Response to Letter to the Editor on "Deriving injury risk curves using survival analysis from biomechanical experiments", Journal of Biomechanics (in press).

The authors thank the commenters for their interest. They are pleased to note that the authors’ study (Yoganandan et al., 2016) addressed some of the concerns documented in the paper by the commenters (McMurry and Poplin, 2015), although the original aim of the authors’ study was to improve and provide a more robust and generalized process to derive injury risk curves than the currently existing ISO method (ISO, 2014). In any PMHS experimental data, as with most real-world outputs, the true data-generating distribution will always be unknown (Hastie et al., 2001; Vapnik, 1998). The authors believe that assuming a particular distributional form holds for all types of impact biomechanics data, ignoring all other competing or equivalent functional forms without investigation or validation, is quite a stretch. It is also worth noting and well known that simulations have their limitations (Hastie et al., 2001). For example, simulated data for survival times require assumption of a probability distribution function (which could be Weibull), assumption of a censoring distribution (which could be something quite arbitrary, such as a Uniform distribution), and assumption of nature of dependence of the censoring on the survival distribution [often one assumes censoring independent of the survival distribution] (Therneau and Grambsch, 2000). Thus, simulated survival data sets need not reflect the actual survival time generating distribution after imposition of censoring, nor should it be expected that the assumptions for a simulated scenario mimic all possible real world conditions (Therneau and Grambsch, 2000). The AIC is a well-accepted metric for choosing an appropriate model in usual regression analysis and for parametric survival models (Harrell, 2001; Hurvich and Chih0Ling, 1989; Klein and Moeschberger, 2003). As with most statistical procedures, the efficiency of the AIC improves with increase in sample size. However, the AIC is still a principled way of choosing a particular functional form, rather than guessing an ad-hoc single candidate form for observed data. It is also worth noting that many candidate probability distribution functions have similar risk profiles, noted by the commenters in their work. Biomechanical considerations and the experts/experimenter's perspectives are definitely important considerations in the determination of the risk curve. As stated in the authors’ paper (Yoganandan et al., 2016), the judgment of the “experimental group and subject matter expert” should help decide overly-influential/outlier observations and also the final metric depending on the application, e.g., injury assessment risk curve for a dummy. The