The R Package threg to Implement Threshold Regression Models

Abstract

This paper introduces the R package threg, which implements the estimation procedure of a threshold regression model, which is based on the first-hitting-time of a boundary by the sample path of a Wiener diffusion process. The threshold regression methodology is well suited to applications involving survival and time-to-event data, and serves as an important alternative to the Cox proportional hazards model.

This new package includes four functions: threg, and the methods hr, predict and plot for ‘threg’ objects returned by threg. The threg function is the model-fitting function which is used to calculate regression coefficient estimates, asymptotic standard errors and p values. The hr method for ‘threg’ objects is the hazard-ratio calculation function which provides the estimates of hazard ratios at selected time points for specified scenarios (based on given categories or value settings of covariates). The predict method for ‘threg objects is used for prediction. And the plot method for ‘threg’ objects provides plots for curves of estimated hazard functions, survival functions and probability density functions of the first-hitting-time; function curves corresponding to different scenarios can be overlaid in the same plot for comparison to give additional research insights.