A bootstrap approach for lower injury levels of the risk curves

Survival analysis is widely applied to develop injury risk curves from biomechanical data. To obtain more accurate estimation of confidence intervals of parameters, bootstrap method was evaluated by a designed simulation process. Four censoring schemes and various sample sizes were considered to investigate failure time parameters corresponding to low-level injury probabilities. In the numerical simulations, the confidence interval ranges developed by bootstrapping were about two-third of the corresponding ranges calculated by asymptotical normal approximation and showed highest reduction for censored datasets with smaller sample size (≤40). In analysis of two experimental datasets with reduced sample sizes and mixed censored data, it was shown that the bootstrapping reduce significantly the confidence intervals as well. The results presented in this study recommend using bootstrapping in development of more accurate confidence intervals for risk curves in injury biomechanics, which consequently will lead to better regulations and safer vehicle designs.