Regression models for bivariate survival data

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.

Dynamic mechanical analysis of binary and ternary polymer blends based on nylon copolymer/EPDM rubber and EPM grafted maleic anhydride compatibilizer

The dynamic mechanical properties such as storage modulus, loss modulus and damping properties of blends of nylon copolymer (PA6,66) with ethylene propylene diene (EPDM) rubber was investigated with special reference to the effect of blend ratio and compatibilisation over a temperature range –100°C to 150°C at different frequencies. The effect of change in the composition of the polymer blends on tanδ was studied to understand the extent of polymer miscibility and damping characteristics. The loss tangent curve of the blends exhibited two transition peaks, corresponding to the glass transition temperature (Tg) of individual components indicating incompatibility of the blend systems. The morphology of the blends has been examined by using scanning electron microscopy. The Arrhenius relationship was used to calculate the activation energy for the glass transition of the blends. Finally, attempts have been made to compare the experimental data with theoretical models.