Nonparametric Estimation of Specific Occurrence/Exposure Rate in Risk and Survival Analysis
研究在风险与生存分析中，基于删失数据非参数估计特定发生/暴露率（SOER），证明其渐近正态性，并比较多种自助法构建置信区间的效果。
Abstract A cohort of individuals exposed to some risk is followed up to a point of time M, and observations on two random variables (Y, Δ) are recorded for each individual. The variable Δ refers to one of the four possible events that can occur for an individual in the period [0, M]: (i) dies of a specific disease, say cancer, (ii) dies of a natural cause, (iii) withdraws from the study, and (iv) is alive and still under study at time M. The variable Y refers to the time at which an event occurs. Based on such data for n individuals, we consider the problem of estimation of a specific occurrence/exposure rate (SOER), which is a risk ratio defined as the ratio of probability of death due to cancer in the interval [0, M] to the mean lifetime of all individuals up to the time point M. The asymptotic distribution of a nonparametric estimator of SOER is shown to be normal, and the asymptotic variance involves unknown parameters. Various ways of bootstrapping are discussed for construction of confidence intervals for SOER and compared. Some numerical illustrations are provided.