Monotonic single-index models to assess drug interactions

Although single-index models have been extensively studied, the monotonicity of the link function f in the single-index model is rarely studied. In many situations, it is desirable that f is monotonic, which results in a monotonic single-index model that can be very useful in economics and biometrics. In this article, we propose a monotonic single-index model in which the link function is constructed using penalized I-splines along with constraints on coefficients to achieve monotonicity of the link function f. An algorithm to estimate the single-index parameters and the link function is developed, and the sandwich estimate of the variance of the index parameters is provided. We propose to apply this monotonic single-index model to estimate the dose–response surface and assess drug interactions while considering the variability of the observed data. An extensive simulation study was carried out to evaluate the performance of the proposed monotonic single-index model. A case study is provided to illustrate the application of the proposed model to estimate the dose–response surface and assess drug interactions. Both the simulation and case study show that the proposed monotonic single-index model works very well.