Characteristics of a ratio used to estimate failure rates: occurrences per person year of exposure.
Characteristics of a ratio used to estimate failure rates: occurrences per person year of exposure.
复制标题
用于估计故障率的比率特征：每人暴露年份的发生次数。
作者：
M. C. Sheps
摘要 已知样本中观察到的“失败”数量与总暴露时间的比率是单位时间风险恒定的同质群体中风险的最大似然、一致估计量。这里针对同质和异质群体提出了两个模型，这些模型面临着失去观察和失败的风险。得出该比率的精确分布，并使用近似值来研究其在这些群体中的小样本特性。对于同质群体，比率的偏差（不大）及其相当大的偏度会随着样本量的增加而减小，但往往会随着观察持续时间的增加而加剧。对于异质群体，该比率的预期值是观察持续时间的递减函数。特别是当包括损失时，该比率可能非常不稳定，以至于不能说它可以估计任何利息数量，也不能说是对几个组进行比较的有意义的方法。
SUMMARY The ratio of the number of 'failures' observed in a sample to the total exposure time is known to be a maximum likelihood, consistent estimator of risk in a homogeneous population with constant risk per unit time. Two models are here presented for both homogeneous and heterogeneous populations that are subject to risks of being lost to observation as well as of failure. The exact distribution of the ratio is derived and approximations are used to study its small sample properties in these populations. For homogeneous populations, the bias in the ratio (which is not large) and its considerable skewness are diminished with increasing sample size but tend to be aggravated with increasing duration of observations. For heterogeneous populations, the expected value of the ratio is a decreasing function of the duration of the observations. Particularly when losses are included, the ratio may be so erratic that it cannot be said to estimate any quantity of interest or to be a meaningful approach to the comparison of several groups.