# Seminar at SMU Delhi

October 31, 2012 (Wednesday) , 3:30 PM at Webinar
Speaker: Suchismita Das, IISER, Kolkata
Title: On Some (Dynamic) Proportional and Additive Models
Abstract of Talk
In the area of reliability and survival analysis, sometimes it is important to investigate the effect of risk factor on failure of a machine, an organ, an individual, or the completion of a certain task. In literature, some proportional regression models have been introduced for modeling and analyzing lifetime data where the covariates are taken to be constant. But in some practical situations, the covariates may not be constant over the whole time interval $[0; \infty)$, but they may vary over different time intervals $t_{i-1} \leq t \leq t_i$, for $i = 1, 2, \dotsc,$ with $t_0 \equiv 0$. In a more general case, when the intervals $[t_{i-1}, t_i)$ become smaller and smaller, we get a model where the covariates are time dependent. It is worth mentioning here that the time-dependent covariate could also be used in a regression model with time-varying slopes. It is well known that regression model is used in different situations, especially when forecasting is required. In case of a time-dependent covariate model with left-censored data, the observed values can be analyzed using the properties of the covariate function to get some idea of the past scenario. In order to take care of this kind of problems, we introduce the dynamic proportional hazard rate (DPHR) model, the dynamic proportional reversed hazard rate (DPRHR) model, the dynamic proportional mean residual life (DPMRL) model. Although proportional hazard rate model is mostly studied in literature, sometimes it becomes important to study the additive hazard rate model as well. Again, the mean residual life function is found to be more relevant than the hazard rate function and when hazard rate function is not monotone then it is important to study the behavior of the mean residual life function. With this in mind, parallel to additive hazard rate model, we define a new model called dynamic additive mean residual life (DAMRL) model. Preservation of some aging classes and that of some stochastic orders under these models have been discussed.