Road traffic accidents are still among the top major global causes of death, injury, and disability. Despite this cause for alarm and several preventive initiatives, global road accident statistics are not improving. This study modeled annual road accidents (ARAs) as a function of demographic, economic, passenger movement, freight movement, and road capital investment indicators. The research is based on 22 years of data from more than 36 Organization for Economic Co-operation and Development (OECD) member and partner countries. Artificial neural network (ANN), multiple linear regression (MLR), and Poisson regression (PR) analysis were employed for this purpose. The ANN model outperformed the regression models by far, thus making it possible for reliable new insights and accurate results to be obtained. The ANN’s superior performance was shown to be a result of the non-linear relationship between ARA and some of the predicting variables. The average relative contribution of each variable in describing the ARA models was estimated using connection weight analysis (from the ANN model) and relative weight analysis for the regression model. The profile method was used to perform sensitivity analysis and to establish the partial variation trend of the ARA with each of the variables. The Existing Road Maintenance Investment (ERMI) and New Road Infrastructural Investment (NRII) showed a nonlinear concave-up relationship with ARA for given demography, economy, freight, and passenger movements. A combination of per capita NRII and ERMI corresponding to the minimum ARA exists. These sets of NRII and ERMI were considered safe road investment limits. The ANN-ARA model was utilized to estimate these limits with their relative proportion for diverse combinations of demography, economy, freight level, and passenger movement.