Modelling current status data using Generalized Additive Models with flexible link: the additive gamma-logit model

Abstract

When using Generalized Linear Models (GLMs), misspecification of the link is very likely to occur due to the fact that the information, necessary to correctly choose this function, is usually unavailable. To overcome this problem, new developments emerged which also gave rise to more flexible models. As a result, survival analysis has also benefited from this new line of research due to the correspondence that can be established between models in binary regression analysis and in survival analysis. In fact, the gamma-logit survival model may be viewed as a GLM with binary response and unknown link function belonging to the one-parameter Aranda-Ordaz family of transformations. We believe a greater flexibility can be achieved by also allowing non linear covariate effects. Hence, we propose the use of flexible parametric link families in Generalized Additive Models (GAMs) with binary response. If we now consider the referred Aranda-Ordaz transformations family, a generalization of the gamma-logit model will be obtained, which we will denote by additive gamma-logit model. Based on the local scoring algorithm, the estimation procedure minimizes the deviance through the use of a deviance profile plot. A quality evaluation of the link parameter estimates, as well as the comparison of the performance of the proposed GAM with that of the GLM with the same parametric link, were carried out for simulated data. The proposed methodology was applied to a real current status data set.