An Actuarial Survey of Statistical Models for Decrement and Transition Data, III. Counting Process Models

1996 ◽  
Vol 2 (3) ◽  
pp. 703-726 ◽  
Author(s):  
A.S. Macdonald
Keyword(s):  
Counting Process ◽  
Parametric Models ◽  
Process Models ◽  
Survival Models ◽  
Stochastic Integrals ◽  
Counting Processes ◽  
Normal Distributions ◽  
Moment Estimates ◽  
Multiple State ◽  
Asymptotic Normal

ABSTRACTCounting processes and their compensators are introduced at a heuristic level. The martingale property of stochastic integrals with respect to a compensated counting process leads to moment estimates and asymptotic normal distributions for statistics arising in multiple state, non-parametric and semi-parametric models. The place of survival models in actuarial education is discussed.

A NOTE ON THE CLASS OF GEOMETRIC COUNTING PROCESSES

2013 ◽  
Vol 27 (2) ◽  
pp. 177-185 ◽  
Author(s):  
Ji Hwan Cha ◽  
Maxim Finkelstein
Keyword(s):  
Poisson Process ◽  
Probabilistic Analysis ◽  
Counting Process ◽  
Geometric Distribution ◽  
Survival Models ◽  
Dependence Structure ◽  
Counting Processes ◽  
External Shocks ◽  
New Class ◽  
Independent Increments

In this paper, we suggest a new class of counting processes, called the Class of Geometric Counting Processes (CGCP), where each member of the counting process in the class has increments described by the geometric distribution. Distinct from the Poisson process, they do not possess the property of independent increments, which usually complicates probabilistic analysis. The suggested CGCP is defined and the dependence structure shared by the members of the class is discussed. As examples of useful applications, we consider stochastic survival models under external shocks. We show that the corresponding survival probabilities under reasonable assumptions can be effectively described by the CGCP without specifying the dependence structure.

Statistical approach for describing failures and lifetimes of water mains

1998 ◽  
Vol 38 (6) ◽  
pp. 209-217 ◽  
Author(s):  
Jianhua Lei ◽  
Sveinung Sægrov
Keyword(s):  
Data Base ◽  
Ductile Iron ◽  
Counting Process ◽  
Statistical Approach ◽  
Process Models ◽  
Average Lifetime ◽  
Maintenance Practice ◽  
Water Mains ◽  
Near Future

This paper demonstrates the statistical approach for describing failures and lifetimes of water mains. The statistical approach is based on pipe inventory data and the maintenance data registered in the data base. The approach consists of data pre-processing and statistical analysis. Two classes of statistical models are applied, namely counting process models and lifetime models. With lifetime models, one can estimate the probability which a pipe will fail within a time horizon. With counting process models one can see the deteriorating (or improving) trend in time of a group of “identical” pipes and their rates of occurrence of failure (ROCOF). The case study with the data base from Trondheim municipality (Norway) demonstrates the applicability of the statistical approach and leads to the following results: 1). In the past 20 years, Trondheim municipality has experienced approximately 250 to 300 failures per year. However, the number of failures per year will significantly increase in the near future unless better maintenance practice is implemented now. 2). Unprotected ductile iron pipes have a higher probability of failures than other materials. The average lifetime of unprotected ductile iron pipes is approximately 30 to 40 years shorter than the lifetime of a cast iron pipe. 3). Pipes installed 1963 and 1975 are most likely to fail in the future; 4) The age of a pipe does not play a significant role for the remaining lifetime of the pipe; 5). After 2 to 3 failures, a pipe enters a fast-failure stage (i.e., frequent multiple between failures).

scholarly journals Mixture survival models methodology: an application to cancer immunotherapy assessment in clinical trials

2019 ◽  
Author(s):  
Lizet Sanchez ◽  
Patricia Lorenzo-Luaces ◽  
Claudia Fonte ◽  
Agustin Lage
Keyword(s):  
Lung Cancer ◽  
Clinical Trials ◽  
Parametric Models ◽  
Survival Models ◽  
Advanced Lung Cancer ◽  
Control Group ◽  
Term Survival ◽  
Survival Expectations ◽  
Multimodality Test

Abstract Progress in immunotherapy revolutionized the treatment landscape for advanced lung cancer, raising survival expectations beyond those that were historically anticipated with this disease. In the present study, we describe the methods for the adjustment of mixture parametric models of two populations for survival analysis in the presence of long survivors. A methodology is proposed in several five steps: first, it is proposed to use the multimodality test to decide the number of subpopulations to be considered in the model, second to adjust simple parametric survival models and mixture distribution models, to estimate the parameters and to select the best model fitted the data, finally, to test the hypotheses to compare the effectiveness of immunotherapies in the context of randomized clinical trials. The methodology is illustrated with data from a clinical trial that evaluates the effectiveness of the therapeutic vaccine CIMAvaxEGF vs the best supportive care for the treatment of advanced lung cancer. The mixture survival model allows estimating the presence of a subpopulation of long survivors that is 44% for vaccinated patients. The differences between the treated and control group were significant in both subpopulations (population of short-term survival: p = 0.001, the population of long-term survival: p = 0.0002). For cancer therapies, where a proportion of patients achieves long-term control of the disease, the heterogeneity of the population must be taken into account. Mixture parametric models may be more suitable to detect the effectiveness of immunotherapies compared to standard models.

Explicit asymptotic results for open times in ion channel models

1997 ◽  
Vol 29 (04) ◽  
pp. 947-964
Author(s):  
Valeri T. Stefanov ◽  
Geoffrey F. Yeo
Keyword(s):  
Single Channel ◽  
Exponential Families ◽  
Markov Renewal Process ◽  
Actual Process ◽  
Asymptotic Results ◽  
Normal Distributions ◽  
Special Cases ◽  
The Difference ◽  
Asymptotic Normal ◽  
Receptor Channel

The dynamical aspects of single channel gating can be modelled by a Markov renewal process, with states aggregated into two classes corresponding to the receptor channel being open or closed, and with brief sojourns in either class not detected. This paper is concerned with the relation between the amount of time, for a given record, in which the channel appears to be open compared to the amount in which it is actually open and the difference in their proportions; this may be used to obtain information on the unobserved actual process from the observed one. Results, with extensions, on exponential families have been applied to obtain relevant generating functions and asymptotic normal distributions, including explicit forms for the parameters. Numerical results are given as illustration in special cases.

First crossing of basic counting processes with lower non-linear boundaries: A unified approach through pseudopolynomials (I)

1996 ◽  
Vol 28 (03) ◽  
pp. 853-876 ◽  
Author(s):  
Philippe Picard ◽  
Claude Lefèvre
Keyword(s):  
General Framework ◽  
Counting Process ◽  
Lower Boundary ◽  
Exact Distribution ◽  
Applied Probability ◽  
Renewal Processes ◽  
Counting Processes ◽  
Unified Approach ◽  
Non Linear ◽  
Birth Processes

The paper is concerned with the distribution of the levelNof the first crossing of a counting process trajectory with a lower boundary. Compound and simple Poisson or binomial processes, gamma renewal processes, and finally birth processes are considered. In the simple Poisson case, expressing the exact distribution ofNrequires the use of a classical family of Abel–Gontcharoff polynomials. For other cases convenient extensions of these polynomials into pseudopolynomials with a similar structure are necessary. Such extensions being applicable to other fields of applied probability, the central part of the present paper has been devoted to the building of these pseudopolynomials in a rather general framework.

scholarly journals Environmental impact modeling of selective laser sintering processes

2014 ◽  
Vol 20 (6) ◽  
pp. 459-470 ◽  
Author(s):  
Karel Kellens ◽  
Renaldi Renaldi ◽  
Wim Dewulf ◽  
Jean-pierre Kruth ◽  
Joost R. Duflou
Keyword(s):  
Environmental Impact ◽  
Selective Laser Sintering ◽  
Laser Sintering ◽  
Resource Consumption ◽  
Parametric Models ◽  
Process Models ◽  
Environmental Footprint ◽  
Design Features ◽  
Content Type ◽  
Impact Reduction

Purpose – This paper aims to present parametric models to estimate the environmental footprint of the selective laser sintering (SLS)’ production phase, covering energy and resource consumption as well as process emissions. Additive manufacturing processes such as (SLS) are often considered to be more sustainable then conventional manufacturing methods. However, quantitative analyses of the environmental impact of these processes are still limited and mainly focus on energy consumption. Design/methodology/approach – The required Life Cycle Inventory data are collected using the CO2PE! – Methodology, including time, power, consumables and emission studies. Multiple linear regression analyses have been applied to investigate the interrelationships between product design features on the one hand and production time (energy and resource consumption) on the other hand. Findings – The proposed parametric process models provide accurate estimations of the environmental footprint of SLS processes based on two design features, build height and volume, and help to identify and quantify measures for significant impact reduction of both involved products and the supporting machine tools. Practical implications – The gained environmental insight can be used as input for ecodesign activities, as well as environmental comparison of alternative manufacturing process plans. Originality/value – This article aims to overcome the current lack of environmental impact models, covering energy and resource consumption as well as process emissions for SLS processes.

scholarly journals HHLA2 and NEBL as novel prognostic biomarkers based on Rayleigh survival model in colorectal cancer

2021 ◽  
Author(s):  
Altaf Khan ◽  
Mohammed Azhar Aziz ◽  
Ghada T Alatar ◽  
Amal AlGhamdi ◽  
Mohammed A Hussein ◽  
...  
Keyword(s):  
Colorectal Cancer ◽  
Clinical Decision Making ◽  
Cox Model ◽  
Parametric Models ◽  
Prognostic Biomarkers ◽  
Survival Models ◽  
Diagnostic Tools ◽  
Brier Score ◽  
Small Subset ◽  
Parametric Survival

Abstract Background The primary focus for this study was investigation of prognostic biomarkers in colorectal cancer (CRC), since biomarkers are instrumental in clinical decision making and patient management as well as playing pivotal roles in precision medicine.Methods We analyzed indigenous dataset from colorectal cancer patients. Exon microarray dataset was used and 135 genes were identified as novel candidate biomarkers. 135 genes were further split into two groups: low and high gene expression values via ’maxstat’ algorithm, they were analyzed using Kaplan-Meier (K-M) analysis and univariate Cox model, and a set of 33 genes were identified as statistically significant (p¡0.05). Furthermore, using the ’VARCLUS’ algorithms (a SAS software procedure) which is a useful tool for variable reduction, based on the divisive clustering techniques, a small subset of 5 genes were selected out of 33 significant genes as potential candidates to build survival models. Both parametric and semi-parametric survival models were utilized to assess whether these 5 genes could be used as prognostic biomarkers.Results HHLA2 (p < 0.01) and NEBL (p < 0.01) genes emerged as potential biomarkers, based on the para- and semi-parametric models such as: Rayleigh, Exponential probability distributions, and Cox models and were also validated on independent datasets, apart from validation with qPCR test as well as with the cell lines patients data in the laboratory. A rigorous statistical evaluation for model’s performance were done via Harrell’s index, Brier score, Shoenfeld residual plots as well as with comparing several predictive model plots. We also made the comparison of Akaike and Bayesian Information(AIC and BIC) criteria as well as log-likelihood estimates. The Tukey-Anscome plot and Quantile-Quantile plot as diagnostic tools were applied to validate the parametric survival models. Conclusion Based on predictive models HHLA2 and NEBL novel biomarkers were found as statically significant.

scholarly journals Vitality Models Found Useful in Modeling Tag-Failure Times in Acoustic-tag Survival Studies

2020 ◽  
Author(s):  
John R. Skalski ◽  
Steven L. Whitlock
Keyword(s):  
Failure Time ◽  
Meta Analysis ◽  
Parametric Models ◽  
Survival Models ◽  
Battery Life ◽  
Research Attention ◽  
Failure Times ◽  
Demographic Heterogeneity ◽  
Acoustic Tags ◽  
Survival Studies

Abstract Acoustic telemetry studies often rely on the assumption that premature tag failure does not affect the validity of inferences. However, in some cases this assumption is possibly or likely invalid and it is necessary to apply a correction to estimation procedures. The question of which approaches and specific models are best suited to modeling acoustic tag failures has received little research attention. In this short communication, we present a meta-analysis of 42 acoustic tag-life studies, originally used to correct survival studies involving outmigrating juvenile salmonids in the Columbia/Snake river basin. We compare the performance of nine alternative parametric models including common failure-time/survival models and vitality models of Li and Anderson (2009 and 2013), which characterize demographic heterogeneity in the mortality of populations. The tag-life studies used acoustic tags from three different tag manufacturers, had expected lifetimes between 12 and 61 days, and had dry weights ranging from 0.22 to 1.65 grams. In 57% of the cases, the vitality models of Li and Anderson (2009 and 2013) fit the tag failure-times best. The vitality models were also the second-best choices in 17% of the cases. Together, the vitality models, log-logistic, (19%), and gamma models (14%) accounted for 90% of the models selected. Unlike more traditional failure-time models, the vitality models are capable of characterizing both the early onset of tag failure due to manufacturing errors and the anticipated battery life. We provide further guidance on appropriate sample sizes (50–100 tags) and procedures to be considered when applying precise tag-life corrections in release-recapture survival studies.

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