Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name



Theoretical Statistics and Mathematics Unit (TSMU-Kolkata)


Sengupta, Debasis (ASU-Kolkata; ISI)

Abstract (Summary of the Work)

Time-to-event data arises from measurements of time till the occurrence of an event of interest. Such data are common in the fields of biology, epidemiology, pub- lic health, medical research, economics and industry. The event of interest can be the death of a human being (Klein and Moeschberger, 2003), failure of a machine (Zhiguo et al., 2007), onset of menarche in adolescent and young adult females (Bergsten-Brucefors, 1976; Chumlea et al., 2003; Mirzaei, Sengupta and Das, 2015), onset (or relapse) of a disease (Klein and Moeschberger, 2003), dental develop- ment (Demirjian, Goldstien and Tanner, 1973; Eveleth and Tanner, 1990), breast development (C'ameron, 2002; Aksglaede et al., 2009), beginning of a criminal ca- reer (Hosmer, 2008), marriage or birth of the first child (Allison, 1982), end of a work career (LeClere, 2005), end of a strike (Hosmer. Lemeshom and May, 2008), discontinuation of breast-feeding (Clements et al., 1997), healing a wound (Nelson et al., 2004) and so on. The time-to-event can be measured in days, weeks, уears, etc.Data on time-to-event are variously described as duration data, survival data, lifetime data or failure time data, even though the event of interest is not neces- sarily failure or death. Models and methods for the collection and analysis of such data comprise the feld of survival analysis.While traditional parametric and nonparametric methods of inference are some-times used in the analysis of survival data, special methods are often needed because of the pattern of incompleteness in such data. Incomplete observations contain only partial information about the random variable of interest. i.e., we do not know the exact times-to-event in all the cases. Some typical forms of in- completeness in survival data are truncation, grouping and censoring. Truncation occurs when certain individuals are screened out of the study in such a way that individual instances of screening are not observable even though the screening criterion is known. Grouping happens when one is able to ohserve the mumber of events occurring in certain specified time intervals, rather than the exact times of those occurrences. Censoring occurs when one has knowledge of either the actual time of occurrence or an interval containing it.In many clinical and epidemiological studies, a subject may be observed only up to a certain time, and there may be no follow up after that. In some cases, a subject may be observed after the event of interest has already taken place. In case the event is not known to have taken place, one would know that it has happened after the date of the last observation. In case the event is found to have taken place by the date of first observation, one would know that it has happened at an earlier time. These are instances of censoring from the right and from the left, respectively. When a subject is not continuously monitored, it is also possible that one would only know an interval of time, when the event of interest has taken place. This is called interval censoring. Left-, right- or interval-censored data can occur along with uncensored (complete) data also.


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Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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