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Abstract:
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Multivariate lifetime data arise in various forms including recurrent event
data when individuals are followed to observe the sequence of occurrences of a
certain type of event; correlated lifetime when an individual is followed for the
occurrence of two or more types of events, or when distinct individuals have
dependent event times. In most studies there are covariates such as treatments, group
indicators, individual characteristics, or environmental conditions, whose
relationship to lifetime is of interest. This leads to a consideration of regression
models.The well known Cox proportional hazards model and its variations, using the
marginal hazard functions employed for the analysis of multivariate survival data in
literature are not sufficient to explain the complete dependence structure of pair of
lifetimes on the covariate vector. Motivated by this, in Chapter 2, we introduced a
bivariate proportional hazards model using vector hazard function of Johnson and
Kotz (1975), in which the covariates under study have different effect on two
components of the vector hazard function. The proposed model is useful in real life
situations to study the dependence structure of pair of lifetimes on the covariate
vector . The well known partial likelihood approach is used for the estimation of
parameter vectors. We then introduced a bivariate proportional hazards model for
gap times of recurrent events in Chapter 3. The model incorporates both marginal
and joint dependence of the distribution of gap times on the covariate vector . In
many fields of application, mean residual life function is considered superior
concept than the hazard function. Motivated by this, in Chapter 4, we considered a
new semi-parametric model, bivariate proportional mean residual life time model, to
assess the relationship between mean residual life and covariates for gap time of
recurrent events. The counting process approach is used for the inference procedures of the gap time of recurrent events. In many survival studies, the distribution of
lifetime may depend on the distribution of censoring time. In Chapter 5, we
introduced a proportional hazards model for duration times and developed inference
procedures under dependent (informative) censoring. In Chapter 6, we introduced a
bivariate proportional hazards model for competing risks data under right censoring.
The asymptotic properties of the estimators of the parameters of different models
developed in previous chapters, were studied. The proposed models were applied to
various real life situations. |