We present an improved method for in-vivo proton range verification by prompt gamma-ray timing based on multivariate statistical modelling. To this end, prompt gamma-ray timing distributions acquired during pencil beam irradiation of an acrylic glass phantom with air cavities of different thicknesses were analysed. Relevant distribution features were chosen using forward variable selection and the Least Absolute Shrinkage and Selection Operator (LASSO) from a feature assortment based on recommendations of the Image Biomarker Standardisation Initiative. Candidate models were defined by multivariate linear regression and evaluated based on their coefficient of determination R² and root mean square error RMSE. The newly developed models showed a clearly improved predictive power (R² > 0.7) compared to the previously used models (R² < 0.5) and allowed for the identification of introduced air cavities in a scanned treatment field. These results demonstrate that elaborate statistical models can enhance prompt gamma-ray based treatment verification and increase its potential for routine clinical application.