Modelling of Time to Event Breast Cancer Data Using Accelerated Failure Time (Aft) in South India Women

Most of the studies have been widely studied between breast cancer and risk factor using the classical way of statistical methods. This paper aims to implement a class of flexible parametric survival models through accelerated failure time models for identifying risk factors for breast cancer time to death among South India women. This study also attempts to explore the survival experience of breast cancer patients. Since the death due to severity of the stages varies with age; the age is broadly classified into two groups <50 years & 50 years. The survival experiences between these age groups are presented using Kaplan-Meier survival curves and there is no significant difference between groups. However, the stages differ significantly in each group. The accelerated failure time (AFT) models using Exponential, Weibull, Gamma, Log logistic and lognormal were explored and compared by using the AIC and deviance. The Gamma and log normal models produced similar results. ABSTRACT There are two types of regression models that have been developed for time to event survival data. The first model is based on the hazard func- tion in patient groups compared to a baseline population by means of a multiplicative effect on hazards scale. The multiplicative factor is assumed to be constant over time, in which case the model forces the hazards in the different patient groups to be proportional(Cox 1972). The second model is applied for modeling the survival time directly along with covariates assumed to act multiplicatively on the time scale. The accelerated failure time (AFT) model is of the second type and it is a class of linear regression model in which the response variable is the logarithm or a known monotone transformation of a failure time (Kalbfleisch and Prentice, 1980). When using semi-parametric models for the analysis of time to event data, it is needed to provide a reduced set of assumption for forming the hazard ratio from the coefficients that can be easily interrupted and clinically meaningful (Richard and Nelson, 2002). The AFT model is not frequently used model to analyze survivorship data, but it offers a potentially useful statistical approach which is based upon the survival curve rather than the hazard function. Wei (1992) suggested that since the parameters in the AFT models are interpreted as effects on the time scale, they may be more easily un- derstood than the hazard ratios. We desire to emphasize that all AFT models are named for the distribution of T rather than the distribution of T log . The reason for allowing a different distribution assumption is that they have different implications for the shape of hazard function. Three parametric regression models, namely the exponential, gamma and Weibull are used to compare a contrast the analysis of right cen- sored cancer trail data with covariate effects, through a proportional hazards interpretation (Hayat et al., 2010). The other two parametric survival models, the log-logistic and log normal are to be described in the other way to proportional hazards.