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Partially Paramertic Estimation of Survival Function in the Right-censored Data

100%
Rossa A., University of Łódź I. o. E. a. S.
Acta Universitatis Lodziensis. Folia Oeconomica
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2003
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vol. 164
EN
Abstract. In many medical, biological or economic follow-up studies the subject of observation is survival, failure or duration time, that is the length of time elapsed from a specific starting point to an event of interest. In engineering applications it may be the time to failure of piece of equipment, in medical trials - time to occurrence of a particular disease or time to death of a patient due to some specific disease, in economic studies - time of being unemployed and so on. In the analysis of survival-type variables one is often faced with right-censored observations. Sometimes it is impossible to measure the true failure time of an individual due to previous occurrence of some other event called competing event, which result in interruption of observation before the event occurs. It may be withdrawal of the subject from the study or failure from some causes other the one of interest or simply limitation on the length of study. If we are only interested in failure time, then the competing events can be regarded as right-censoring the event of interest. It means that for each individual we observe either the time to failure or the time to censoring and for censored individuals we know only that the time to failure is greater then the censoring time. In reliability studies censoring is often planned in order to obtain information sooner than it is otherwise possible. Instead of testing m units until they fail, the Type I censoring design is employed in which more then m units are tested but observation is terminated earlier at the end of some specified period x*. Those units, which failed before this time yield complete observations and the rest of them is right-censored. Despite such incompleteness of the data it is often desired to estimate survival function that is the probability P(X > x) that the true failure time X in the population of individuals exceeds x. The paper deals with a problem of estimating survival function in the right-censored data. Some improvements of the well-known Kaplan - Meier estimator are discussed and their properties are studied.
PL
W pracy omówione są dwa estymatory funkcji przeżycia, będące modyfikacją estymatora Kaplana-Meiera. Podstawowe własności statystyczne estymatorów zostały porównane za pomocą metod symulacyjnych.
2
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Simulation study of two-sample Kolmogorov-Smirnov test in randomly censored data

80%
Rossa A., University of Łódź D. o. S. M.
Acta Universitatis Lodziensis. Folia Oeconomica
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2002
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vol. 156
PL
W artykule przedstawione są trzy wersje testu zgodności Kołmogorowa-Smimowa dla danych prawostronnie cenzurowanych. Poszczególne testy różnią się sposobem podejścia do obserwacji cenzurowanych. Moc testów została zbadana i porównana za pomocą symulacji Monte Carlo.
EN
The paper deals with a problem of testing the non-parametric hypothesis that two populations are equally distributed in the situation when the observations are subject to random censoring. A general metric for measuring the distance between two distributions is the Kolmogorov metric and the corresponding test is the Two-Sample Kolmogorov-Smirnov test. In the report below we present results of a simulation study performed for three versions of the Two-Sample Kolmogorov-Smirnov test for censored data. These three versions are generated by three methods of treating censored observations. Basic statistical properties of these tests are inspected by means of Monte Carlo simulations.
3
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Analysis of Censored Life-tables with Covariates by Means of Log-linear Models

80%
Rossa A., University of Łódź D. o. S. M.
Acta Universitatis Lodziensis. Folia Oeconomica
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2004
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vol. 175
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.
4
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Unbiased Estimation of Survival Probabilities for Censored Data with Known Censoring Times

80%
Rossa A., University of Łódź C. o. S. M.
Acta Universitatis Lodziensis. Folia Oeconomica
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2005
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vol. 194
5
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Single Functional Index Quantile Regression for Independent Functional Data Under Right-Censoring

41%
Hamri M. M., Mekki S. D., Rabhi A., Kadiri N.
Econometrics. Ekonometria. Advances in Applied Data Analytics
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2022
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vol. 26
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issue 1
31-62
PL
Głównym celem artykułu jest prezentacja nieparametrycznej estymacji kwantyli rozkładu warunkowego na podstawie modelu jednoindeksowego w modelu cenzury, gdy próba jest traktowana jako niezależne zmienne losowe o identycznym rozkładzie. Przede wszystkim wprowadzono estymator jądrowy dla funkcji skumulowanego rozkładu warunkowego (cond-cdf). Następnie podano oszacowanie kwantyli przez odwrócenie oszacowanego cond-cdf. Właściwości asymptotyczne są określane, gdy obserwacje są połączone ze strukturą jednoindeksową. Na koniec przeprowadzono badanie symulacyjne, aby ocenić skuteczność tego oszacowania.
EN
The main objective of this paper was to estimate non-parametrically the quantiles of a conditional distribution based on the single-index model in the censorship model when the sample is considered as independent and identically distributed (i.i.d.) random variables. First of all, a kernel type estimator for the conditional cumulative distribution function (cond-cdf) is introduced. Then the paper gives an estimation of the quantiles by inverting this estimated cond-cdf, the asymptotic properties are stated when the observations are linked with a single-index structure. Finally, a simulation study was carried out to evaluate the performance of this estimate.
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