<p>In order to analyze the relationship between the conversion time from mild cognitive impairment to Alzheimer’s disease and the hippocampal radial distance curves as well as several scalar predictors, a new partially linear varying coefficient model with functional single-index interactions is proposed, as well as the statistical inference and application for the proposed model when the response is censored randomly are considered. The coefficient function and slope function are approximated via B-spline and functional principal component analysis, respectively. An iterated two-stage orthogonality-projection estimation method and generalized least-squares approach are applied to update the estimators of the parameter, coefficient function and slope function of the complex joint model. Under some mild assumptions, the asymptotic normality and convergence rates of the proposed estimators are established. In addition, the mean squared prediction error of the response variable is obtained. Furthermore, extensive simulation studies are conducted to evaluate the finite sample performance of the proposed model and methods. Finally, an Alzheimer’s disease dataset is analyzed to confirm that the large-dimensional functional hippocampal surface distance may be an important marker for predicting time to conversion to Alzheimer’s disease.</p>