We consider the hearing loss injury among subjects in a crowd with a wide spectrum of individual intrinsic injury probabilities due to biovariability. For multiple acoustic impulses, the observed injury risk of a crow...We consider the hearing loss injury among subjects in a crowd with a wide spectrum of individual intrinsic injury probabilities due to biovariability. For multiple acoustic impulses, the observed injury risk of a crowd vs the effective combined dose follows the logistic dose-response relation. The injury risk of a crowd is the average fraction of injured. The injury risk was measured in experiments as follows: each subject is individually exposed to a sequence of acoustic impulses of a given intensity and the injury is recorded;results of multiple individual subjects were assembled into data sets to mimic the response of a crowd. The effective combined dose was adjusted by varying the number of impulses in the sequence. The most prominent feature observed in experiments is that the injury risk of the crowd caused by multiple impulses is significantly less than the value predicted based on assumption that all impulses act independently in causing injury and all subjects in the crowd are statistically identical. Previously, in the case where all subjects are statistically identical (i.e., no biovariability), we interpreted the observed injury risk caused by multiple impulses in terms of the immunity effects of preceding impulses on subsequent impulses. In this study, we focus on the case where all sound exposure events act independently in causing injury regardless of whether one is preceded by another (i.e., no immunity effect). Instead, we explore the possibility of interpreting the observed logistic dose-response relation in the framework of biovariability of the crowd. Here biovariability means that subjects in the crowd have their own individual injury probabilities. That is, some subjects are biologically less or more susceptible to hearing loss injury than others. We derive analytically the distribution of individual injury probability that produces the observed logistic dose-response relation. For several parameter values, we prove that the derived distribution is mathematically a proper density function. W展开更多
文摘We consider the hearing loss injury among subjects in a crowd with a wide spectrum of individual intrinsic injury probabilities due to biovariability. For multiple acoustic impulses, the observed injury risk of a crowd vs the effective combined dose follows the logistic dose-response relation. The injury risk of a crowd is the average fraction of injured. The injury risk was measured in experiments as follows: each subject is individually exposed to a sequence of acoustic impulses of a given intensity and the injury is recorded;results of multiple individual subjects were assembled into data sets to mimic the response of a crowd. The effective combined dose was adjusted by varying the number of impulses in the sequence. The most prominent feature observed in experiments is that the injury risk of the crowd caused by multiple impulses is significantly less than the value predicted based on assumption that all impulses act independently in causing injury and all subjects in the crowd are statistically identical. Previously, in the case where all subjects are statistically identical (i.e., no biovariability), we interpreted the observed injury risk caused by multiple impulses in terms of the immunity effects of preceding impulses on subsequent impulses. In this study, we focus on the case where all sound exposure events act independently in causing injury regardless of whether one is preceded by another (i.e., no immunity effect). Instead, we explore the possibility of interpreting the observed logistic dose-response relation in the framework of biovariability of the crowd. Here biovariability means that subjects in the crowd have their own individual injury probabilities. That is, some subjects are biologically less or more susceptible to hearing loss injury than others. We derive analytically the distribution of individual injury probability that produces the observed logistic dose-response relation. For several parameter values, we prove that the derived distribution is mathematically a proper density function. W
