2013 Volume 3 Issue 1 Pages 1-16
In medical research, various indices are used to measure the advance grade of a disease, and these indexes are determined using some background factor and/or biomarkers (e.g., T index for colorectal cancer). Tian and Tibshriani (2010) proposed an adaptive index model (AIM) for the exploration of such indices. AIM is constructed using the linear combination of index functions based on covariates, and regression parameters are estimated using the maximum likelihood of a generalized linear model framework. Then, AIM can be applied to numerical, binary, and survival outcomes. Moreover, Tian and Tibshriani (2011) suggested a modified AIM for the evaluation of prognosis factors. In this paper, we extend AIM to the investigation of prognosis and predictive factors, namely the extended adaptive index model (EAIM). In the model building procedure, the multivariate adaptive regression spline (MARS) algorithm is applied in EAIM, while the forward stepwise algorithm is applied in AIM. The usefulness of the EAIM method was illustrated using real data in phase Ⅲ clinical trials for infectious diseases and small scale simulations
