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EN
Sewers deteriorate sooner or later. Two types of models have been developed recently for modelling this deterioration process, using CCTV-inspection results. They are based on methods of survival analysis and Markov processes. These approaches are introduced and described. Examples illustrate the calibration of theses models and interpretation of their results. Potential problems of the two approaches are shown and discussed. The paper concludes with an introduction of further applications of the resulting deterioration model for individual sewer networks.
PL
Kanały sanitarne w trakcie eksploatacji ulegają nieuchronnemu procesowi pogarszania się ich stanu technicznego. W ostatnim czasie opracowano dwa modele opisujące proces pogarszania się stanu technicznego kanałów, bazujące na rezultatach inspekcji telewizyjnych. Podstawą tych modeli są metody matematyczne analizy niezawodności oraz procesu Markowa. Ujęcia rozpatrywanego zagadnienia zostały wprowadzone i opisane. Przykłady zawarte w pracy ilustrują kalibrację modeli oraz interpretację wyników. Wskazane zostały problemy związane z aplikacją prezentowanych modeli starzenia kanałów. W podsumowaniu pracy zaprezentowano możliwości zastosowania opisywanych modeli starzenia do określania przyszłego stanu technicznego konkretnych kanałów.
EN
Research background: Researchers traditionally assume that learning is a product of experience. In general, it means that learning can only take place through the attempt to solve a problem and therefore only takes place during activity (Arrow, 1962). On the ground of organizational theory, it has two implications. First, we can agree that repeated activity requires less effort. Second, we can argue that firms undertake activities, with which they have been the most successful in the past and that they expect to be the most successful in the future. Purpose of the article: The aim of the research is twofold. Firstly, this article aims to investigate if we can identify a relationship between the experience in PPP projects and the performance of initiatives of this kind. Secondly, the article aims to provide an interpretation of the relationship between experience and PPP performance. Methods: This research investigates factors influencing the survival of PPP projects in Poland over the period 2009?2015. Cox proportional hazard model is utilized to distinguish between PPPs that succeeded to the operation phase and those that were canceled on the procurement stage. Findings & Value added: The research confirms the existence of a positive relationship between experience in PPP and the outcome of a PPP development.
EN
In survival analysis the subject of observation is duration of time until some event called failure event. Often in such studies only partial information on the length of failure time is available what yields the so-called right-censored observations. The main interest in survival analysis is either to estimate the distribution of the true failure time or to identify the relationship between the true failure time and a set of some covariates. Additional troublesome point of theory and application of survival techniques is treatment of grouped observations (life-tables) along with incorporating covariates. In the paper a new approach is considered which allows to treat the censored life-table with qualitative covariates as a standard contingency table. Such a table can be further analysed by means of log-linear models or other standard multivariate inference techniques.
PL
W pracy przedstawiono propozycję analizy tablicy trwania życia dla danych prawostronnie cenzurowanych. Przedstawiona metoda pozwala na sprowadzenie takiej tablicy do wielowymiarowej tablicy kontyngencyjnej, którą można analizować standardowymi technikami wielowymiarowego wnioskowania statystycznego, np. za pomocą modeli logarytmiczno-liniowych.
EN
The aim of the study is to achieve initial recognition of the factors that determine the survival rate of Polish micro and small enterprises. The research, conducted in June 2011 and covering a sample of 147 entities, constitutes a pilot study. We explore the determinants of companies’ survival and test whether firms with different characteristics exhibit different performances in terms of the duration of survival. The results indicate substantial differences in the survival rates. The factors taken into account in this study, which to the greatest extent possible differentiates the whole sample in view of survival, are: running the business with employees or alone and specialist vs. popular activity as regards the required competences. Larger firms (with employees) are significantly less likely to close than smaller firms. Firms in highly competitive markets are more prone to closure.
EN
The paper presents results of survey concerning the influence of gender, age and education of the unemployed on job searching time. For the sake of specificity of survey, especially in case of censored data, the Cox’s proportional hazard model has been used for the identification of determinants and research their influence for time needed to take up a job. To the model, except independent variables, their interactions that enable the calculation of interplay of researched variables have been included. 20846 persons registered as unemployed in the Local Labour Office in Szczecin and due to various reasons unregistered in 2010 have been included in the research. If unregistering occurred due to different reasons than finding a job, such an observation has been considered as censored.
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Content available remote Adaptive robust estimation in the Cox regression model
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EN
A family of robust estimators of the regression parameter for the Cox regression model proposed and recommended by Bednarski in [3] depends on the true unknown parameter. It is demonstrated that an adaptive procedure, making use of preliminary robust estimators, leads to asymptotically equivalent estimation procedures. Discussion of data analysis for a real data case is given.
PL
Rodzina odpornych estymatorów parametru regresji w modelu Coxa, zaproponowana przez Bednarskiego (3), zależy od wartości nieznanego parametru. Dowodzi się, że procedura adaptacyjna polegająća na zastąpieniu parametru przez "prowizoryczny" odporny estymator, nie zmienia asymptotycznych własności wyjściowego estymatora. Praca zawiera także statystyczną analizę rzeczywistego zbioru danych.
EN
Background: Premature deaths constitute 31.1% of all deaths in Łódź. Analysis of the causes of premature deaths may be helpful in the evaluation of health risk factors. Moreover, findings of this study may enhance prophylactic measures. Material and Methods: In 2001, 1857 randomly selected citizens, aged 18-64, were included in the Countrywide Integrated Noncommunicable Diseases Intervention (CINDI) Programme. In 2009, a follow-up study was conducted and information on the subjects of the study was collected concerning their health status and if they continued to live in Łódź. The Cox proportional hazards model was used for evaluation of hazard coefficients. We adjusted our calculations for age and sex. The analysis revealed statistically significant associations between the number of premature deaths of the citizens of Łódź and the following variables: a negative self-evaluation of health - HR = 3.096 (95% CI: 1.729-5.543), poor financial situation - HR = 2.811 (95% CI: 1.183‑6.672), occurring in the year preceding the study: coronary pain - HR = 2.754 (95% CI: 1.167-6.494), depression - HR = 2.001 (95% CI: 1.222-3.277) and insomnia - HR = 1.660 (95% CI: 1.029-2.678). Our research study also found a negative influence of smoking on the health status - HR = 2.782 (95% CI: 1.581-4.891). Moreover, we conducted survival analyses according to sex and age with Kaplan-Meier curves. Conclusions: The risk factors leading to premature deaths were found to be highly significant but possible to reduce by modifying lifestyle-related health behaviours. The confirmed determinants of premature mortality indicate a need to spread and intensify prophylactic activities in Poland, which is a post-communist country, in particular, in the field of cardiovascular diseases.
EN
The aim of the research was an assessment of the relative risk of liquidation of a company depending on its age. The research covered economic entities established in Szczecin in the period 1990-2010. The analysis was carried out with the use of a logit model. The risk of company liquidation was examined depending on the entity’s age expressed both in months (continuous variable) and in grouped intervals (year, half-year). In this way, attention was drawn to the benefits of continuous variable coding (rank and 0-1 coding). The research covered companies established during 1990-2010 in total (over 120 thousand) and in time periods resulting from the cyclical character of liquidation of companies (in accordance with the earlier research findings). The research showed that the risk of company liquidation decreases as the company grows older (the use of a continuous variable and a rank variable). On the other hand, the risk of subsequent age groups (using the 0-1 variable) prevents the risk from being monotonous.
EN
The aim of this paper was to compare the new technique (survival analysis) used in the credit risk models with the traditional one (discriminant analysis), analyse the strengths and weaknesses of both methods and their usage in practice. This study attempts to use macroeconomic data to build models and examine its impact to the prediction. For this purpose, a number of models was built on the basis of the sample of 1547 enterprises including 494 defaults. The time range covered by sample was 2002-2012.
EN
Clinical investigations yield huge amount of experimental data which need appropriate processing. High degree of their variability decreases quality of prognostic and classification results. Frequently problem of strong redundancy of variables incorporated into model occurs, produces computational instabilities and in multifactorial models makes the appropriate interpretation of obtained results hindered. In this paper we present the set of mathematical procedures used in comparative analysis of two treatment methods for patients with advanced cervical cancer: radiotherapy and combined treatment of ionizing irradiation and chemotherapy.
EN
Modele predykcji upadłości MŚP w Polsce – analiza z wykorzystaniem modelu przeżycia Coxa i modelu regresji logistycznej
EN
This paper aims at identifying factors (external and internal) affecting the ability of an enterprise to survive on the market. The analysis is based on the results of a retrospective study conducted in 2012 on a sample of enterprises from Malopolska voivodeship. Methods and models of event history analysis, including semiparametric Cox’s model were applied to analyse enterprises’ survival. The approach based on the event history analysis allows us to include dynamics of the process. The results provided extensive data on how factors such as size, activity sector, market range, legal form and internals conditions like: owner characteristics, investments, profits, reported barriers affect the survival of enterprises.
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Content available remote Slábne v ČR mezigenerační přenos rozvodu?
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EN
This study investigates changes in the effect of parental divorce on the odds of union dissolution in children in the Czech Republic. Using survival analysis and Czech GGS data, it shows that the intergeneration transmission of divorce varied over marital cohorts to a significant degree. While parental divorce had insignificant effect in the oldest marriage cohort, it subsequently grew. In the 1980–1989 marriage cohort, the risk of divorce was 3.7 times higher among children of divorced parents than among children whose parents did not divorce. In the most recent marriage cohort (1990–2005), the parental divorce effect weakened but was still significant: children of divorced parents experienced a divorce risk that was twice as high that of children from intact families. This convergence of divorce risks resulted from two parallel trends: the rising divorce risk among children from non-divorced families and the declining divorce risk among children of divorce.
PL
Analiza przeżycia zajmuje się modelowaniem statystycznym przebiegów czasowych, dla których interesujące są czasy trwania pomiędzy wybraną chwilą a oczekiwanym zdarzeniem. Zdarzenie to nazywane jest rezultatem lub punktem końcowym. Dane do analizy przeżycia mogą być także traktowane, jako czas do zaistnienia zdarzenia, czas przeżycia, czas do awarii, czas niezawodności, czas trwania itp. Analiza takich danych jest ważna zarówno w medycynie 1, naukach społecznych 2 jak i w inżynierii 3. Analiza przeżycia znalazła tez zastosowanie w technice nurkowej [1]. W artykule zostały przedstawione podstawy analizy przeżycia, które posłużą do szacowania możliwości wystąpienia symptomów tlenowej toksyczności ośrodkowej przedstawione w części czwartej cyklu artykułów.
EN
Survival analysis deals with statistical modelling of time elapsed between a particular moment and an expected event. The event is referred to as a result or an end point. The data used in survival analysis may also be treated as the time until an event occurs, time of survival, time until a failure, time of reliability, duration, etc. An analysis of such data is equally important for medicine 1, social sciences2 and engineering3. Survival analysis can also be applied to diving [1]. The article presents the basics of survival analysis which will serve in estimating the probability of an occurrence of central oxygen toxicity symptoms, which will be listed in the fourth part of the cycle of articles.
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Cox proportional hazard model is one of the most common methods used in time to event analysis. The idea of the model is to define a hazard level as a dependent variable which is explained by the time-related component (so-called baseline hazard) and the covariates- related component. The model is based on several restrictive assumptions one of which is the assumption of proportional hazard. However, if this assumption is violated, this does not necessarily prevent an analyst from using Cox model. The current paper presents two ways of model modification in the case of non-proportional hazards: introducing interactions of selected covariates with function of time and stratification model. Calculations performed give the evidence that both methods result in better model fit as compared with the original model. Additionally, they allow interpreting the parameters estimates more precisely, taking into account the effect of the covariate at the hazard level that is changing over time. The choice of the appropriate method of tied events handling however is not straightforward and should be adjusted to the particular analysis purpose.
17
Content available remote Mobilita mezi zaměstnaností a nezaměstnaností u starších pracovníků v ČR
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EN
There is a sharp discrepancy between the emphasis being placed on active ageing and labour market participation in older age and the high unemployment rates observed among older workers. Cross-sectional data in the Czech Republic consistently present evidence of job insecurity and employment vulnerability in older age groups. Aggregated data and statistical indices do not, however, offer a sufficiently detailed picture of the social processes (e.g. exit from the labour market, duration of unemployment, and exit from unemployment) behind the numbers. This article takes a dynamic look at the position of older workers in the labour market by investigating transitions between employment and unemployment using a sub-sample of older workers (50 year and over) from the Czech EU-SILC, who were interviewed repeatedly in a panel survey between 2004 and 2009. The authors use survival analysis methods to study the time-dependence of transitions into and out of unemployment and both with and without covariates. The results suggest that older workers are not at a higher risk of exiting the labour market (compared to other age groups), but once they are unemployed, their odds of getting back into employment are significantly lower. Even when controls (such as education level) are included in the model this disadvantage persists. Interestingly, while education generally protects people from labour market exit, this protective effect is weaker among older workers.
18
Content available remote Partnerské dráhy prvorodiček bez partnera ve společné domácnosti
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EN
We investigate partnership transitions of mothers who had no coresidential partner at the time of birth of their first child (‘solo mothers’). Using retrospective partnership and co-residence histories from the Czech 2005 GGS, we investigate mothers’ entry into the first subsequent co-residential partnership using event history methods. We test several hypotheses derived from the individualisation theory. While approximately one half of ‘solo mothers’ had no co-residential partner at the time they had their first child, almost 50% of them did enter a co-residential partnership subsequently. The probability of transitioning into a co-residential partnership increased over cohorts. Whereas about 25% of solo mothers from the oldest cohort (first child born before entered a co-residential partnership with the 20 years after having their first child, in the youngest cohort the figure was almost two-thirds. The highest odds are among very young solo mothers. Well-educated solo mothers are more likely to remain without a co-residential partner and the effect of education increases over cohorts, perhaps reflecting their growing ability and willingness to remain solo.
PL
Analiza przeżycia to zespół metod służących do modelowania czasu trwania kohorty, której jednostki są obserwowane od zdefiniowanego momentu początkowego do zdefiniowanego zdarzenia końcowego. Czas trwania jest traktowany jako zmienna losowa ciągła. Specyfika metod analizy przeżycia związana jest z występowaniem obserwacji cenzurowanych (uciętych) oraz tym, iż funkcje gęstości obserwowanej zmiennej są często nieznane, a rozkłady silnie asymetryczne, co uniemożliwia stosowanie metod klasycznej statystyki. Podstawową funkcją stosowaną w analizie przeżycia jest funkcja dalszego trwania wyrażająca prawdopodobieństwo, że jednostka nie doświadczy zdarzenia końcowego przed czasem t. Metodą oceny, czy pewne zmienne mają wpływ na zróżnicowanie czasu trwania jednostek, jest przeprowadzanie testów porównujących krzywe przeżycia na podstawie dwóch (lub więcej prób). Znaczna liczba tych testów została zaproponowana w ostatnich latach, w tym testy: Log-rank, będący jednym z lub najpopularniejszym, test Gehana, Tarone-Ware, Peto-Peto, Harringtona-Fleminga, testy typu Renyi. W literaturze mało uwagi poświęca się jednakże porównaniu własności tych testów. W poniższym opracowaniu przeprowadzono, przy wykorzystaniu metody Monte Carlo, analizę porównawczą mocy predykcyjnej testów dla dwóch krzywych przeżycia w małych próbach z różnym udziałem jednostek cenzurowanych. Losowano próby z populacji o założonym rozkładzie Weibulla przy różnych proporcjach jednostek kompletnych i cenzurowanych (o losowej kolejności pojawiania się ustalanej w oparciu o rozkład jednostajny) w celu określenia efektywnej wielkości prób dla poszczególnych testów. Szczególną wagę poświęcono problemowi krzyżowania się krzywych przeżycia i zdolności testów do wykrywania różnic między krzywymi przeżycia w takiej sytuacji.
EN
The purpose of this study is to estimate the future duration of a loan contract on the basis of several factors. The main methodology consists of a brief explanation of a survival analysis and a thorough application of a survival analysis in loan management. A real dataset from a credit institution (situated in Varna) is used. All contracts were signed for 30 days but some contracts were ended earlier, others - later. The main research question concerns the following statement. We may try to predict future loan duration by making an econometric model describing the dependency between the loan duration (as a dependent variable) and several independent variables. The dataset is analysed by calculating life tables, applying the Kaplan-Maier method and using Cox regression within SPSS. It is has been proved that the main covariates affecting loan duration are the variables: born in the region, month of birth and age. The formulated conclusions are valid for the analysed credit institution. This work provides a methodology for adapting duration models in credit institutions. The presented methodology (in this paper) may be applied over the dataset of other credit institutions (including banks) for loan duration prediction.
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