understanding the diverse clinical outcomes for patients. To investigate the differences in metabolic pathways among patients with acute myeloid leukemia (AML) and differential survival outcomes, we systematically conducted microarray data analysis of the metabolic gene expression profiles from 384 patients available from the Gene Expression Omnibus and Cancer Genome Atlas databases. Pathway enrichment analysis of differentially expressed genes (DEGs) showed that the metabolic differences between low-risk and high-risk patients mainly existed in two pathways: biosynthesis of unsaturated fatty acids and oxidative phosphorylation. Using the gene-pathway bipartite network, 62 metabolic genes were identified from 272 DEGs involved in 88 metabolic pathways. Based on the expression patterns of the 62 genes, patients with shorter overall survival (OS) durations in the training set (hazard ratio (HR) = 1.58, p = 0.038) and in two test sets (HR = 1.69 and 1.56 and p = 0.089 and 0.029, respectively) were well discriminated by hierarchical clustering analysis. Notably, the expression profiles of ALAS2, BCAT1, BLVRB, and HK3 showed distinct differences between the low-risk and high-risk patients. In addition, models for predicting the OS outcome of AML from the 62 gene signatures achieved improved performance compared with previous studies. In conclusion, our findings reveal significant differences in metabolic processes of patients with AML with diverse survival durations and provide valuable information for clinical translation.